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Multi-head attention mechanism: “queries”, “keys”, and “values,” over and over again

April 7, 2021/in Artificial Intelligence, Data Mining, Data Science, Data Science Hack, Deep Learning, Machine Learning, Main Category, Predictive Analytics, Python, Tutorial, Use Case/by Yasuto Tamura

*A comment added on 04/05/2022: Thanks to a comment by Mr. Maier, I found a major mistake in my visualization. To be concrete, there is a mistake in expressing how to get each colored divided group of tokens by applying linear transformations. That corresponds to the section 3.2.2 in the paper “Attention Is All You Need.” There would be no big differences in the main point of this article, the relations of keys, queries, and values, but please bear that in your mind if you need Transformer at a practical work. Besides checking the implementation by Tensorflow, I will soon prepare a modified version of visualization. For further details, please see comments at the bottom of this article.

This is the third article of my article series named “Instructions on Transformer for people outside NLP field, but with examples of NLP.”

In the last article, I explained how attention mechanism works in simple seq2seq models with RNNs, and it basically calculates correspondences of the hidden state at every time step, with all the outputs of the encoder. However I would say the attention mechanisms of RNN seq2seq models use only one standard for comparing them. Using only one standard is not enough for understanding languages, especially when you learn a foreign language. You would sometimes find it difficult to explain how to translate a word in your language to another language. Even if a pair of languages are very similar to each other, translating them cannot be simple switching of vocabulary. Usually a single token in one language is related to several tokens in the other language, and vice versa. How they correspond to each other depends on several criteria, for example “what”, “who”, “when”, “where”, “why”, and “how”. It is easy to imagine that you should compare tokens with several criteria.

Transformer model was first introduced in the original paper named “Attention Is All You Need,” and from the title you can easily see that attention mechanism plays important roles in this model. When you learn about Transformer model, you will see the figure below, which is used in the original paper on Transformer. This is the simplified overall structure of one layer of Transformer model, and you stack this layer N times. In one layer of Transformer, there are three multi-head attention, which are displayed as boxes in orange. These are the very parts which compare the tokens on several standards. I made the head article of this article series inspired by this multi-head attention mechanism.

The figure below is also from the original paper on Transfromer. If you can understand how multi-head attention mechanism works with the explanations in the paper, and if you have no troubles understanding the codes in the official Tensorflow tutorial, I have to say this article is not for you. However I bet that is not true of majority of people, and at least I need one article to clearly explain how multi-head attention works. Please keep it in mind that this article covers only the architectures of the two figures below. However multi-head attention mechanisms are crucial components of Transformer model, and throughout this article, you would not only see how they work but also get a little control over it at an implementation level.

1 Multi-head attention mechanism

When you learn Transformer model, I recommend you first to pay attention to multi-head attention. And when you learn multi-head attentions, before seeing what scaled dot-product attention is, you should understand the whole structure of multi-head attention, which is at the right side of the figure above. In order to calculate attentions with a “query”, as I said in the last article, “you compare the ‘query’ with the ‘keys’ and get scores/weights for the ‘values.’ Each score/weight is in short the relevance between the ‘query’ and each ‘key’. And you reweight the ‘values’ with the scores/weights, and take the summation of the reweighted ‘values’.” Sooner or later, you will notice I would be just repeating these phrases over and over again throughout this article, in several ways.

*Even if you are not sure what “reweighting” means in this context, please keep reading. I think you would little by little see what it means especially in the next section.

The overall process of calculating multi-head attention, displayed in the figure above, is as follows (Please just keep reading. Please do not think too much.): first you split the V: “values”, K: “keys”, and Q: “queries”, and second you transform those divided “values”, “keys”, and “queries” with densely connected layers (“Linear” in the figure). Next you calculate attention weights and reweight the “values” and take the summation of the reiweighted “values”, and you concatenate the resulting summations. At the end you pass the concatenated “values” through another densely connected layers. The mechanism of scaled dot-product attention is just a matter of how to concretely calculate those attentions and reweight the “values”.

*In the last article I briefly mentioned that “keys” and “queries” can be in the same language. They can even be the same sentence in the same language, and in this case the resulting attentions are called self-attentions, which we are mainly going to see. I think most people calculate “self-attentions” unconsciously when they speak. You constantly care about what “she”, “it” , “the”, or “that” refers to in you own sentence, and we can say self-attention is how these everyday processes is implemented.

Let’s see the whole process of calculating multi-head attention at a little abstract level. From now on, we consider an example of calculating multi-head self-attentions, where the input is a sentence “Anthony Hopkins admired Michael Bay as a great director.” In this example, the number of tokens is 9, and each token is encoded as a 512-dimensional embedding vector. And the number of heads is 8. In this case, as you can see in the figure below, the input sentence “Anthony Hopkins admired Michael Bay as a great director.” is implemented as a $9\times 512$ matrix. You first split each token into $512/8=64$ dimensional, 8 vectors in total, as I colored in the figure below. In other words, the input matrix is divided into 8 colored chunks, which are all $9\times 64$ matrices, but each colored matrix expresses the same sentence. And you calculate self-attentions of the input sentence independently in the 8 heads, and you reweight the “values” according to the attentions/weights. After this, you stack the sum of the reweighted “values” in each colored head, and you concatenate the stacked tokens of each colored head. The size of each colored chunk does not change even after reweighting the tokens. According to Ashish Vaswani, who invented Transformer model, each head compare “queries” and “keys” on each standard. If the a Transformer model has 4 layers with 8-head multi-head attention , at least its encoder has $4\times 8 = 32$ heads, so the encoder learn the relations of tokens of the input on 32 different standards.

I think you now have rough insight into how you calculate multi-head attentions. In the next section I am going to explain the process of reweighting the tokens, that is, I am finally going to explain what those colorful lines in the head image of this article series are.

*Each head is randomly initialized, so they learn to compare tokens with different criteria. The standards might be straightforward like “what” or “who”, or maybe much more complicated. In attention mechanisms in deep learning, you do not need feature engineering for setting such standards.

2 Calculating attentions and reweighting “values”

If you have read the last article or if you understand attention mechanism to some extent, you should already know that attention mechanism calculates attentions, or relevance between “queries” and “keys.” In the last article, I showed the idea of weights as a histogram, and in that case the “query” was the hidden state of the decoder at every time step, whereas the “keys” were the outputs of the encoder. In this section, I am going to explain attention mechanism in a more abstract way, and we consider comparing more general “tokens”, rather than concrete outputs of certain networks. In this section each $[ \cdots ]$ denotes a token, which is usually an embedding vector in practice.

Please remember this mantra of attention mechanism: “you compare the ‘query’ with the ‘keys’ and get scores/weights for the ‘values.’ Each score/weight is in short the relevance between the ‘query’ and each ‘key’. And you reweight the ‘values’ with the scores/weights, and take the summation of the reweighted ‘values’.” The figure below shows an overview of a case where “Michael” is a query. In this case you compare the query with the “keys”, that is, the input sentence “Anthony Hopkins admired Michael Bay as a great director.” and you get the histogram of attentions/weights. Importantly the sum of the weights 1. With the attentions you have just calculated, you can reweight the “values,” which also denote the same input sentence. After that you can finally take a summation of the reweighted values. And you use this summation.

*I have been repeating the phrase “reweighting ‘values’ with attentions,” but you in practice calculate the sum of those reweighted “values.”

Assume that compared to the “query” token “Michael”, the weights of the “key” tokens “Anthony”, “Hopkins”, “admired”, “Michael”, “Bay”, “as”, “a”, “great”, and “director.” are respectively 0.06, 0.09, 0.05, 0.25, 0.18, 0.06, 0.09, 0.06, 0.15. In this case the sum of the reweighted token is 0.06″Anthony” + 0.09″Hopkins” + 0.05″admired” + 0.25″Michael” + 0.18″Bay” + 0.06″as” + 0.09″a” + 0.06″great” 0.15″director.”, and this sum is the what wee actually use.

*Of course the tokens are embedding vectors in practice. You calculate the reweighted vector in actual implementation.

You repeat this process for all the “queries.” As you can see in the figure below, you get summations of 9 pairs of reweighted “values” because you use every token of the input sentence “Anthony Hopkins admired Michael Bay as a great director.” as a “query.” You stack the sum of reweighted “values” like the matrix in purple in the figure below, and this is the output of a one head multi-head attention.

3 Scaled-dot product

This section is a only a matter of linear algebra. Maybe this is not even so sophisticated as linear algebra. You just have to do lots of Excel-like operations. A tutorial on Transformer by Jay Alammar is also a very nice study material to understand this topic with simpler examples. I tried my best so that you can clearly understand multi-head attention at a more mathematical level, and all you need to know in order to read this section is how to calculate products of matrices or vectors, which you would see in the first some pages of textbooks on linear algebra.

We have seen that in order to calculate multi-head attentions, we prepare 8 pairs of “queries”, “keys” , and “values”, which I showed in 8 different colors in the figure in the first section. We calculate attentions and reweight “values” independently in 8 different heads, and in each head the reweighted “values” are calculated with this very simple formula of scaled dot-product: $Attention(\boldsymbol{Q}, \boldsymbol{K}, \boldsymbol{V})$ $=softmax(\frac{\boldsymbol{Q} \boldsymbol{K} ^T}{\sqrt{d}_k})\boldsymbol{V}$ . Let’s take an example of calculating a scaled dot-product in the blue head.

At the left side of the figure below is a figure from the original paper on Transformer, which explains one-head of multi-head attention. If you have read through this article so far, the figure at the right side would be more straightforward to understand. You divide the input sentence into 8 chunks of matrices, and you independently put those chunks into eight head. In one head, you convert the input matrix by three different fully connected layers, which is “Linear” in the figure below, and prepare three matrices $Q, K, V$ , which are “queries”, “keys”, and “values” respectively.

*Whichever color attention heads are in, the processes are all the same.

*You divide $\frac{\boldsymbol{Q}} {\boldsymbol{K}^T}$ by $\sqrt{d}_k$ in the formula. According to the original paper, it is known that re-scaling $\frac{\boldsymbol{Q} }{\boldsymbol{K}^T}$ by $\sqrt{d}_k$ is found to be effective. I am not going to discuss why in this article.

As you can see in the figure below, calculating $Attention(\boldsymbol{Q}, \boldsymbol{K}, \boldsymbol{V})$ is virtually just multiplying three matrices with the same size (Only K is transposed though). The resulting $9\times 64$ matrix is the output of the head.

$softmax(\frac{\boldsymbol{Q} \boldsymbol{K} ^T}{\sqrt{d}_k})$ is calculated like in the figure below. The softmax function regularize each row of the re-scaled product $\frac{\boldsymbol{Q} \boldsymbol{K} ^T}{\sqrt{d}_k}$ , and the resulting $9\times 9$ matrix is a kind a heat map of self-attentions.

The process of comparing one “query” with “keys” is done with simple multiplication of a vector and a matrix, as you can see in the figure below. You can get a histogram of attentions for each query, and the resulting 9 dimensional vector is a list of attentions/weights, which is a list of blue circles in the figure below. That means, in Transformer model, you can compare a “query” and a “key” only by calculating an inner product. After re-scaling the vectors by dividing them with $\sqrt{d_k}$ and regularizing them with a softmax function, you stack those vectors, and the stacked vectors is the heat map of attentions.

You can reweight “values” with the heat map of self-attentions, with simple multiplication. It would be more straightforward if you consider a transposed scaled dot-product $\boldsymbol{V}^T \cdot softmax(\frac{\boldsymbol{Q} \boldsymbol{K} ^T}{\sqrt{d}_k})^T$ . This also should be easy to understand if you know basics of linear algebra.

One column of the resulting matrix ( $\boldsymbol{V}^T \cdot softmax(\frac{\boldsymbol{Q} \boldsymbol{K} ^T}{\sqrt{d}_k})^T$ ) can be calculated with a simple multiplication of a matrix and a vector, as you can see in the figure below. This corresponds to the process or “taking a summation of reweighted ‘values’,” which I have been repeating. And I would like you to remember that you got those weights (blue) circles by comparing a “query” with “keys.”

