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

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 “” 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.

*Hannibal Lecter, I mean Athony Hopkins, also wrote a letter to the staff of “Breaking Bad,” and he told them the tv show let him regain his passion. He is a kind of admiring around, and I am a little worried that he might be getting senile. He played a role of a father forgetting his daughter in his new film “The Father.” I must see it to check if that is really an acting, or not.


[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

[3] “Neural machine translation with attention,” Tensorflow Core

[4] Jay Alammar, “The Illustrated Transformer,”

[5] “Stanford CS224N: NLP with Deep Learning | Winter 2019 | Lecture 14 – Transformers and Self-Attention,” stanfordonline, (2019)

[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)

[8]Rosemary Rossi, “Anthony Hopkins Compares ‘Genius’ Michael Bay to Spielberg, Scorsese,” yahoo! entertainment, (2017)

* 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: And if you have any advice for making my materials more understandable to learners, I would appreciate hearing it.

Web Scraping Using R..!

In this blog, I’ll show you, How to Web Scrape using R..?

What is R..?

R is a programming language and its environment built for statistical analysis, graphical representation & reporting. R programming is mostly preferred by statisticians, data miners, and software programmers who want to develop statistical software.

R is also available as Free Software under the terms of the Free Software Foundation’s GNU General Public License in source code form.

Reasons to choose R

Reasons to choose R

Let’s begin our topic of Web Scraping using R.

Step 1- Select the website & the data you want to scrape.

I picked this website “” and want to scrape data of Top 50 sites in India.

Data we want to scrape

Data we want to scrape

Step 2- Get to know the HTML tags using SelectorGadget.

In my previous blog, I already discussed how to inspect & find the proper HTML tags. So, now I’ll explain an easier way to get the HTML tags.

You have to go to Google chrome extension (chrome://extensions) & search SelectorGadget. Add it to your browser, it’s a quite good CSS selector.

Step 3- R Code

Evoking Important Libraries or Packages

I’m using RVEST package to scrape the data from the webpage; it is inspired by libraries like Beautiful Soup. If you didn’t install the package yet, then follow the code in the snippet below.

Step 4- Set the url of the website

Step 5- Find the HTML tags using SelectorGadget

It’s quite easy to find the proper HTML tags in which your data is present.

Firstly, I have to click on data using SelectorGadget which I want to scrape, it automatically selects the data which are similar to selected HTML tags. Before going forward, cross-check the selected values, are they correct or some junk data is also gets selected..? If you noticed our page has only 50 values, but you can see 156 values are selected.

Selection by SelectorGadget

Selection by SelectorGadget

So I need to remove unwanted values who get selected, once you click on them to deselect it, it turns red and others will turn yellow except our primary selection which turn to green. Now you can see only 50 values are selected as per our primary requirement but it’s not enough. I have to again cross-check that some required values are not exchanged with junk values.

If we satisfy with our selection then copy the HTML tag & include it into the code, else repeat this exercise.

Modified Selection by SelectorGadget

Step 6- Include the tag in our Code

After including the tags, our code is like this.

Code Snippet

If I run the code, values in each list object will be 50.

Data Stored in List Objects

Step 7- Creating DataFrame

Now, we create a dataframe with our list-objects. So for creating a dataframe, we always need to remember one thumb rule that is the number of rows (length of all the lists) should be equal, else we get an error.

Error appears when number of rows differs

Finally, Our DataFrame will look like this:

Our Final Data

Step 8- Writing our DataFrame to CSV file

We need our scraped data to be available locally for further analysis & model building or other purposes.

Our final piece of code to write it in CSV file is:

Writing to CSV file

Step 9- Check the CSV file

Data written in CSV file


I tried to explain Web Scraping using R in a simple way, Hope this will help you in understanding it better.

Find full code on

If you have any questions about the code or web scraping in general, reach out to me on LinkedIn!

Okay, we will meet again with the new exposer.

Till then,

Happy Coding..!

Test-data management  support in Test Automation Development

Data is centric in testing of several applications because data is critical to organizations. Businesses are becoming more data-driven, and hence it is imperative that as Automation Test developers, the value of the test-data is understood and  completely harnessed during Test Automation development. The test-data involved in both Manual/Automation testing encompasses the test-data inputs, test-data outputs, and the test-data flow. is the world’s first free cloud-based, community-powered test automation platform which caters to this important aspect of Test Automation development. The tool successfully adheres to the importance of keeping test-data centric in Automation Test solutions.