Again and again, let’s repeat the mantra of attention mechanism together: “you compare the ‘query’ with the ‘keys’ and get scores/weights for the ‘values.’ Each score/weight is in short the relevance between the ‘query’ and each ‘key’. And you reweight the ‘values’ with the scores/weights, and take the summation of the reweighted ‘values’.” If you have been patient enough to follow my explanations, I bet you have got a clear view on how multi-head attention mechanism works.

We have been seeing the case of the blue head, but you can do exactly the same procedures in every head, at the same time, and this is what enables parallelization of multi-head attention mechanism. You concatenate the outputs of all the heads, and you put the concatenated matrix through a fully connected layers.

If you are reading this article from the beginning, I think this section is also showing the same idea which I have repeated, and I bet more or less you no have clearer views on how multi-head attention mechanism works. In the next section we are going to see how this is implemented.

4 Tensorflow implementation of multi-head attention

Let’s see how multi-head attention is implemented in the Tensorflow official tutorial. If you have read through this article so far, this should not be so difficult. I also added codes for displaying heat maps of self attentions. With the codes in this Github page, you can display self-attention heat maps for any input sentences in English.

The multi-head attention mechanism is implemented as below. If you understand Python codes and Tensorflow to some extent, I think this part is relatively easy. The multi-head attention part is implemented as a class because you need to train weights of some fully connected layers. Whereas, scaled dot-product is just a function.

*I am going to explain the create_padding_mask() and create_look_ahead_mask() functions in upcoming articles. You do not need them this time.

Let’s see a case of using multi-head attention mechanism on a (1, 9, 512) sized input tensor, just as we have been considering in throughout this article. The first axis of (1, 9, 512) corresponds to the batch size, so this tensor is virtually a (9, 512) sized tensor, and this means the input is composed of 9 512-dimensional vectors. In the results below, you can see how the shape of input tensor changes after each procedure of calculating multi-head attention. Also you can see that the output of the multi-head attention is the same as the input, and you get a $9\times 9$ matrix of attention heat maps of each attention head.

I guess the most complicated part of this implementation above is the split_head() function, especially if you do not understand tensor arithmetic. This part corresponds to splitting the input tensor to 8 different colored matrices as in one of the figures above. If you cannot understand what is going on in the function, I recommend you to prepare a sample tensor as below.

This is just a simple (1, 9, 512) sized tensor with sequential integer elements. The first row (1, 2, …., 512) corresponds to the first input token, and (4097, 4098, … , 4608) to the last one. You should try converting this sample tensor to see how multi-head attention is implemented. For example you can try the operations below.

These operations correspond to splitting the input into 8 heads, whose sizes are all (9, 64). And the second axis of the resulting (1, 8, 9, 64) tensor corresponds to the index of the heads. Thus sample_sentence[0][0] corresponds to the first head, the blue $9\times 64$ matrix. Some Tensorflow functions enable linear calculations in each attention head, independently as in the codes below.

Very importantly, we have been only considering the cases of calculating self attentions, where all “queries”, “keys”, and “values” come from the same sentence in the same language. However, as I showed in the last article, usually “queries” are in a different language from “keys” and “values” in translation tasks, and “keys” and “values” are in the same language. And as you can imagine, usualy “queries” have different number of tokens from “keys” or “values.” You also need to understand this case, which is not calculating self-attentions. If you have followed this article so far, this case is not that hard to you. Let’s briefly see an example where the input sentence in the source language is composed 9 tokens, on the other hand the output is composed 12 tokens.

As I mentioned, one of the outputs of each multi-head attention class is $9\times 9$ matrix of attention heat maps, which I displayed as a matrix composed of blue circles in the last section. The the implementation in the Tensorflow official tutorial, I have added codes to display actual heat maps of any input sentences in English.

*If you want to try displaying them by yourself, download or just copy and paste codes in this Github page. Please maker “datasets” directory in the same directory as the code. Please download “spa-eng.zip” from this page, and unzip it. After that please put “spa.txt” on the “datasets” directory. Also, please download the “checkpoints_en_es” folder from this link, and place the folder in the same directory as the file in the Github page. In the upcoming articles, you would need similar processes to run my codes.

After running codes in the Github page, you can display heat maps of self attentions. Let’s input the sentence “Anthony Hopkins admired Michael Bay as a great director.” You would get a heat maps like this.

In fact, my toy implementation cannot handle proper nouns such as “Anthony” or “Michael.” Then let’s consider a simple input sentence “He admired her as a great director.” In each layer, you respectively get 8 self-attention heat maps.

I think we can see some tendencies in those heat maps. The heat maps in the early layers, which are close to the input, are blurry. And the distributions of the heat maps come to concentrate more or less diagonally. At the end, presumably they learn to pay attention to the start and the end of sentences.

You have finally finished reading this article. Congratulations.

You should be proud of having been patient, and you passed the most tiresome part of learning Transformer model. You must be ready for making a toy English-German translator in the upcoming articles. Also I am sure you have understood that Michael Bay is a great director, no matter what people say.

[References]

[1] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N. Gomez, Lukasz Kaiser, Illia Polosukhin, “Attention Is All You Need” (2017)

[2] “Transformer model for language understanding,” Tensorflow Core
https://www.tensorflow.org/overview

[3] “Neural machine translation with attention,” Tensorflow Core
https://www.tensorflow.org/tutorials/text/nmt_with_attention

[4] Jay Alammar, “The Illustrated Transformer,”
http://jalammar.github.io/illustrated-transformer/

[5] “Stanford CS224N: NLP with Deep Learning | Winter 2019 | Lecture 14 – Transformers and Self-Attention,” stanfordonline, (2019)
https://www.youtube.com/watch?v=5vcj8kSwBCY

[6]Tsuboi Yuuta, Unno Yuuya, Suzuki Jun, “Machine Learning Professional Series: Natural Language Processing with Deep Learning,” (2017), pp. 91-94
坪井祐太、海野裕也、鈴木潤著, 「機械学習プロフェッショナルシリーズ深層学習による自然言語処理」, (2017), pp. 191-193

[7]”Stanford CS224N: NLP with Deep Learning | Winter 2019 | Lecture 8 – Translation, Seq2Seq, Attention”, stanfordonline, (2019)
https://www.youtube.com/watch?v=XXtpJxZBa2c

[8]Rosemary Rossi, “Anthony Hopkins Compares ‘Genius’ Michael Bay to Spielberg, Scorsese,” yahoo! entertainment, (2017)
https://www.yahoo.com/entertainment/anthony-hopkins-transformers-director-michael-bay-guy-genius-010058439.html

* I make study materials on machine learning, sponsored by DATANOMIQ. I do my best to make my content as straightforward but as precise as possible. I include all of my reference sources. If you notice any mistakes in my materials, including grammatical errors, please let me know (email: yasuto.tamura@datanomiq.de). And if you have any advice for making my materials more understandable to learners, I would appreciate hearing it.

Why Is Physical Security Vital for Data Security?

March 30, 2021/in Data Security/by Shannon Flynn

Modern businesses hold on to an increasing amount of sensitive and sometimes confidential data. As a result, they’ve had to invest in new technology and practices to keep that data safe.

Many of these businesses, when developing their data security or cybersecurity protocols, focus on the security of their hardware, software and business network. Prioritizing these assets is essential — however, if physical security gets left behind, even the best digital tech may not keep a company’s data safe.

There’s practically no stopping someone with physical access to your data storage from stealing info or compromising your business network.

This is why companies that prioritize digital security also need to carefully consider physical security — and what may happen when physical security is neglected.

Physical Access Can Allow Criminals to Bypass Even the Best Digital Security

It’s almost impossible to protect any device from a physical attack. If a hacker has sustained access to device hardware, they’ll be able to breach its defenses eventually — potentially giving them access to the information on that device, as well as any stored security credentials.

Devices that are digitally secured but not physically secured — like a laptop left behind in a coffee shop, or an IoT sensor in an unlocked case — can provide a valuable vector of attack for hackers. In some cases, that vector may be all they need to create serious trouble for a company.

In some cases, poor building security may enable hackers to sneak into server rooms or gain access to off-site devices, like IoT sensors. Often, hackers also gain access to hardware either by theft — for example, swiping a laptop left sitting in a coffee shop — or by using social engineering to gain remote access.

Even large devices that are rarely moved or accessed by staff — like servers in a data center — can be at risk.

This is why large, high-budget data centers often have what’s colloquially called a mantrap — a set of two interlocking doors, somewhat like an airlock, that one has to pass through to reach the server hardware. These doors serve as a final access check for the data center and help to minimize the risk of unauthorized server access.

These threats aren’t an abstraction — hackers and other criminals have used physical access to steal data in the past.

In 2015, for example, hackers stole five servers from the offices of a British charity, PlanUK. Those servers contained a wealth of information on donators, including names, addresses, bank account numbers and sort codes.

In 2018, the theft of a laptop exposed the data of more than 43,000 patients of the West Virginia-based Coplin Health System — part of the reason that laptop theft is ranked the number one cause of health data breaches.

Valuable Hardware and Essential Systems May Be at High Risk

Hackers may also use physical attack vectors if they need to gain access to critical infrastructure, which may otherwise be air-gapped from internet-connected systems and impossible to attack with digital-only methods.

This is part of why major physical security manufacturers dedicate entire product lines to physical security for nuclear power plants, for example, or airports or international organizations — and why those kinds of institutions take physical security so seriously.

Enterprise-grade computer hardware can also be very valuable — making that hardware a major target. While you may expect criminals to be driven more by data or network access than by the resale value of your servers, theft for resale or reuse has happened before.

In 2018, for example, Icelandic criminals stole 600 bitcoin-mining servers in one of the biggest tech heists on record. Rising cryptocurrency prices may encourage some criminals to plan similar heists of powerful hardware. Owners of data centers, rendering farms and other facilities with high-value hardware should be aware of these risks, as well as how good physical security is necessary to keep their hardware safe.

Using Physical Security to Complement Your Digital Security Planning

Without strong physical security practices, your data can be vulnerable — even if you have a great digital security plan in place.

Hackers, when faced with strong cyber defenses, sometimes turn to physical attacks to gain access to critical hardware. In other cases, they may also be after the hardware for sale or personal use.

Even a basic physical security plan — one that involves ID verification and access control — can go a long way in complementing a digital security strategy and keeping data safe.

Support Vector Machines for Text Recognition

Hand Written Alphabet recognition Using Support Vector Machine

March 20, 2021/in Artificial Intelligence, Data Science, Data Science Hack, Machine Learning, Main Category, R Statistics/by Mohan Rai

We have used image classification as an task in many cases, more often this has been done using an module like openCV in python or using pre-trained models like in case of MNIST data sets. The idea of using Support Vector Machines for carrying out the same task is to give a simpler approach for a complicated process. There are some pro’s and con’s in every algorithm. Support vector machine for data with very high dimension may prove counter productive. But in case of image data we are actually using a array. If its a mono chrome then its just a 2 dimensional array, if grey scale or color image stack then we may have a 3 dimensional array processing to be considered. You can get more clarity on the array part if you go through this article on Machine learning using only numpy array. While there are certainly advantages of using OCR packages like Tesseract or OpenCV or GPTs, I am putting forth this approach of using a simple SVM model for hand written text classification. As a student while doing linear regression, I learn’t a principle “Occam’s Razor”, Basically means, keep things simple if they can explain what you want to. In short, the law of parsimony, simplify and not complicate. Applying the same principle on Hand written Alphabet recognition is an attempt to simplify using a classic algorithm, the Support Vector Machine. We break the problem of hand written alphabet recognition into a simple process rather avoiding usage of heavy packages. This is an attempt to create the data and then build a model using Support Vector Machines for Classification.

Data Preparation

Manually edit the data instead of downloading it from the web. This will help you understand your data from the beginning. Manually write some letters on white paper and get the photo from your mobile phone. Then store it on your hard drive. As we are doing a trial we don’t want to waste a lot of time in data creation at this stage, so it’s a good idea to create two or three different characters for your dry run. You may need to change the code as you add more instances of classes, but this is where the learning phase begins. We are now at the training level.

Data Structure

You can create the data yourself by taking standard pictures of hand written text in a 200 x 200 pixel dimension. Alternatively you can use a pen tab to manually write these alphabets and save them as files. If you know and photo editing tools you can use them as well. For ease of use, I have already created a sample data and saved it in the structure as below.

Image Source : From Author

You can download the data which I have used, right click on this download data link and open in new tab or window. Then unzip the folders and you should be able to see the same structure and data as above in your downloads folder. I would suggest, you should create your own data and repeat the process. This would help you understand the complete flow.

Install the Dependency Packages for RStudio

We will be using the jpeg package in R for Image handling and the SVM implementation from the kernlab package. Also we need to make sure that the image data has dimension’s of 200 x 200 pixels, with a horizontal and vertical resolution of 120dpi. You can vary the dimension’s like move it to 300 x 300 or reduce it to 100 x 100. The higher the dimension, you will need more compute power. Experiment around the color channels and resolution later once you have implemented it in the current form.

# install package "jpeg"

install.packages("jpeg", dependencies = TRUE)

# install the "kernlab" package for building the model using support vector machines

install.packages("kernlab", dependencies = TRUE)

Load the training data set

# load the "jpeg" package for reading the JPEG format files

library(jpeg)

# set the working directory for reading the training image data set

setwd("C:/Users/mohan/Desktop/alphabet_folder/Train")

# extract the directory names for using as image labels

f_train<-list.files()

# Create an empty data frame to store the image data labels and the extracted new features in training environment

df_train<- data.frame(matrix(nrow=0,ncol=5))

Feature Transformation

Since we don’t intend to use the typical CNN, we are going to use the white, grey and black pixel values for new feature creation. We will use the summation of all the pixel values of a image and save it as a new feature called as “sum”, the count of all pixels adding up to zero as “zero”, the count of all pixels adding up to “ones” and the sum of all pixels between zero’s and one’s as “in_between”. The “label” feature names are extracted from the names of the folder

# names the columns of the data frame as per the feature name schema

names(df_train)<- c("sum","zero","one","in_between","label")

# loop to compute as per the logic

counter<-1

for(i in 1:length(f_train))

{

setwd(paste("C:/Users/mohan/Desktop/alphabet_folder/Train/",f_train[i],sep=""))

data_list<-list.files()

for(j in 1:length(data_list))

{

temp<- readJPEG(data_list[j])

df_train[counter,1]<- sum(temp)

df_train[counter,2]<- sum(temp==0)

df_train[counter,3]<- sum(temp==1)

df_train[counter,4]<- sum(temp > 0 & temp < 1)

df_train[counter,5]<- f_train[i]

counter=counter+1

}

# Convert the labels from text to factor form

df_train$label<- factor(df_train$label)

Support Vector Machine model

# load the "kernlab" package for accessing the support vector machine implementation

library(kernlab)

# build the model using the training data

image_classifier <- ksvm(label~.,data=df_train)

Evaluate the Model on the Testing Data Set

# set the working directory for reading the testing image data set

setwd("C:/Users/mohan/Desktop/alphabet_folder/Test")

# extract the directory names for using as image labels

f_test <- list.files()

# Create an empty data frame to store the image data labels and the extracted new features in training environment

df_test<- data.frame(matrix(nrow=0,ncol=5))

# Repeat of feature extraction in test data

names(df_test)<- c("sum","zero","one","in_between","label")

# loop to compute as per the logic

for(i in 1:length(f_test))

{

temp<- readJPEG(f_test[i])

df_test[i,1]<- sum(temp)

df_test[i,2]<- sum(temp==0)

df_test[i,3]<- sum(temp==1)

df_train[counter,4]<- sum(temp > 0 & temp < 1)

df_test[i,5]<- strsplit(x = f_test[i],split = "[.]")[[1]][1]

}

# Use the classifier named "image_classifier" built in train environment to predict the outcomes on features in Test environment

df_test$label_predicted<- predict(image_classifier,df_test)

# Cross Tab for Classification Metric evaluation

table(Actual_data=df_test$label,Predicted_data=df_test$label_predicted)

I would recommend you to learn concepts of SVM which couldn’t be explained completely in this article by going through my free Data Science and Machine Learning video courses. We have created the classifier using the Kerlab package in R, but I would advise you to study the mathematics involved in Support vector machines to get a clear understanding.

Data Security for Data Scientists & Co. – Infographic

March 9, 2021/in Data Science News, Data Security, Education / Certification, Gerneral, Insights, Main Category/by Benjamin Aunkofer

Data becomes information and information becomes knowledge. For this reason, companies are nowadays also evaluated with regard to their data and their data quality. Furthermore, data is also the material that is needed for management decisions and artificial intelligence. For this reason, IT Security is very important and special consulting and auditing companies offer their own services specifically for the security of IT systems.

However, every Data Scientist, Data Analyst and Data Engineer rarely only works with open data, but rather intensively with customer data. Therefore, every expert for the storage and analysis of data should at least have a basic knowledge of Data Security and work according to certain principles in order to guarantee the security of the data and the legality of the data processing.

There are a number of rules and principles for data security that must be observed. Some of them – in our opinion the most important ones – we from DATANOMIQ have summarized in an infographic for Data Scientists, Data Analysts and Data Engineers. You can download the infographic here: DataSecurity_Infographic

Data Security for Data Scientists, Data Analysts and Data Engineers

Download Infographic as PDF

Infographic – Data Security for Data Scientists, Data Analysts and Data Engineers

In-memory Caching in Finance

March 5, 2021/in InMemory, Insights, Main Category/by Edward Huskin

Big data has been gradually creeping into a number of industries through the years, and it seems there are no exceptions when it comes to what type of business it plans to affect. Businesses, understandably, are scrambling to catch up to new technological developments and innovations in the areas of data processing, storage, and analytics. Companies are in a race to discover how they can make big data work for them and bring them closer to their business goals. On the other hand, consumers are more concerned than ever about data privacy and security, taking every step to minimize the data they provide to the companies whose services they use. In today’s ever-connected, always online landscape, however, every company and consumer engages with data in one way or another, even if indirectly so.

Despite the reluctance of consumers to share data with businesses and online financial service providers, it is actually in their best interest to do so. It ensures that they are provided the best experience possible, using historical data, browsing histories, and previous purchases. This is why it is also vital for businesses to find ways to maximize the use of data so they can provide the best customer experience each time. Even the more traditional industries like finance have gradually been exploring the benefits they can gain from big data. Big data in the financial services industry refers to complex sets of data that can help provide solutions to the business challenges financial institutions and banking companies have faced through the years. Considered today as a business imperative, data management is increasingly leveraged in finance to enhance processes, their organization, and the industry in general.

How Caching Can Boost Performance in Finance

In computing, caching is a method used to manage frequently accessed data saved in a system’s main memory (RAM). By using RAM, this method allows quick access to data without placing too much load on the main data stores. Caching also addresses the problems of high latency, network congestion, and high concurrency. Batch jobs are also done faster because request run times are reduced—from hours to minutes and from minutes to mere seconds. This is especially important today, when a host of online services are available and accessible to users. A delay of even a few seconds can lead to lost business, making both speed and performance critical factors to business success. Scalability is another aspect that caching can help improve by allowing finance applications to scale elastically. Elastic scalability ensures that a business is equipped to handle usage peaks without impacting performance and with the minimum required effort.

Below are the main benefits of big data and in-memory caching to financial services:

Big data analytics integration with financial models
Predictive modeling can be improved significantly with big data analytics so it can better estimate business outcomes. Proper management of data helps improve algorithmic understanding so the business can make more accurate predictions and mitigate inherent risks related to financial trading and other financial services.
Predictive modeling can be improved significantly with big data analytics so it can better estimate business outcomes. Proper management of data helps improve algorithmic understanding so the business can make more accurate predictions and mitigate inherent risks related to financial trading and other financial services.
Real-time stock market insights
As data volumes grow, data management becomes a vital factor to business success. Stock markets and investors around the globe now rely on advanced algorithms to find patterns in data that will help enable computers to make human-like decisions and predictions. Working in conjunction with algorithmic trading, big data can help provide optimized insights to maximize portfolio returns. Caching can consequently make the process smoother by making access to needed data easier, quicker, and more efficient.
Customer analytics
Understanding customer needs and preferences is the heart and soul of data management, and, ultimately, it is the goal of transforming complex datasets into actionable insights. In banking and finance, big data initiatives focus on customer analytics and providing the best customer experience possible. By focusing on the customer, companies are able to Ieverage new technologies and channels to anticipate future behaviors and enhance products and services accordingly. By building meaningful customer relationships, it becomes easier to create customer-centric financial products and seize market opportunities.
Fraud detection and risk management
In the finance industry, risk is the primary focus of big data analytics. It helps in identifying fraud and mitigating operational risk while ensuring regulatory compliance and maintaining data integrity. In this aspect, an in-memory cache can help provide real-time data that can help in identifying fraudulent activities and the vulnerabilities that caused them so that they can be avoided in the future.

What Does This Mean for the Finance Industry?

Big data is set to be a disruptor in the finance sector, with 70% of companies citing big data as a critical factor of the business. In 2015 alone, financial service providers spent $6.4 billion on data-related applications, with this spending predicted to increase at a rate of 26% per year. The ability to anticipate risk and pre-empt potential problems are arguably the main reasons why the finance industry in general is leaning toward a more data-centric and customer-focused model. Data analysis is also not limited to customer data; getting an overview of business processes helps managers make informed operational and long-term decisions that can bring the company closer to its objectives. The challenge is taking a strategic approach to data management, choosing and analyzing the right data, and transforming it into useful, actionable insights.

Die Notwendigkeit von DevOps in Data Science

February 24, 2021/in Data Engineering/by Lea Krause

Datenwissenschaft und maschinelles Lernen werden häufig mit Mathematik, Statistik, Algorithmen und Datenstreitigkeiten in Verbindung gebracht. Während diese Fähigkeiten für den Erfolg der Implementierung von maschinellem Lernen in einem Unternehmen von zentraler Bedeutung sind, gewinnt eine Funktion zunehmend an Bedeutung – DevOps for Data Science. DevOps umfasst die Bereitstellung der Infrastruktur, das Konfigurationsmanagement, die kontinuierliche Integration und Bereitstellung, das Testen und die Überwachung. Die DevOps Consulting – Teams haben eng mit den Entwicklungsteams zusammengearbeitet, um den Lebenszyklus von Anwendungen effektiv zu verwalten.

Data Science bringt DevOps zusätzliche Verantwortung. Data Engineering, eine Nischendomäne, die sich mit komplexen Pipelines befasst, die die Daten transformieren, erfordert eine enge Zusammenarbeit von Data Science-Teams mit DevOps. Datenwissenschaftler untersuchen transformierte Daten, um Erkenntnisse und Korrelationen zu finden. Von den DevOps-Teams wird erwartet, dass sie Datenwissenschaftler unterstützen, indem sie Umgebungen für die Datenexploration und -visualisierung erstellen.

Das Erstellen von Modellen für maschinelles Lernen unterscheidet sich grundlegend von der herkömmlichen Anwendungsentwicklung. Die Entwicklung ist nicht nur iterativ, sondern auch heterogen. Datenwissenschaftler und -entwickler verwenden eine Vielzahl von Sprachen, Bibliotheken, Toolkits und Entwicklungsumgebungen, um Modelle für maschinelles Lernen zu entwickeln. Beliebte Sprachen für die Entwicklung des maschinellen Lernens wie Python, R und Julia werden in Entwicklungsumgebungen verwendet, die auf Jupyter Notebooks, PyCharm, Visual Studio Code, RStudio und Juno basieren. Diese Umgebungen müssen Datenwissenschaftlern und Entwicklern zur Verfügung stehen, die ML-Probleme lösen.

Maschinelles Lernen und Deep Learning erfordern eine massive Computerinfrastruktur, die auf leistungsstarken CPUs und GPUs ausgeführt wird. Frameworks wie TensorFlow, Caffe, Apache MXNet und Microsoft CNTK nutzen die GPUs, um komplexe Berechnungen für das Training von ML-Modellen durchzuführen. Das Bereitstellen, Konfigurieren, Skalieren und Verwalten dieser Cluster ist eine typische DevOps-Funktion. DevOps-Teams müssen möglicherweise Skripts erstellen, um die Bereitstellung und Konfiguration der Infrastruktur für eine Vielzahl von Umgebungen zu automatisieren.