To start with, organizing and managing test data is very easy in TestProject. We are aware that as an application gets bigger and more tests are added, test data management becomes more difficult. This tool allows easy and clear management of the elements, tests, parameters by helping the Automation Test Developer associate data, be as an input or output in the UI as follows:

The tool makes the tests maintainable by allowing the Test data to be easily added, deleted, modified  making it  flexible in the perspective when business  requirements change. It also allows test data to be associated with Web, Android and iOS apps, allowing several types of input – web pages, JSON, PDFs etc. The test data can be also tested on several browsers such as Chrome, Firefox, Safari, Edge, Internet Explorer.

TestProject enables easy collaboration in a test automation team- by allowing/dis-allowing sharing of the test cases, test data etc as and when applicable. Eventually the team has shareable test repository which can be easily managed and controlled.

Sharing of parameters is available in levels –Test level and Project level. For example,

Hence, because of this, the test data can be easily re-usable, without having to mention the same test data repeatedly in some cases.

TestProject also has a “Secret Parameter” feature built in the smart test recorder that allows storing sensitive test data in an encrypted state.

There are also powerful Addons available in TestProject that can help the Automation Developers complete their tasks easily and quickly .For example, there are several  Random Data Generator Addons available. ‘Random Login Credentials Addon’ is one such Addon which generates random credentials to be entered for several tests.  Similarly, there are many more Random data generators available, such as for generating random dates, character/word/number etc as per several requirements. This definitely makes the job of an Automation developer much easier, and helps save time.

In TestProject, we can choose the input data source to be the default input parameters or to be associated with the data- driven method as follows :

The Data-driven Testing method of testing is necessarily important in cases when the coverage of any data variable comes into picture. We are aware that Data driven tests are tests that run multiple times, but with different values for some of the variables in the test. For example if you wanted to test that the username field on a login page could handle several different types of inputs you could create a separate test for each input, or you could use a data driven tests to drive the same login test multiple times, but just using a different username input each time. We are aware that Data-driven Testing is a very good approach if you have huge volumes of data to be tested for the same scripts.

One such support for Data driven testing in this tool is the Parameterization of variables. Once the parameters are added, like in the screenshot below, the parameter can be navigated to and picked for use.

In order to run a ‘Data-driven’ test, the Automation Developer would need to associate the test with various Data Sources. One such example is as follows, where the Developer can associate the test with the input CSV data source as follows:

Since it supports Data-driven test development, it results in stronger Test Coverage. That is, large volume of data can be managed and executed thereby improving regression testing and better coverage.

Speaking about data sources, TestProject also provides addons that help to work with several database as PostgreSQL, MySQL, MSSQL, Db2, Oracle. The tool can be easily linked with the databases by providing details as:

All this also shows the fact that the tool clearly separates the test cases and the test data and hence allows testers to test their applications using different data values and parameters without the need for changing test script/cases. While making a change in data sets such as addition, or deletion, doesn’t have implication with test cases.

Also, once the test is generated by the Automation developer, it can be viewed both in the ‘Manual Test’ view or the ‘Test document’ view. In both cases, once either of the options are chosen and they are downloaded, the test data is clearly mentioned in their respective columns in the documents.

For example, the ‘Manual Test’ document that gets generated automatically shows the Test Data used as,

And, the ‘Test’ document that gets generated automatically shows the Test Data’s default values used as,

While assesing the test results,  the tool clearly gives details on failures, helping the automation developer to easily debug the issue/ decide to open a defect. For example, the details are clearly showed as : tool can also be easily integrated with many other tools, such as Jenkins, qTest, Slack etc, and the testcases/test data etc are easily synced during this association. Example, in the cases of Jenkins, we can associate the build step by linking it with the TestProject data source as follows:

Eventually, TestProject has emerged as a powerful test Automation framework, having very attractive features especially to the fact that it imparts the value of Test-data being centric in the  Automation Test tasks. Along with the fact that the tool supports the ideology of having the test-data to be the driving base to the whole Test Automation framework process, it  also enables sharing and syncing with other teams and tools during the development, management and execution of the Test Automation Solution.

Article series: 5 Clean Coding Tips – 5.Put yourself in somebody else’s shoes

This is the fifth of the article series “5 tips for clean coding” to follow as soon as you’ve made the first steps into your coding career, in this article series. Read the introduction here, to find out why it is important to write clean code if you missed it.