Ähnlich wie bei der modernen Anwendungsentwicklung ist die Entwicklung des maschinellen Lernens iterativ.

Wenn ein vollständig trainiertes ML-Modell verfügbar ist, wird von DevOps-Teams erwartet, dass sie das Modell in einer skalierbaren Umgebung hosten, beispielsweise mit Microsoft Azure und die dazugehörige DevOps-Lösung. Sie können Orchestrierungs-Engines wie Apache Mesos oder Kubernetes nutzen, um die Modellbereitstellung zu skalieren.

DevOps-Teams nutzen Container für die Bereitstellung von Entwicklungsumgebungen, Datenverarbeitungs-Pipelines, Schulungsinfrastrukturen und Modellbereitstellungsumgebungen. Neue Technologien wie Kubeflow und MlFlow konzentrieren sich darauf, DevOps-Teams in die Lage zu versetzen, die neuen Herausforderungen im Umgang mit der ML-Infrastruktur zu bewältigen.

Maschinelles Lernen verleiht DevOps eine neue Dimension. Zusammen mit den Entwicklern müssen die Betreiber mit Datenwissenschaftlern und Dateningenieuren zusammenarbeiten, um Unternehmen zu unterstützen, die das ML-Paradigma annehmen.

How to Efficiently Manage Big Data

February 5, 2021/in Big Data, Main Category/by Edward Huskin

The benefits of big data today can’t be ignored, especially since these benefits encompass industries. Despite the misconceptions around big data, it has shown potential in helping organizations move forward and adapt to an ever-changing market, where those that can’t respond appropriately or quickly enough are left behind. Data analytics is the name of the game, and efficient data management is the main differentiator.

A digital integration hub (DIH) will provide the competitive edge an organization needs in the efficient handling of data. It’s an application architecture that aggregates operational data into a low-latency data fabric and helps in digital transformation by offloading from legacy architecture and providing a decoupled API layer that effectively supports modern online applications. Data management entails the governance, organization, and administration of large, and possibly complex, datasets. The rapid growth of data pooIs has left unprepared companies scrambling to find solutions that will help keep them above water. Data in these pools originate from a myriad of sources, including websites, social media sites, and system logs. The variety in data types and their sheer size make data management a fairly complex undertaking.

Big Data Management for Big Wins

In today’s data-driven world, the capability to efficiently analyze and store data are vital factors in enhancing current business processes and setting up new ones. Data has gone beyond the realm of data analysts and into the business mainstream. As such, businesses should add data analysis as a core competency to ensure that the entire organization is on the same page when it comes to data strategy. Below are a few ways you can make big data work for you and your business.

Define Specific Goals

The data you need to capture will depend on your business goals so it’s imperative that you know what these are and ensure that these are shared across the organization. Without definite and specific goals, you’ll end up with large pools of data and nowhere to use them in. As such, it’s advisable to involve the entire team in mapping out a data strategy based on the company’s objectives. This strategy should be part of the organization’s overall business strategy to avoid the collection of irrelevant data that has no impact on business performance. Setting the direction early on will help set you up for long-term success.

Secure Your Data

Because companies have to contend with large amounts of data each day, storage and management could become very challenging. Security is also a main concern; no organization wants to lose it’s precious data after spending time and money processing and storing them. While keeping data accessible for analysis, you should also ensure that it’s kept secure at all times. When handling data, you should have security measures in place, such as firewall security, malware scanning, and spam filtering. Data security is especially important when collecting customer data to avoid violating data privacy regulations. Ideally, it should be one of the main considerations in data management because it’s a critical factor that could mean the difference between a successful venture and a problematic one.

Interlink Your Data

Different channels can be used to access a database, but this doesn’t necessarily mean that you should use several or all of them. There’s no need to deploy different tools for each application your organization uses. One of the ways to prevent miscommunication between applications and ensure that data is synchronized at all times is to keep data interlinked. Synchronicity of data is vital if your organization or team plans to use a single database. An in-memory data grid, cloud storage system, and remote database administrator are just some of the tools a company can use to interlink data.

Ensure Compliance With Audit Regulations

One thing that could be easy to overlook is how compliant systems are to audit regulations. A database and it is conducted to check on the actions of database users and managers. It is typically done for security purposes—to ensure that data or information can be accessed only by those authorized to do so. Adhering to audit regulations is a must, even for offsite database administrators, so it’s critical that they maintain compliant database components.

Be Prepared for Change

There have been significant changes in the field of data processing and management in recent years, which indicates a promising yet constantly changing landscape. To get ahead of the data analytics game, it’s vital that you keep up with current data trends. New tools and technology are made available at an almost regular pace, and keeping abreast of them will ensure that a business keeps its database up to date. It’s also important to be flexible and be able to pivot or restrategize at a moment’s notice so the business can adapt to change accordingly.

Big Data for the Long Haul

Traditional data warehouses and relational database platforms are slowly becoming things of the past. Big data analytics has changed the game, with data management moving away from being a complex, IT-team focused function and becoming a core competency of every business. Ensuring efficient data management means giving your business a competitive edge, and implementing the tips above ensures that a business manages its data effectively. Changes in data strategies are certain, and they may come sooner than later. Equipping your people with the appropriate skills and knowledge will ensure that your business can embrace change with ease.

Data Mining Process flow – Easy Understanding

February 4, 2021/in Artificial Intelligence, Data Mining, Data Science, Deep Learning, Machine Learning, Main Category, Predictive Analytics, Statistics/by Ahamed Al Farabi

1 Overview

Development of computer processing power, network and automated software completely change and give new concept of each business. And data mining play the vital part to solve, finding the hidden patterns and relationship from large dataset with business by using sophisticated data analysis tools like methodology, method, process flow etc.

On this paper, proposed a process flow followed CRISP-DM methodology and has six steps where data understanding does not considered.

Phase of new process flow given below:-

Phase 1: Involved with collection, outliner treatment, imputation, transformation, scaling, and partition dataset in to two sub-frames (Training and Testing). Here as an example for outliner treatment, imputation, transformation, scaling consider accordingly Z score, mean, One hot encoding and Min Max Scaler.

Phase 2: On this Phase training and testing data balance with same balancing algorithm but separately. As an example here SMOTE (synthetic minority oversampling technique) is considered.

Phase 3: This phase involved with reduction, selection, aggregation, extraction. But here for an example considering same feature reduction algorithm (LDA -Linear Discriminant analysis) on training and testing data set separately.

Phase 4: On this Phase Training data set again partition into two more set (Training and Validation).

Phase 5: This Phase considering several base algorithms as a base model like CNN, RNN, Random forest, MLP, Regression, Ensemble method. This phase also involve to find out best hyper parameter and sub-algorithm for each base algorithm. As an example on this paper consider two class classification problems and also consider Random forest (Included CART – Classification and Regression Tree and GINI index impurity) and MLP classifier (Included (Relu, Sigmoid, binary cross entropy, Adam – Adaptive Moment Estimation) as base algorithms.

Phase 6: First, Prediction with validation data then evaluates with Test dataset which is fully unknown for these (Random forest, MLP classifier) two base algorithms. Then calculate the confusion matrix, ROC, AUC to find the best base algorithm.

New method from phase 1 to phase 4 followed CRISP-DM methodology steps such as data collection, data preparation then phase 5 followed modelling and phase 6 followed evaluation and implementation steps.

Structure of proposed process flow for two class problem combined with algorithm and sub-algorithm display on figure – 1.

These articles mainly focus to describe all algorithms which are going to implementation for better understanding.

Figure 1 – Data Mining Process Flow

2 Phase 1: Outlier treatment, Transform, Scaling, Imputation

This phase involved with outlier treatment, imputation, scaling, and transform data.

2.1 Outliner treatment: – Z score

Outlier is a data point which lies far from all other data point in a data set. Outlier need to treat because it may bias the entire result. Outlier treatment with Z score is a common technique. Z score is a standard score in statistics. Z score provides information about data value is smaller or grater then mean that means how many standard deviations away from the mean value. Z score equation display below:

$Z = \frac{(x - \mu)}{\sigma}$

Here x = data point
σ = Standard deviation
μ = mean value

Equation- 1 Z-Score

In a normal distribution Z score represent 68% data lies on +/- 1, 95% data point lies on +/- 2, 99.7% data point lies on +/- 3 standard deviation.

2.2 Imputation data: – mean

Imputation is a way to handle missing data by replacing substituted value. There are many imputation technique represent like mean, median, mode, k-nearest neighbours. Mean imputation is the technique to replacing missing information with mean value. On the mean imputation first calculate the particular features mean value and then replace the missing value with mean value. The next equation displays the mean calculation:

$\mu = \frac{(\sum x)}{n}$

Here x = value of each point
n = number of values
μ = mean value

Equation- 2 Mean

2.3 Transform: – One hot encoding

Encoding is a pre-processing technique which represents data in such a way that computer can understand. For understanding of machine learning algorithm categorical columns convert to numerical columns, this process called categorical encoding. There are multiple way to handle categorical variable but most widely used techniques are label encoding and one host encoding. On label encoding give a numeric (integer number) for each category. Suppose there are 3 categories of foods like apples, orange, banana. When label encoding is used then 3 categories will get a numerical value like apples = 1, banana = 2 and orange = 3. But there is very high probability that machine learning model can capture the relationship in between categories such as apple < banana < orange or calculate average across categories like 1 +3 = 4 / 2 = 2 that means model can understand average of apple and orange together is banana which is not acceptable because model correlation calculation is wrong. For solving this problem one hot encoding appear. The following table displays the label encoding is transformed into one hot encoding.

Table- 1 Encoding example

On hot encoding categorical value split into columns and each column contains 0 or 1 according to columns placement.

2.4 Scaling data: – Min Max Scaler

Feature scaling method is standardized or normalization the independent variable that means it is used to scale the data in a particular range like -1 to +1 or depending on algorithm. Generally normalization used where data distribution does not follow Gaussian distribution and standardization used where data distribution follow Gaussian distribution. On standardization techniques transform data values are cantered around the mean and unit is standard deviation. Formula for standardization given below:

$Standardization X = \frac{(X - \mu)}{\sigma}$

Equation-3 Equations for Standardization

X represent the feature value, µ represent mean of the feature value and σ represent standard deviation of the feature value. Standardized data value does not restrict to a particular range.

Normalization techniques shifted and rescaled data value range between 0 and 1. Normalization techniques also called Min-Max scaling. Formula for normalization given below:

$Normalization X = \frac{(X - X_{min})}{X_{max} - X_{min}}$

Equation – 4 Equations for Normalization

Above X, X_min, X_max are accordingly feature values, feature minimum value and feature maximum value. On above formula when X is minimums then numerator will be 0 ( is 0) or if X is maximums then the numerator is equal to the denominator ( is 1). But when X data value between minimum and maximum then is between 0 and 1. If ranges value of data does not normalized then bigger range can influence the result.

3 Phase 2: – Balance Data

3.1 SMOTE

SMOTE (synthetic minority oversampling technique) is an oversampling technique where synthetic observations are created based on existing minority observations. This technique operates in feature space instead of data space. Under SMOTE each minority class observation calculates k nearest neighbours and randomly chose the neighbours depending on over-sampling requirements. Suppose there are 4 data point on minority class and 10 data point on majority class. For this imbalance data set, balance by increasing minority class with synthetic data point. SMOTE creating synthetic data point but it is necessary to consider k nearest neighbours first. If k = 3 then SMOTE consider 3 nearest neighbours. Figure-2 display SMOTE with k = 3 and x = x1, x2, x3, x4 data point denote minority class. And all circles represent majority class.