It might be a bit repetitive to bring up how important the readability of the code is, let’s do it anyway. In the majority of the cases you are writing for others, therefore you need to put yourself in their shoes to be able to assess how good the readability of your code is. For you, it all might be obvious because you wrote it. But it doesn’t have to be easy to read for someone else. If you have a colleague or a friend that has a bit of time for you and is willing to give you feedback, that is great. If, however, you don’t have such a person, having a few imaginary friends might be helpful in this case. It might sound crazy, but don’t close this page just yet. Having a set of imaginary personas at your disposal, to review your work with their eyes, can help you a lot. Imagine that your code met one of those guys. What would they say about it? If you work in a team or collaborate with people, you probably don’t have to imagine them. You’ve met them.

The_PEP8_guy – He has years of experience. He is used to seeing the code in a very particular way. He quotes the style guide during lunch. His fingers make the perfect line splitting and indentation without even his thoughts reaching the conscious state. He knows that lowercase_with_underscore is for variables, UPPER_CASE_NAMES are for constants and the CapitalizedWords are for classes. He will be lost if you do it in any different way. His expectations will not meet what you wrote, and he will not understand anything, because he will be too distracted by the messed up visual. Depending on the character he might start either crying or shouting. Read the style guide and follow it. You might be able to please this guy at least a little bit with the automatic tools like pylint.

The_ grieving _widow – Imagine that something happens to you. Let’s say, that you get hit by a bus[i]. You leave behind sadness and the_ grieving_widow to manage your code, your legacy. Will the future generations be able to make use of it or were you the only one who can understand anything you wrote? That is a bit of an extreme situation, ok. Alternatively, imagine, that you go for a 5-week vacation to a silent retreat with a strict no-phone policy (or that is what you tell your colleagues). Will they be able to carry on if they cannot ask you anything about the code? Review your code and the documentation from the perspective of the poor grieving_widow.

The_not_your_domain_guy – He is from the outside of the world you are currently in and he just does not understand your jargon. He doesn’t have to know that in data science a feature, a predictor and an x probably mean the same thing. SNR might shout signal-to-noise ratio at you, it will only snort at him. You might use abbreviations that are obvious to you but not to everyone. If you think that the majority of people can understand, and it helps with the code readability keep the abbreviations but just in case, document/comment them. There might be abbreviations specific to your company and, someone from the outside, a new guy, a consultant will not get them. Put yourself in the shoes of that guy and maybe make your code a bit more democratic wherever possible.

The_foreigner– You might be working in an environment, where every single person speaks the same language you speak, and it happens not to be English. So, you and your colleagues name variables and write the comments in your language. However, unless you work in a team with rules a strict as Athletic Bilbao, there might be a foreigner joining your team in the future. It is hard to argue that English is the lingua franca in programming (and in the world), these days. So, it might be worth putting yourself in the_foreigner’s shoes, while writing your code, to avoid a huge amount of work in the future, that the translation and explanation will require. And even if you are working on your own, you might want to make your code public one day and want as many people as possible to read it.

The_hurry_up_guy – we all know this guy. Sometimes he doesn’t have a body or a face, but we can feel his presence. You might want to write a perfect solution, comment it in the best possible way and maybe add a bit of glitter on top but sometimes you just need to give in and do it his way. And that’s ok too.



Article series: 5 Clean Coding Tips – 4. Stop commenting the obvious

This is the fourth of the article series “5 tips for clean coding” to follow as soon as you’ve made the first steps into your coding career, in this article series. Read the introduction here, to find out why it is important to write clean code if you missed it.

Everyone will tell you that you need to comment your code. You do it for yourself, for others, it might help you to put down a structure of your code before you get down to coding properly. Writing a lot of comments might give you a false sense of confidence, that you are doing a good job. While in reality, you are commenting your code a lot with obvious, redundant statements that are not bringing any value. The role of a comment it to explain, not to describe. You need to realize that any piece of comment has to add information to the code you already have, not to double it.

Keep in mind, you are not narrating the code, adding ‘subtitles’ to python’s performance. The comments are there to clarify what is not explicit in the code itself. Adding a comment saying what the line of code does is completely redundant most of the time:

A good rule of thumb would be: if it starts to sound like an instastory, rethink it. ‘So, I am having my breakfast, with a chai latte and my friend, the cat is here as well’. No.

It is also a good thing to learn to always update necessary comments before you modify the code. It is incredibly easy to modify a line of code, move on and forget the comment. There are people who claim that there are very few crimes in the world worse than comments that contradict the code itself.

Of course, there are situations, where you might be preparing a tutorial for others and you want to narrate what the code is doing. Then writing that load function will load the data is good. It does not have to be obvious for the listener. When teaching, repetitions, and overly explicit explanations are more than welcome. Always have in mind who your reader will be.

Article series: 5 Clean Coding Tips – 3. Take Advantage of the Formatting Tools.

This is the third of the article series “5 tips for clean coding” to follow as soon as you’ve made the first steps into your coding career, in this article series. Read the introduction here, to find out why it is important to write clean code if you missed it.

Unfortunately, no automatic formatting tool will correct the logic in your code, suggest meaningful names of your variables or comment the code for you. Yet. Gmail has lately started suggesting email titles based on email content. AI-powered variable naming can be next, who knows. Anyway, the visual level of the code is much easier to correct and there are tools that will do some of the code formatting on the visual level job for you. Some of them might be already existing in your IDE, you just need to look for them a bit, others need to be installed. One of the most popular formatting tools is pylint[i]. It is worth checking it out and learning to use it in an efficient way.

Beware that as convenient as it may seem to copy and paste your code into a quick online ‘beautifier’ it is not always a good idea. The online tools might store your code. If you are working on something that shouldn’t just freely float in the world wide web, stick to reliable tools like pylint, that will store the data within your working directory.

These tools can become very good friends of yours but also very annoying ones. They will not miss single whitespace and will not keep their mouth shut when your line length jumps from 79 to 80 characters. They will be shouting with an underscoring of some worrying color and/or exclamation marks. You will need to find your way to coexist and retain your sanity. It can be very distracting when you are in a working flow and warnings pop up all the time about formatting details that have nothing to do with what you are trying to solve. Sometimes, it might be better to turn those warnings off while you are in your most concentrated/creative phase of writing and turn them back on while the dust of your genius settles down a little bit. Usually the offer a lot of flexibility, regarding which warnings you want to be ignored and other features. The good thing is, they also teach you what are mistakes that you are making and after some time you will just stop making them in the first place.



Einführung in die Welt der Autoencoder

An wen ist der Artikel gerichtet?

In diesem Artikel wollen wir uns näher mit dem neuronalen Netz namens Autoencoder beschäftigen und wollen einen Einblick in die Grundprinzipien bekommen, die wir dann mit einem vereinfachten Programmierbeispiel festigen. Kenntnisse in Python, Tensorflow und neuronalen Netzen sind dabei sehr hilfreich.

Funktionsweise des Autoencoders

Ein Autoencoder ist ein neuronales Netz, welches versucht die Eingangsinformationen zu komprimieren und mit den reduzierten Informationen im Ausgang wieder korrekt nachzubilden.

Die Komprimierung und die Rekonstruktion der Eingangsinformationen laufen im Autoencoder nacheinander ab, weshalb wir das neuronale Netz auch in zwei Abschnitten betrachten können.




Der Encoder

Der Encoder oder auch Kodierer hat die Aufgabe, die Dimensionen der Eingangsinformationen zu reduzieren, man spricht auch von Dimensionsreduktion. Durch diese Reduktion werden die Informationen komprimiert und es werden nur die wichtigsten bzw. der Durchschnitt der Informationen weitergeleitet. Diese Methode hat wie viele andere Arten der Komprimierung auch einen Verlust.

In einem neuronalen Netz wird dies durch versteckte Schichten realisiert. Durch die Reduzierung von Knotenpunkten in den kommenden versteckten Schichten werden die Kodierung bewerkstelligt.

Der Decoder

Nachdem das Eingangssignal kodiert ist, kommt der Decoder bzw. Dekodierer zum Einsatz. Er hat die Aufgabe mit den komprimierten Informationen die ursprünglichen Daten zu rekonstruieren. Durch Fehlerrückführung werden die Gewichte des Netzes angepasst.

Ein bisschen Mathematik

Das Hauptziel des Autoencoders ist, dass das Ausgangssignal dem Eingangssignal gleicht, was bedeutet, dass wir eine Loss Funktion haben, die L(x , y) entspricht.

L(x, \hat{x})

Unser Eingang soll mit x gekennzeichnet werden. Unsere versteckte Schicht soll h sein. Damit hat unser Encoder folgenden Zusammenhang h = f(x).