Figure- 2 SMOTE example

4 Phase 3: – Feature Reduction

4.1 LDA

LDA stands for Linear Discriminant analysis supervised technique are commonly used for classification problem. On this feature reduction account continuous independent variable and output categorical variable. It is multivariate analysis technique. LDA analyse by comparing mean of the variables. Main goal of LDA is differentiate classes in low dimension space. LDA is similar to PCA (Principal component analysis) but in addition LDA maximize the separation between multiple classes. LDA is a dimensionality reduction technique where creating synthetic feature from linear combination of original data set then discard less important feature. LDA calculate class variance, it maximize between class variance and minimize within class variance. Table-2 display the process steps of LDA.

Table- 2 LDA process

5 Phase 5: – Base Model

Here we consider two base model ensemble random forest and MLP classifier.

5.1 Random Forest

Random forest is an ensemble (Bagging) method where group of weak learner (decision tree) come together to form a strong leaner. Random forest is a supervised algorithm which is used for regression and classification problem. Random forests create several decisions tree for predictions and provide solution by voting (classification) or mean (regression) value. Working process of Random forest given below (Table -3).

Table-3 Random Forest process

When training a Random forest root node contains a sample of bootstrap dataset and the feature is as same as original dataset. Suppose the dataset is D and contain d record and m number of columns. From the dataset D random forest first randomly select sample of rows (d^’) with replacement and sample of features (n^’) and give it to the decision tree. Suppose Random forest created several decision trees like T₁, T₂, T₃, T₄ . . . T_n. Then randomly selected dataset D^’ = d^’ + n^’ is given to the decision tree T₁, T₂, T₃, T₄ . . . T_n where D^’ < D, m > n^’ and d > d^’. After taking the dataset decision tree give the prediction for binary classification 1 or 0 then aggregating the decision and select the majority voted result. Figure-3 describes the structure of random forest process.

Figure- 3 Random Forest process

On Random forest base learner Decision Tree grows complete depth where bias (properly train on training dataset) is low and variance is high (when implementing test data give big error) called overfitting. On Random forest using multiple decision trees where each Decision tree is high variance but when combining all decision trees with the respect of majority vote then high variance converted into low variance because using row and feature sampling with replacement and taking the majority vote where decision is not depend on one decision tree.

CART (Classification and Regression Tree) is binary segmentation technique. CART is a Gini’s impurity index based classical algorithm to split a dataset and build a decision tree. By splitting a selected dataset CART created two child nodes repeatedly and builds a tree until the data no longer be split. There are three steps CART algorithm follow:

Find best split for each features. For each feature in binary split make two groups of the ordered classes. That means possibility of split for k classes is k-1. Find which split is maximized and contain best splits (one for each feature) result.
Find the best split for nodes. From step 1 find the best one split (from all features) which maximized the splitting criterion.
Split the best node from step 2 and repeat from step 1 until fulfil the stopping criterion.

For splitting criteria CART use GINI index impurity algorithm to calculate the purity of split in a decision tree. Gini impurity randomly classified the labels with the same distribution in the dataset. A Gini impurity of 0 (lowest) is the best possible impurity and it is achieve when everything is in a same class. Gini index varies from 0 to 1. 0 indicate the purity of class where only one class exits or all element under a specific class. 1 indicates that elements are randomly distributed across various classes. And 0.5 indicate equal elements distributed over classes. Gini index (GI) described by mathematically that sum of squared of probabilities of each class (p_i) deducted from one (Equation-5).

Equation – 5 Gini impurities

Here (Equation-5) p_i represent the probability (probability of p+ or yes and probability of p- or no) of distinct class with classified element. Suppose randomly selected feature (a1) which has 8 yes and 4 no. After the split right had side (b1 on equation-6) has 4 yes and 4 no and left had side (b2 on equation – 7) has 4 yes and 0 no. here b2 is a pure split (leaf node) because only one class yes is present. By using the GI (Gini index) formula for b1 and b2:-

Equation- 6 & 7 – Gini Impurity b1 & Gini Impurity b2

Here for b1 value 0.5 indicates that equal element (yes and no) distribute over classes which is not pure split. And b2 value 0 indicates pure split. On GINI impurity indicates that when probability (yes or no) increases GINI value also increases. Here 0 indicate pure split and .5 indicate equal split that means worst situation. After calculating the GINI index for b1 and b2 now calculate the reduction of impurity for data point a1. Here total yes 8 (b1 and b2 on Equation – 8) and total no 4 (b1) so total data is 12 on a1. Below display the weighted GINI index for feature a1:

Total data point on b1 with Gini index (m) = 8/12 * 0.5 = 0.3333

Total data point on b2 with Gini index (n) = 4/12 * 0 = 0

Weighted Gini index for feature a1 = m + n = 0.3333

Equation- 8 Gini Impurity b1 & b2

After computing the weighted Gini value for every feature on a dataset taking the highest value feature as first node and split accordingly in a decision tree. Gini is less costly to compute.

5.2 Multilayer Perceptron Classifier (MLP Classifier)

Multilayer perceptron classifier is a feedforward neural network utilizes supervised learning technique (backpropagation) for training. MLP Classifier combines with multiple perceptron (hidden) layers. For feedforward taking input send combining with weight bias and then activation function from one hidden layer output goes to other hidden and this process continuing until reached the output. Then output calculates the error with error algorithm. These errors send back with backpropagation for weight adjustment by decreasing the total error and process is repeated, this process is call epoch. Number of epoch is determined with the hyper-parameter and reduction rate of total error.

5.2.1 Back-Propagation

Backpropagation is supervised learning algorithm that is used to train neural network. A neural network consists of input layer, hidden layer and output layer and each layer consists of neuron. So a neural network is a circuit of neurons. Backpropagation is a method to train multilayer neural network the updating of the weights of neural network and is done in such a way so that the error observed can be reduced here, error is only observed in the output layer and that error is back propagated to the previous layers and previous layer is proportionally updated weight. Backpropagation maintain chain rule to update weight. Mainly three steps on backpropagation are (Table-4):

Step	Process
Step 1	Forward Pass
Step 2	Backward Pass
Step 3	Sum of all values and calculate updated weight value with Chain – rules.

Table-4 Back-Propagation process

5.2.2 Forward pass/ Forward propagation

Forward propagation is the process where input layer send the input value with randomly selected weight and bias to connected neuron and inside neuron selected activation function combine them and forward to other connected neuron layer after layer then give an output with the help of output layer. Below (Figure-4) display the forward propagation.

Figure-4 Forward passes

Input layer take the input of X (X₁, X₂) combine with randomly selected weight for each connection and with fixed bias (different hidden layer has different bias) send it to first hidden layer where first multiply the input with corresponding weight and added all input with single bias then selected activation function (may different form other layer) combine all input and give output according to function and this process is going on until reach in output layer. Output layer give the output like Y (Y₁, Y₂) (here output is binary classification as an example) according to selected activation function.

5.2.3 Backward Pass

After calculating error (difference between Forward pass output and actual output) backward pass try to minimize the error with optimisation function by sending backward with proportionally distribution and maintain a chain rule. Backward pass distribution the error in such a way where weighted value is taking under consideration. Below (Figure-5) diagram display the Backward pass process.

Figure-5 Backward passes

Backpropagation push back the error which is calculated with error function or loss function for update proportional distribution with the help of optimisation algorithm. Division of Optimisation algorithm given below on Figure – 6

Figure -6 Division of Optimisation algorithms

Gradient decent calculate gradient and update value by increases or decreases opposite direction of gradients unit and try to find the minimal value. Gradient decent update just one time for whole dataset but stochastic gradient decent update on each training sample and it is faster than normal gradient decent. Gradient decent can be improve by tuning parameter like learning rate (0 to 1 mostly use 0.5). Adagrad use time step based parameter to compute learning rate for every parameter. Adam is Adaptive Moment Estimation. It calculates different parameter with different learning rate. It is faster and performance rate is higher than other optimization algorithm. On the other way Adam algorithm is squares the calculated exponential weighted moving average of gradient.

5.2.4 Chain – rules

Backpropagation maintain chain-rules to update weighted value. On chain-rules backpropagation find the derivative of error respect to any weight. Suppose E is output error. w is weight for input a and bias b and ac neuron output respect of activation function and summation of bias with weighted input (w*a) input to neuron is net. So partial derivative for error respect to weight is ∂E / ∂w display the process on figure-7.

Figure- 7 Partial derivative for error respect to weight

On the chain rules for backward pass to find (error respect to weight) ∂E / ∂w = ∂E / ∂ac * ∂ac / ∂net * ∂net / ∂w. here find to error respect to weight are error respect to output of activation function multiply by activation function output respect to input in a neuron multiply by input in a neuron respect to weight.

5.2.5 Activation function

Activation function is a function which takes the decision about neuron to activate or deactivate. If the activate function activate the neuron then it will give an output on the basis of input. Input in a activation function is sum of input multiply with corresponding weight and adding the layered bias. The main function of a activate function is non-linearity output of a neuron.

Figure-8 Activation function

Figure – 8 display a neuron in a hidden layer. Here several input (1, 2, 3) with corresponding weight (w1, w2, w3) putting in a neuron input layer where layer bias add with summation of multiplication with input and weight. Equation-9 display the output of an activate function.

Output from activate function y = Activate function (Ʃ (weight * input) + bias)

y = f (Ʃ (w*x) +b)

Equation- 9 Activate function

There are many activation functions like linear function for regression problem, sigmoid function for binary classification problem where result either 0 or 1, Tanh function which is based on sigmoid function but mathematically shifted version and values line -1 to 1. RELU function is Rectified linear unit. RELU is less expensive to compute.

5.2.6 Sigmoid

Sigmoid is a squashing activate function where output range between 0 and 1. Sigmoidal name comes from Greek letter sigma which looks like letter S when graphed. Sigmoid function is a logistic type function, it mainly use in output layer in neural network. Sigmoid is non-linear, fixed output range (between 0 and 1), monotonic (never decrees or never increases) and continuously differentiated function. Sigmoid function is good at classification and output from sigmoid is nonlinear. But Sigmoid has a vanishing gradient problem because output variable is very less to change in input variable. Figure- 9 displays the output of a Sigmoid and derivative of Sigmoid. Here x is any number (positive or negative). On sigmoid function 1 is divided by exponential negative input with adding 1.

Figure – 9 Sigmoid Functions

4.5.2.7 RELU

RELU stands for Rectified Linear Units it is simple, less expensive in computation and rectifies the gradient vanishing problem. RELU is nonlinear activation function. It gives output either positive (infinity) or 0. RELU has a dying problem because if neurons stop for responding to variation because of gradient is 0 or nothing has to change. Figure- 10 displays the output of an RELU and derivative of RELU. Here x is any positive input and if x is grater then 0 give the output as x or give output 0. RELU function gives the output maximum value of input, here max (0, x).

Figure – 10 RELU Function

4.5.2.8 Cost / loss function (Binary Cross-Entropy)

Cost or loss function compare the predictive value (model outcome) with actual value and give a quantitative value which give the indication about how much good or bad the prediction is.

Figure- 11 Cost function work process

Figure-11 x1 and x2 are input in a activate function f(x) and output y1_out which is sum of weighted input added with bias going through activate function. After model output activate function compare the output with actual output and give a quantitative value which indicate how good or bad the prediction is.

There are many type of loss function but choosing of optimal loss function depends on the problem going to be solved such as regression or classification. For binary classification problem binary cross entropy is used to calculate cost. Equation-10 displays the binary cross entropy where y is actual binary value and y^p predictive outcome range 0 and 1. And i is scalar vale range between 1 to model output size (N).

Equation-10 displays the binary cross entropy

6 Phase 6: – Evaluation

6.1 Confusion matrix

In a classification confusion matrix describe the performance of actual value against predictive value. Confusion Matrix does the performance measurement. So confusion matrix classifies and display predicted and actual value (Visa, S., Ramsay 2011).

Table- 5 Confusion Matrix

Confusion Matrix (Table-5) combines with True Positive (TP), True Negative (TN), False Positive (FP), and False Negative (FN). True Positive is prediction positive and true. True Negative is prediction negative and that is true. False positive is prediction positive and it’s false. False negative is prediction negative and that is false. False positive is known as Type1 error and false negative is known as Type 2 error. Confusion matrix can able to calculate several list of rates which are given below on Table- 6.