Die Rekonstruktion im Decoder kann mit r = g(h) beschrieben werden. Bei unserem einfachen Autoencoder handelt es sich um ein Feed-Forward Netz ohne rückkoppelten Anteil und wird durch Backpropagation oder zu deutsch Fehlerrückführung optimiert.

Formelzeichen Bedeutung
\mathbf{x}, \hat{\mathbf{x}} Eingangs-, Ausgangssignal
\mathbf{W}, \hat{\mathbf{W}} Gewichte für En- und Decoder
\mathbf{B}, \hat{\mathbf{B}} Bias für En- und Decoder
\sigma, \hat{\sigma} Aktivierungsfunktion für En- und Decoder
L Verlustfunktion

Unsere versteckte Schicht soll mit \latex h gekennzeichnet werden. Damit besteht der Zusammenhang:

(1)   \begin{align*} \mathbf{h} &= f(\mathbf{x}) = \sigma(\mathbf{W}\mathbf{x} + \mathbf{B}) \\ \hat{\mathbf{x}} &= g(\mathbf{h}) = \hat{\sigma}(\hat{\mathbf{W}} \mathbf{h} + \hat{\mathbf{B}}) \\ \hat{\mathbf{x}} &= \hat{\sigma} \{ \hat{\mathbf{W}} \left[\sigma ( \mathbf{W}\mathbf{x} + \mathbf{B} )\right]  + \hat{\mathbf{B}} \}\\ \end{align*}

Für eine Optimierung mit der mittleren quadratischen Abweichung (MSE) könnte die Verlustfunktion wie folgt aussehen:

(2)   \begin{align*} L(\mathbf{x}, \hat{\mathbf{x}}) &= \mathbf{MSE}(\mathbf{x}, \hat{\mathbf{x}}) = \|  \mathbf{x} - \hat{\mathbf{x}} \| ^2 &=  \| \mathbf{x} - \hat{\sigma} \{ \hat{\mathbf{W}} \left[\sigma ( \mathbf{W}\mathbf{x} + \mathbf{B} )\right]  + \hat{\mathbf{B}} \} \| ^2 \end{align*}


Wir haben die Theorie und Mathematik eines Autoencoder in seiner Ursprungsform kennengelernt und wollen jetzt diese in einem (sehr) einfachen Beispiel anwenden, um zu schauen, ob der Autoencoder so funktioniert wie die Theorie es besagt.

Dazu nehmen wir einen One Hot (1 aus n) kodierten Datensatz, welcher die Zahlen von 0 bis 3 entspricht.

    \begin{align*} [1, 0, 0, 0] \ \widehat{=}  \ 0 \\ [0, 1, 0, 0] \ \widehat{=}  \ 1 \\ [0, 0, 1, 0] \ \widehat{=}  \ 2 \\ [0, 0, 0, 1] \ \widehat{=} \  3\\ \end{align*}

Diesen Datensatz könnte wie folgt kodiert werden:

    \begin{align*} [1, 0, 0, 0] \ \widehat{=}  \ 0 \ \widehat{=}  \ [0, 0] \\ [0, 1, 0, 0] \ \widehat{=}  \ 1 \ \widehat{=}  \  [0, 1] \\ [0, 0, 1, 0] \ \widehat{=}  \ 2 \ \widehat{=}  \ [1, 0] \\ [0, 0, 0, 1] \ \widehat{=} \  3 \ \widehat{=}  \ [1, 1] \\ \end{align*}

Damit hätten wir eine Dimensionsreduktion von vier auf zwei Merkmalen vorgenommen und genau diesen Vorgang wollen wir bei unserem Beispiel erreichen.

Programmierung eines einfachen Autoencoders


Typische Einsatzgebiete des Autoencoders sind neben der Dimensionsreduktion auch Bildaufarbeitung (z.B. Komprimierung, Entrauschen), Anomalie-Erkennung, Sequenz-to-Sequenz Analysen, etc.


Wir haben mit einem einfachen Beispiel die Funktionsweise des Autoencoders festigen können. Im nächsten Schritt wollen wir anhand realer Datensätze tiefer in gehen. Auch soll in kommenden Artikeln Variationen vom Autoencoder in verschiedenen Einsatzgebieten gezeigt werden.