Here N = Total number of observation, TP = True Positive, TN = True Negative

FP = False Positive, FN = False Negative, Total Actual No (AN) = TN + FP,

Total Predictive Yes (PY) = FP + TP. Total Actual Yes (AY) = FN + TP

Rate	Description	Mathematical Description
Accuracy	Classifier, overall how often correctly identified	(TP+TN) / N
Misclassification Rate	Classifier, overall how often wrongly identified	(FP + FN) / N
True Positive Rate (Sensitivity / Recall)	Classifier, how often predict correctly yes when it is actually yes.	TP / AY
False Positive Rate	Classifier, how often predict wrongly yes when it is actually no.	FP / AN
True Negative Rate (Specificity)	Classifier, how often predict correctly no when it is actually no.	TN / AN
Precision	Classifier how often predict yes when it is correct.	TP / PY
Prevalence	Yes conditions how often occur in a sample.	AY / N

Table – 6 Confusion matrixes Calculation

From confusion matrix F1 score can be calculated because F1 score related to precision and recall. Higher F1 score is better. If precision or recall any one goes down F1 score also go down.

$F1 = \frac{2 * Precision * Recall}{Precision + Recall}$

4.6.2 ROC (Receiver Operating Characteristic) curve

In statistics ROC is represent in a graph with plotting a curve which describe a binary classifiers performance as its differentiation threshold is varied. ROC (Equation-11) curve created true positive rate (TPR) against false positive rate (FPR). True positive rate also called as Sensitivity and False positive rate also known as Probability of false alarm. False positive rate also called as a probability of false alarm and it is calculated as 1 – Specificity.

$True Positive Rate = \frac{True Positive}{True Positive + False Negative} = Recall or Sensivity$

$False Positive Rate = \frac{True Negative}{True Negative + False Positive} = 1 - Specificity$

Equation- 11 ROC

So ROC (Receiver Operation Characteristic) curve allows visual representation between sensitivity and specificity associated with different values of the test result (Grzybowski, M. and Younger, J.G., 1997)

On ROC curve each point has different Threshold level. Below (Figure – 12) display the ROC curve. Higher the area curve covers is better that means high sensitivity and high specificity represent more accuracy. ROC curve also represent that if classifier predict more often true than it has more true positive and also more false positive. If classifier predict true less often then fewer false positive and also fewer true positive.

ROC Curve

Figure – 12 ROC curve description

4.6.3 AUC (Area under Curve)

Area under curve (AUC) is the area surrounded by the ROC curve and AUC also represent the degree of separability that means how good the model to distinguished between classes. Higher the AUC value represents better the model performance to separate classes. AUC = 1 for perfect classifier, AUC = 0 represent worst classifier, and AUC = 0.5 means has no class separation capacity. Suppose AUC value is 0.6 that means 60% chance that model can classify positive and negative class.

Figure- 13 to Figure – 16 displays an example of AUC where green distribution curve for positive class and blue distribution curve for negative class. Here threshold or cut-off value is 0.5 and range between ‘0’ to ‘1’. True negative = TN, True Positive = TP, False Negative = FN, False Positive = FP, True positive rate = TPR (range 0 to 1), False positive rate = FPR (range 0 to 1).

On Figure – 13 left distribution curve where two class curves does not overlap that means both class are perfectly distinguished. So this is ideal position and AUC value is 1. On the left side ROC also display that TPR for positive class is 100% occupied.

ROC distributions (perfectly distinguished

Figure – 14 two class overlap each other and raise false positive (Type 1), false negative (Type 2) errors. Here error could be minimize or maximize according to threshold. Suppose here AUC = 0.6, that means chance of a model to distinguish two classes is 60%. On ROC curve also display the curve occupied for positive class is 60%.

ROC distributions (class partly overlap distinguished)

Figure- 15 displayed that positive and negative overlap each other. Here AUC value is 0.5 or near to 0.5. On this position classifier model does not able distinguish positive and negative classes. On left side ROC curve become straight that means TPR and FPR are equal.

ROC distributions (class fully overlap distinguished)

Figure- 16 positive and negative class swap position and on this position AUC = 0. That means classified model predict positive as a negative and negative as a positive. On the left ROC curve display that curve on FPR side fully fitted.

ROC distributions (class swap position distinguished)

7 Summaries

This paper describes a data mining process flow and related model and its algorithm with textual representation. One hot encoding create dummy variable for class features and min-max scaling scale the data in a single format. Balancing by SMOTE data where Euclidian distance calculates the distance in-between nearest neighbour to produce synthetic data under minority class. LDA reduce the distance inside class and maximise distance in-between class and for two class problem give a single dimension features which is less costly to calculate accuracy by base algorithm (random forest and MLP classifier). Confusion matrix gives the accuracy, precision, sensitivity, specificity which is help to take a decision about base algorithm. AUC and ROC curve also represent true positive rate against false positive rate which indicate base algorithm performance.

Base algorithm Random forest using CART with GINI impurity for feature selection to spread the tree. Here CART is selected because of less costly to run. Random forest algorithm is using bootstrap dataset to grow trees, and aggregation using majority vote to select accuracy.

MLP classifier is a neural network algorithm using backpropagation chain-rule to reducing error. Here inside layers using RLU activation function. Output layers using Sigmoid activation function and binary cross entropy loss function calculate the loss which is back propagate with Adam optimizer to optimize weight and reduce loss.

References:

Visa, S., Ramsay, B., Ralescu, A.L. and Van Der Knaap, E., 2011. Confusion Matrix-based Feature Selection. MAICS, 710, pp.120-127.
Grzybowski, M. and Younger, J.G., 1997. Statistical methodology: III. Receiver operating characteristic (ROC) curves. Academic Emergency Medicine, 4(8), pp.818-826.

On the difficulty of language: prerequisites for NLP with deep learning

January 27, 2021/in Artificial Intelligence, Big Data, Data Mining, Data Science, Data Science Hack, Deep Learning, Machine Learning, Main Category, Natural Language Processing, Python, TensorFlow, Text Mining/by Yasuto Tamura

This is the first article of my article series “Instructions on Transformer for people outside NLP field, but with examples of NLP.”

1 Preface

This section is virtually just my essay on language. You can skip this if you want to get down on more technical topic.

As I do not study in natural language processing (NLP) field, I would not be able to provide that deep insight into this fast changing deep leaning field throughout my article series. However at least I do understand language is a difficult and profound field, not only in engineering but also in many other study fields. Some people might be feeling that technologies are eliminating languages, or one’s motivations to understand other cultures. First of all, I would like you to keep it in mind that I am not a geek who is trying to turn this multilingual world into a homogeneous one and rebuild Tower of Babel, with deep learning. I would say I am more keen on social or anthropological sides of language.

I think you would think more about languages if you have mastered at least one foreign language. As my mother tongue is Japanese, which is totally different from many other Western languages in terms of characters and ambiguity, I understand translating is not what learning a language is all about. Each language has unique characteristics, and I believe they more or less influence one’s personalities. For example, many Western languages make the verb, I mean the conclusion, of sentences clear in the beginning part of the sentences. That is also true of Chinese, I heard. However in Japanese, the conclusion comes at the end, so that is likely to give an impression that Japanese people are being obscure or indecisive. Also, Japanese sentences usually omit their subjects. In German as well, the conclusion of a sentences tend to come at the end, but I am almost 100% sure that no Japanese people would feel German people make things unclear. I think that comes from the structures of German language, which tends to make the number, verb, relations of words crystal clear.

Source: https://twitter.com/nakamurakihiro

Let’s take an example to see how obscure Japanese is. A Japanese sentence 「頭が赤い魚を食べる猫」can be interpreted in five ways, depending on where you put emphases on.

Common sense tells you that the sentence is likely to mean the first two cases, but I am sure they can mean those five possibilities. There might be similarly obscure sentences in other languages, but I bet few languages can be as obscure as Japanese. Also as you can see from the last two sentences, you can omit subjects in Japanese. This rule is nothing exceptional. Japanese people usually don’t use subjects in normal conversations. And when you read classical Japanese, which Japanese high school students have to do just like Western students learn some of classical Latin, the writings omit subjects much more frequently.

*However interestingly we have rich vocabulary of subjects. The subject “I” can be translated to 「私」、「僕」、「俺」、「自分」、「うち」etc, depending on your personality, who you are talking to, and the time when it is written in.

I believe one can see the world only in the framework of their language, and it seems one’s personality changes depending on the language they use. I am not sure whether the language originally determines how they think, or how they think forms the language. But at least I would like you to keep it in mind that if you translate a conversation, for example a random conversation at a bar in Berlin, into Japanese, that would linguistically sound Japanese, but not anthropologically. Imagine that such kind of random conversation in Berlin or something is like playing a catch, I mean throwing a ball named “your opinion.” On the other hand, normal conversations of Japanese people are in stead more of, I would say, “resonance” of several tuning forks. They do their bests to show that they are listening to each other, by excessively nodding or just repeating “Really?”, but usually it seems hardly any constructive dialogues have been made.

*I sometimes feel you do not even need deep learning to simulate most of such Japanese conversations. Several-line Python codes would be enough.

My point is, this article series is mainly going to cover only a few techniques of NLP in deep learning field: sequence to sequence model (seq2seq model) , and especially Transformer. They are, at least for now, just mathematical models and mappings of a small part of this profound field of language (as far as I can cover in this article series). But still, examples of language would definitely help you understand Transformer model in the long run.

2 Tokens and word embedding

*Throughout my article series, “words” just means the normal words you use in daily life. “Tokens” means more general unit of NLP tasks. For example the word “Transformer” might be denoted as a single token “Transformer,” or maybe as a combination of two tokens “Trans” and “former.”

One challenging part of handling language data is its encodings. If you started learning programming in a language other than English, you would have encountered some troubles of using keyboards with different arrangements or with characters. Some comments on your codes in your native languages are sometimes not readable on some software. You can easily get away with that by using only English, but when it comes to NLP you have to deal with this difficulty seriously. How to encode characters in each language should be a first obstacle of NLP. In this article we are going to rely on a library named BPEmb, which provides word embedding in various languages, and you do not have to care so much about encodings in languages all over the world with this library.

In the first section, you might have noticed that Japanese sentence is not separated with spaces like Western languages. This is also true of Chinese language, and that means we need additional tasks of separating those sentences at least into proper chunks of words. This is not only a matter of engineering, but also of some linguistic fields. Also I think many people are not so conscious of how sentences in their native languages are grammatically separated.

The next point is, unlike other scientific data, such as temperature, velocity, voltage, or air pressure, language itself is not measured as numerical data. Thus in order to process language, including English, you first have to map language to certain numerical data, and after some processes you need to conversely map the output numerical data into language data. This section is going to be mainly about one-hot encoding and word embedding, the ways to convert word/token into numerical data. You might already have heard about this

You might have learnt about word embedding to some extent, but I hope you could get richer insight into this topic through this article.

2.1 One-hot encoding

One-hot encoding would be the most straightforward way to encode words/tokens. Assume that you have a dictionary whose size is $|\mathcal{V}|$ , and it includes words from “a”, “ablation”, “actually” to “zombie”, “?”, “!”

In a mathematical manner, in order to choose a word out of those $|\mathcal{V}|$ words, all you need is a $|\mathcal{V}|$ dimensional vector, one of whose elements is $1$ , and the others are $0$ . When you want to choose the No. i word, which is “indeed” in the example below, its corresponding one-hot vector is $\boldsymbol{v} = (0, \dots, 1, \dots, 0 )$ , where only the No. i element is $1$ . One-hot encoding is also easy to understand, and that’s all. It is easy to imagine that people have already come up with more complicated and better way to encoder words. And one major way to do that is word embedding.

2.2 Word embedding

Source: Francois Chollet, Deep Learning with Python,(2018), Manning

Actually word embedding is related to one-hot encoding, and if you understand how to train a simple neural network, for example densely connected layers, you would understand word embedding easily. The key idea of word embedding is denoting each token with a $D$ dimensional vector, whose dimension is fewer than the vocabulary size $|\mathcal{V}|$ . The elements of the resulting word embedding vector are real values, I mean not only 0 or 1. Obviously you can encode much richer variety of tokens with such vectors. The figure at the left side is from “Deep Learning with Python” by François Chollet, and I think this is an almost perfect and simple explanation of the comparison of one-hot encoding and word embedding. But the problem is how to get such convenient vectors. The answer is very simple: you have only to train a network whose inputs are one-hot vector of the vocabulary.

The figure below is a simplified model of word embedding of a certain word. When the word is input into a neural network, only the corresponding element of the one-hot vector is 1, and that virtually means the very first input layer is composed of one neuron whose value is 1. And the only one neuron propagates to the next D dimensional embedding layer. These weights are the very values which most other study materials call “an embedding vector.”

When you input each word into a certain network, for example RNN or Transformer, you map the input one-hot vector into the embedding layer/vector. The examples in the figure are how inputs are made when the input sentences are “You’ve got the touch” and “You’ve got the power.” Assume that you have a dictionary of one-hot encoding, whose vocabulary is {“the”, “You’ve”, “Walberg”, “touch”, “power”, “Nights”, “got”, “Mark”, “Boogie”}, and the dimension of word embeding is 6. In this case $|\mathcal{V}| = 9, D=6$ . When the inputs are “You’ve got the touch” or “You’ve got the power” , you put the one-hot vector corresponding to “You’ve”, “got”, “the”, “touch” or “You’ve”, “got”, “the”, “power” sequentially every time step $t$ .

In order to get word embedding of certain vocabulary, you just need to train the network. We know that the words “actually” and “indeed” are used in similar ways in writings. Thus when we propagate those words into the embedding layer, we can expect that those embedding layers are similar. This is how we can mathematically get effective word embedding of certain vocabulary.

More interestingly, if word embedding is properly trained, you can mathematically “calculate” words. For example, $\boldsymbol{v}_{king} - \boldsymbol{v}_{man} + \boldsymbol{v}_{woman} \approx \boldsymbol{v}_{queen}$ , $\boldsymbol{v}_{Japan} - \boldsymbol{v}_{Tokyo} + \boldsymbol{v}_{Vietnam} \approx \boldsymbol{v}_{Hanoi}$ .

*I have tried to demonstrate this type of calculation on several word embedding, but none of them seem to work well. At least you should keep it in mind that word embedding learns complicated linear relations between words.

I should explain word embedding techniques such as word2vec in detail, but the main focus of this article is not NLP, so the points I have mentioned are enough to understand Transformer model with NLP examples in the upcoming articles.

3 Language model

Language models is one of the most straightforward, but crucial ideas in NLP. This is also a big topic, so this article is going to cover only basic points. Language model is a mathematical model of the probabilities of which words to come next, given a context. For example if you have a sentence “In the lecture, he opened a _.”, a language model predicts what comes at the part “_.” It is obvious that this is contextual. If you are talking about general university students, “_” would be “textbook,” but if you are talking about Japanese universities, especially in liberal art department, “_” would be more likely to be “smartphone. I think most of you use this language model everyday. When you type in something on your computer or smartphone, you would constantly see text predictions, or they might even correct your spelling or grammatical errors. This is language modelling. You can make language models in several ways, such as n-gram and neural language models, but in this article I can explain only general formulations for such models.

*I am not sure which algorithm is used in which services. That must be too fast changing and competitive for me to catch up.

As I mentioned in the first article series on RNN, a sentence is usually processed as sequence data in NLP. One single sentence is denoted as $\boldsymbol{X} = (\boldsymbol{x}^{(1)}, \dots, \boldsymbol{x}^{(\tau)})$ , a list of vectors. The vectors are usually embedding vectors, and the $(t)$ is the index of the order of tokens. For example the sentence “You’ve go the power.” can be expressed as $\boldsymbol{X} = (\boldsymbol{x}^{(1)}, \boldsymbol{x}^{(2)}, \boldsymbol{x}^{(3)}, \boldsymbol{x}^{(4)})$ , where $\boldsymbol{x}^{(1)}, \boldsymbol{x}^{(2)}, \boldsymbol{x}^{(3)}, \boldsymbol{x}^{(4)}$ denote “You’ve”, “got”, “the”, “power”, “.” respectively. In this case $\tau = 4$ .

In practice a sentence $\boldsymbol{X}$ usually includes two tokens $BOS$ and $EOS$ at the beginning and the end of the sentence. They mean “Beginning Of Sentence” and “End Of Sentence” respectively. Thus in many cases $\boldsymbol{X} = (\boldsymbol{BOS} , \boldsymbol{x}^{(1)}, \dots, \boldsymbol{x}^{(\tau)}, \boldsymbol{EOS} )$ . $\boldsymbol{BOS}$ and $\boldsymbol{EOS}$ are also both vectors, at least in the Tensorflow tutorial.

$P(\boldsymbol{X} =$ $(\boldsymbol{BOS}, \boldsymbol{x}^{(1)}, \dots, \boldsymbol{x}^{(\tau)}, \boldsymbol{EOS})$ is the probability of incidence of the sentence. But it is easy to imagine that it would be very hard to directly calculate how likely the sentence $\boldsymbol{X}$ appears out of all possible sentences. I would rather say it is impossible. Thus instead in NLP we calculate the probability $P(\boldsymbol{X})$ as a product of the probability of incidence or a certain word, given all the words so far. When you’ve got the words $(\boldsymbol{x}^{(1)}, \dots, \boldsymbol{x}^{(t-1})$ so far, the probability of the incidence of $\boldsymbol{x}^{(t)}$ , given the context is $P(\boldsymbol{x}^{(t)}|\boldsymbol{x}^{(1)}, \dots, \boldsymbol{x}^{(t-1)})$ . $P(\boldsymbol{BOS})$ is a probability of the the sentence $\boldsymbol{X}$ being $(\boldsymbol{BOS})$ , and the probability of $\boldsymbol{X}$ being $(\boldsymbol{BOS}, \boldsymbol{x}^{(1)})$ can be decomposed this way: $P(\boldsymbol{BOS}, \boldsymbol{x}^{(1)}) =$ $P(\boldsymbol{x}^{(1)}|\boldsymbol{BOS})P(\boldsymbol{BOS})$ .

Just as well $P(\boldsymbol{BOS}, \boldsymbol{x}^{(1)}, \boldsymbol{x}^{(2)}) =$ $P(\boldsymbol{x}^{(2)}| \boldsymbol{BOS}, \boldsymbol{x}^{(1)}) P( \boldsymbol{BOS}, \boldsymbol{x}^{(1)})=$ $P(\boldsymbol{x}^{(2)}| \boldsymbol{BOS}, \boldsymbol{x}^{(1)}) P(\boldsymbol{x}^{(1)}| \boldsymbol{BOS}) P( \boldsymbol{BOS})$ .

Hence, the general probability of incidence of a sentence $\boldsymbol{X}$ is $P(\boldsymbol{X})=P(\boldsymbol{BOS}, \boldsymbol{x}^{(1)}, \boldsymbol{x}^{(2)}, \dots, \boldsymbol{x}^{(\tau -1)}, \boldsymbol{x}^{(\tau)}, \boldsymbol{EOS}) =$ $P(\boldsymbol{EOS}| \boldsymbol{BOS}, \boldsymbol{x}^{(1)}, \dots, \boldsymbol{x}^{(\tau)})$ $P(\boldsymbol{x}^{(\tau)}| \boldsymbol{BOS}, \boldsymbol{x}^{(1)}, \dots, \boldsymbol{x}^{(\tau - 1)})$ $\cdots$ $P(\boldsymbol{x}^{(2)}| \boldsymbol{BOS}, \boldsymbol{x}^{(1)})$ $P(\boldsymbol{x}^{(1)}| \boldsymbol{BOS})$ $P(\boldsymbol{BOS})$ .

Let $\boldsymbol{x}^{(0)}$ be $\boldsymbol{BOS}$ and $\boldsymbol{x}^{(\tau + 1)}$ be $\boldsymbol{EOS}$ . Plus, let $P(\boldsymbol{x}^{(t+1)}|\boldsymbol{X}_{[0, t]})$ be $P(\boldsymbol{x}^{(t+1)}|\boldsymbol{x}^{(0)}, \dots, \boldsymbol{x}^{(t)})$ , then $P(\boldsymbol{X}) = P(\boldsymbol{x}^{(0)})\prod_{t=0}^{\tau}{P(\boldsymbol{x}^{(t+1)}|\boldsymbol{X}_{[0, t]})}$ . Language models calculate which words to come sequentially in this way.

Here’s a question: how would you evaluate a language model?

I would say the answer is, when the language model generates words, the more confident the language model is, the better the language model is. Given a context, when the distribution of the next word is concentrated on a certain word, we can say the language model is confident about which word to come next, given the context.

*For some people, it would be more understandable to call this “entropy.”

Let’s take the vocabulary {“the”, “You’ve”, “Walberg”, “touch”, “power”, “Nights”, “got”, “Mark”, “Boogie”} as an example. Assume that $P(\boldsymbol{X}) =$ $P(\boldsymbol{BOS}, \boldsymbol{You've}, \boldsymbol{got}, \boldsymbol{the}, \boldsymbol{touch}, \boldsymbol{EOS}) =$ $P(\boldsymbol{BOS}, \boldsymbol{x}^{(1)}, \boldsymbol{x}^{(2)}, \boldsymbol{x}^{(3)}, \boldsymbol{x}^{(4)}, \boldsymbol{EOS})=$ $P(\boldsymbol{x}^{(0)})\prod_{t=0}^{4}{P(\boldsymbol{x}^{(t+1)}|\boldsymbol{X}_{[0, t]})}$ . Given a context $(\boldsymbol{BOS}, \boldsymbol{x}^{(1)})$ , the probability of incidence of $\boldsymbol{x}^{(2)}$ is $P(\boldsymbol{x}^{2}|\boldsymbol{BOS}, \boldsymbol{x}^{(1)})$ . In the figure below, the distribution at the left side is less confident because probabilities do not spread widely, on the other hand the one at the right side is more confident that next word is “got” because the distribution concentrates on “got”.

*You have to keep it in mind that the sum of all possible probability $P(\boldsymbol{x}^{(2)} | \boldsymbol{BOS}, \boldsymbol{x}^{(1)})$ is $1$ , that is, $P(\boldsymbol{the}| \boldsymbol{BOS}, \boldsymbol{x}^{(1)}) +$ $P(\boldsymbol{You've}| \boldsymbol{BOS}, \boldsymbol{x}^{(1)}) + \cdots$ $+ P(\boldsymbol{Boogie}| \boldsymbol{BOS}, \boldsymbol{x}^{(1)}) = 1$ .

While the language model generating the sentence “BOS You’ve got the touch EOS”, it is better if the language model keeps being confident. If it is confident, $P(\boldsymbol{X})=$ $P(\boldsymbol{BOS})$ $P(\boldsymbol{x}^{(1)}|\boldsymbol{BOS}}P(\boldsymbol{x}^{(3)}|\boldsymbol{BOS}, \boldsymbol{x}^{(1)}, \boldsymbol{x}^{(2)})$ $P(\boldsymbol{x}^{(4)}|\boldsymbol{BOS}, \boldsymbol{x}^{(1)}, \boldsymbol{x}^{(2)}, \boldsymbol{x}^{(3)})$ $P(\boldsymbol{EOS}|\boldsymbol{BOS}, \boldsymbol{x}^{(1)}, \boldsymbol{x}^{(2)}, \boldsymbol{x}^{(3)}, \boldsymbol{x}^{(4)})}$ gets higher. Thus $(-1) \{ log_{b}{P(\boldsymbol{BOS})} +$ $log_{b}{P(\boldsymbol{x}^{(1)}|\boldsymbol{BOS}}) +$ $log_{b}{P(\boldsymbol{x}^{(3)}|\boldsymbol{BOS}, \boldsymbol{x}^{(1)}, \boldsymbol{x}^{(2)})} +$ $log_{b}{P(\boldsymbol{x}^{(4)}|\boldsymbol{BOS}, \boldsymbol{x}^{(1)}, \boldsymbol{x}^{(2)}, \boldsymbol{x}^{(3)})} +$ $log_{b}{P(\boldsymbol{EOS}|\boldsymbol{BOS}, \boldsymbol{x}^{(1)}, \boldsymbol{x}^{(2)}, \boldsymbol{x}^{(3)}, \boldsymbol{x}^{(4)})} \}$ gets lower, where usually $b=2$ or $b=e$ .

This is how to measure how confident language models are, and the indicator of the confidence is called perplexity. Assume that you have a data set for evaluation $\mathcal{D} = (\boldsymbol{X}_1, \dots, \boldsymbol{X}_n, \dots, \boldsymbol{X}_{|\mathcal{D}|})$ , which is composed of $|\mathcal{D}|$ sentences in total. Each sentence $\boldsymbol{X}_n =$ $(\boldsymbol{x}^{(0)})\prod_{t=0}^{\tau ^{(n)}}{P(\boldsymbol{x}_{n}^{(t+1)}|\boldsymbol{X}_{n, [0, t]})}$ has $\tau^{(n)}$ tokens in total excluding $\boldsymbol{BOS}, \boldsymbol{EOS}$ . And let $|\mathcal{V}|$ be the size of the vocabulary of the language model. Then the perplexity of the language model is $b^z$ , where $z = \frac{-1}{|\mathcal{V}|}\sum_{n=1}^{|\mathcal{D}|}{\sum_{t=0}^{\tau ^{(n)}}{log_{b}P(\boldsymbol{x}_{n}^{(t+1)}|\boldsymbol{X}_{n, [0, t]})}$ . The $b$ is usually $2$ or $e$ .

For example, assume that $\mathcal{V}$ is vocabulary {“the”, “You’ve”, “Walberg”, “touch”, “power”, “Nights”, “got”, “Mark”, “Boogie”}. Also assume that the evaluation data set for perplexity of a language model is $\mathcal{D} = (\boldsymbol{X}_1, \boldsymbol{X}_2)$ , where $\boldsymbol{X_1} =(\boldsymbol{You've}, \boldsymbol{got}, \boldsymbol{the}, \boldsymbol{touch})$ $\boldsymbol{X_2} = (\boldsymbol{You've}, \boldsymbol{got}, \boldsymbol{the }, \boldsymbol{power})$ . In this case $|\mathcal{V}|=9,$ $|\mathcal{D}|=2$ . I have already showed you how to calculate the perplexity of the sentence “You’ve got the touch.” above. You just need to do a similar thing on another sentence “You’ve got the power”, and then you can get the perplexity of the language model.

*If the network is not properly trained, it would also be confident of generating wrong outputs. However, such network still would give high perplexity because it is “confident” at any rate. I’m sorry I don’t know how to tackle the problem. Please let me put this aside, and let’s get down on Transformer model soon.

Appendix

Let’s see how word embedding is implemented with a very simple example in the official Tensorflow tutorial. It is a simple binary classification task on IMDb Dataset. The dataset is composed to comments on movies by movie critics, and you have only to classify if the commentary is positive or negative about the movie. For example when you get you get an input “To be honest, Michael Bay is a terrible as an action film maker. You cannot understand what is going on during combat scenes, and his movies rely too much on advertisements. I got a headache when Mark Walberg used a Chinese cridit card in Texas. However he is very competent when it comes to humorous scenes. He is very talented as a comedy director, and I have to admit I laughed a lot.“, the neural netowork has to judge whether the statement is positive or negative.

This networks just takes an average of input embedding vectors and regress it into a one dimensional value from 0 to 1. The shape of embedding layer is (8185, 16). Weights of neural netowrks are usually implemented as matrices, and you can see that each row of the matrix corresponds to emmbedding vector of each token.

*It is easy to imagine that this technique is problematic. This network virtually taking a mean of input embedding vectors. That could mean if the input sentence includes relatively many tokens with negative meanings, it is inclined to be classified as negative. But for example, if the sentence is “This masterpiece is a dark comedy by Charlie Chaplin which depicted stupidity of the evil tyrant gaining power in the time. It thoroughly mocked Germany in the time as an absurd group of fanatics, but such propaganda could have never been made until ‘Casablanca.'” , this can be classified as negative, because only the part “masterpiece” is positive as a token, and there are much more words with negative meanings themselves.

The official Tensorflow tutorial provides visualization of word embedding with Embedding Projector, but I would like you to take more control over the data by yourself. Please just copy and paste the codes below, installing necessary libraries. You would get a map of vocabulary used in the text classification task. It seems you cannot find clear tendency of the clusters of the tokens. You can try other dimension reduction methods to get maps of the vocabulary by for example using Scikit Learn.

import tensorflow as tf

from tensorflow import keras

from tensorflow.keras import layers

import tensorflow_datasets as tfds

tfds.disable_progress_bar()

(train_data, test_data), info = tfds.load(

'imdb_reviews/subwords8k',

split = (tfds.Split.TRAIN, tfds.Split.TEST),

with_info=True, as_supervised=True)

train_batches = train_data.shuffle(1000).padded_batch(10)

test_batches = test_data.shuffle(1000).padded_batch(10)

embedding_dim=16

encoder = info.features['text'].encoder

model = keras.Sequential([

layers.Embedding(encoder.vocab_size, embedding_dim),

layers.GlobalAveragePooling1D(),

layers.Dense(16, activation='relu'),

layers.Dense(1)

])

print("\n\nThe size of the vocabulary generated from IMDb Dataset is " + str(encoder.vocab_size) + '\n\n')

model.summary()

model.compile(optimizer='adam',

loss=tf.keras.losses.BinaryCrossentropy(from_logits=True),

metrics=['accuracy'])

history = model.fit(

train_batches,

epochs=10,

validation_data=test_batches, validation_steps=20)

word_embedding_vectors = model.layers[0].get_weights()[0]

print("\n\nThe shape of the trained weigths of the embedding layer is " + str(word_embedding_vectors.shape) + '\n\n')

from sklearn.manifold import TSNE

X_reduced = TSNE(n_components = 2, init='pca', random_state=0).fit_transform(word_embedding_vectors)

import numpy as np

embedding_dict = zip(encoder.subwords, np.arange(len(encoder.subwords)))

embedding_dict = dict(embedding_dict)

import matplotlib.pyplot as plt

plt.figure(figsize=(60, 45))

plt.scatter(X_reduced[:, 0], X_reduced[:, 1])

for i in range(0, len(encoder.subwords), 5):

plt.text(X_reduced[i, 0], X_reduced[i, 1], encoder.subwords[i], fontsize=20, color='red')

plt.title("The map of vocabulary of IMDb Dataset mapped to a 2 dimensional space by t-SNE", fontsize=60)

#plt.savefig('imdb_tsne_map.png')

plt.show()

[References]

[1] “Word embeddings” Tensorflow Core
https://www.tensorflow.org/tutorials/text/word_embeddings

[2]Tsuboi Yuuta, Unno Yuuya, Suzuki Jun, “Machine Learning Professional Series: Natural Language Processing with Deep Learning,” (2017), pp. 43-64, 72-85, 91-94
坪井祐太、海野裕也、鈴木潤著, 「機械学習プロフェッショナルシリーズ深層学習による自然言語処理」, (2017), pp. 43-64, 72-85, 191-193

[3]”Stanford CS224N: NLP with Deep Learning | Winter 2019 | Lecture 8 – Translation, Seq2Seq, Attention”, stanfordonline, (2019)
https://www.youtube.com/watch?v=XXtpJxZBa2c

[4] Francois Chollet, Deep Learning with Python,(2018), Manning , pp. 178-185

[5]”2.2. Manifold learning,” scikit-learn
https://scikit-learn.org/stable/modules/manifold.html

Operational Data Store vs. Data Warehouse

January 25, 2021/in Data Engineering, Data Warehousing/by Edward Huskin

One of the main problems with large amounts of data, especially in this age of data-driven tools and near-instant results, is how to store the data. With proper storage also comes the challenge of keeping the data updated, and this is the reason why organizations focus on solutions that will help make data processing faster and more efficient. For many, a digital transformation is in their roadmap, thanks in large part to the changes brought about by the global COVID-19 pandemic. The problem is that organizations often assume that it’s similar to traditional change initiatives, which can’t be any further from the truth. There are a number of challenges to prepare for in digital transformations, however, and without proper planning, non-unified data storage systems and systems of record implemented through the years can slow down or even hinder the process.

Businesses have relied on two main solutions for data storage for many years: traditional data warehouses and operational data stores (ODS). These key data structures provide assistance when it comes to boosting business intelligence so that the business can make sound corporate decisions based on data. Before considering which one will work for your business, it’s important to understand the main differences between the two.

What is a Data Warehouse?

Data warehousing is a common practice because a data warehouse is designed to support business intelligence tools and activities. It’s subject-oriented so data is centered on customers, products, sales, or other subjects that contribute to the business bottom line. Because data comes from a multitude of sources, a data warehouse is also designed to consolidate large amounts of data in a variety of formats, including flat files, legacy database management systems, and relational database management systems. It’s considered an organization’s single source of truth because it houses historical records built through time, which could become invaluable as a source of actionable insights.

One of the main disadvantages of a data warehouse is its non-volatile nature. Non-volatile data is read-only and, therefore, not frequently updated or deleted over time. This leads to some time variance, which means that a data warehouse only stores a time series of periodic data snapshots that show the state of data during specific periods. As such, data loading and data retrieval are the most vital operations for a data warehouse.

What is an Operational Data Store?

Forward-thinking companies turn to an operational data store to resolve the issues with data warehousing, primarily, the issue of always keeping data up-to-date. Similar to a data warehouse, an ODS can aggregate data from multiple sources and report across multiple systems of record to provide a more comprehensive view of the data. It’s essentially a staging area that can receive operational data from transactional sources and can be queried directly. This allows data analytics tools to query ODS data as it’s received from the respective source systems. This offloads the burden from the transactional systems by only providing access to current data that’s queried in an integrated manner. This makes an ODS the ideal solution for those looking for near-real time data that’s processed quickly and efficiently.

Traditional ODS solutions, however, typically suffer from high latency because they are based on either relational databases or disk-based NoSQL databases. These systems simply can’t handle large amounts of data and provide high performance at the same time, which is a common requirement of most modern applications. The limited scalability of traditional systems also leads to performance issues when multiple users access the data store all at the same time. As such, traditional ODS solutions are incapable of providing real-time API services for accessing systems of record.

A Paradigm Shift

As modern real-time digital applications replace previously offline services, companies are going through a paradigm shift and venturing beyond what traditional data storage systems can offer. This has led to the rise of a new breed of ODS solutions that Gartner refers to as digital integration hubs. It’s a cost-effective solution because it doesn’t require a rip-and-replace if you already have a traditional ODS in place. Adopting a digital integration hub can be as simple as augmenting your current system with the missing layers, including the microservices API, smart cache, and event-driven architecture.

While sticking with a data warehouse or traditional ODS may not necessarily hurt your business, the benefits of modernization via a digital integration hub are too great to ignore. Significant improvements in throughput, availability, and scalability will help organizations become more agile so they can drive innovation quicker, helping their industry and pushing the limits of technology further to open up possibilities never before discovered.

1 Multi-head attention mechanism

2 Calculating attentions and reweighting “values”

3 Scaled-dot product

4 Tensorflow implementation of multi-head attention

[References]

Physical Access Can Allow Criminals to Bypass Even the Best Digital Security

Valuable Hardware and Essential Systems May Be at High Risk

Using Physical Security to Complement Your Digital Security Planning

Data Preparation

Data Structure

Install the Dependency Packages for RStudio

Load the training data set

Feature Transformation

Support Vector Machine model

Evaluate the Model on the Testing Data Set

Download Infographic as PDF

How Caching Can Boost Performance in Finance

What Does This Mean for the Finance Industry?

Big Data Management for Big Wins

Define Specific Goals

Secure Your Data

Interlink Your Data

Ensure Compliance With Audit Regulations

Be Prepared for Change

Big Data for the Long Haul

1 Preface

2 Tokens and word embedding

3 Language model

Appendix

[References]

What is a Data Warehouse?

What is an Operational Data Store?

A Paradigm Shift

Interesting links

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