Article series: 5 Clean Coding Tips – 2. Name Variables in a Meaningful Way

This is the second of the article series “5 tips for clean coding” to follow as soon as you’ve made the first steps into your coding career, in this article series. Read the introduction here, to find out why it is important to write clean code if you missed it.

When it comes to naming variables, there are a few official rules in the PEP8 style guide. A variable must start with an underscore or a letter and can be followed by a number of underscores or letters or digits. They cannot be reserved words: True, False, or, not, lambda etc. The preferred naming style is lowercase or lowercase_with_underscore. This all refers to variable names on a visual level. However, for readability purposes, the semantic level is as important, or maybe even more so. If it was for python, the variables could be named like this:

It wouldn’t make the slightest difference. But again, the code is not only for the interpreter to be read. It is for humans. Other people might need to look at your code to understand what you did, to be able to continue the work that you have already started. In any case, they need to be able to decipher what hides behind the variable names, that you’ve given the objects in your code. They will need to remember what they meant as they reappear in the code. And it might not be easy for them.

Remembering names is not an easy thing to do in all life situations. Let’s consider the following situation. You go to a party, there is a bunch of new people that you meet for the first time. They all have names and you try very hard to remember them all. Imagine how much easier would it be if you could call the new girl who came with John as the_girl_who_came_with_John. How much easier would it be to gossip to your friends about her? ‘Camilla is on the 5th glass of wine tonight, isn’t she?!.’ ‘Who are you talking about???’ Your friends might ask. ‘The_Girl_who_came_with_John.’ And they will all know. ‘It was nice to meet you girl_who_came_with_john, see you around.’ The good thing is that variables are not really like people. You can be a bit rude to them, they will not mind. You don’t have to force yourself or anyone else to remember an arbitrary name of a variable, that accidentally came to your mind in the moment of creation. Let your colleagues figure out what is what by a meaningful, straightforward description of it.

There is an important tradeoff to be aware of here. The lines of code should not exceed a certain length (79 characters, according to the PEP 8), therefore, it is recommended that you keep your names as short as possible. It is worth to give it a bit of thought about how you can name your variable in the most descriptive way, keeping it as short as possible. Keep in mind, that
the_blond_girl_in_a_dark_blue_dress_who_came_with_John_to_this_party might not be the best choice.

There are a few additional pieces of advice when it comes to naming your variables. First, try to always use pronounceable names. If you’ve ever been to an international party, you will know how much harder to remember is something that you cannot even repeat. Second, you probably have been taught over and over again that whenever you create a loop, you use i and j to denote the iterators.

It is probably engraved deep into the folds in your brain to write for i in…. You need to try and scrape it out of your cortex. Think about what the i stands for, what it really does and name it accordingly. Is i maybe the row_index? Is it a list_element?

Additionally, think about when to use a noun and where a verb. Variables usually are things and functions usually do things. So, it might be better to name functions with verb expressions, for example: get_id() or raise_to_power().

Moreover, it is a good practice to name constant numbers in the code. First, because when you name them you explain the meaning of the number. Second, because maybe one day you will have to change that number. If it appears multiple times in your code, you will avoid searching and changing it in every place. PEP 8 states that the constants should be named with UPPER_CASE_NAME. It is also quite common practice to explain the meaning of the constants with an inline comment at the end of the line, where the number appears. However, this approach will increase the line length and will require repeating the comment if the number appears more than one time in the code.

How Important is Customer Lifetime Value?

This is the third article of article series Getting started with the top eCommerce use cases.

Customer Lifetime Value

Many researches have shown that cost for acquiring a new customer is higher than the cost of retention of an existing customer which makes Customer Lifetime Value (CLV or LTV) one of the most important KPI’s. Marketing is about building a relationship with your customer and quality service matters a lot when it comes to customer retention. CLV is a metric which determines the total amount of money a customer is expected to spend in your business.

CLV allows marketing department of the company to understand how much money a customer is going  to spend over their  life cycle which helps them to determine on how much the company should spend to acquire each customer. Using CLV a company can better understand their customer and come up with different strategies either to retain their existing customers by sending them personalized email, discount voucher, provide them with better customer service etc. This will help a company to narrow their focus on acquiring similar customers by applying customer segmentation or look alike modeling.

One of the main focus of every company is Growth in this competitive eCommerce market today and price is not the only factor when a customer makes a decision. CLV is a metric which revolves around a customer and helps to retain valuable customers, increase revenue from less valuable customers and improve overall customer experience. Don’t look at CLV as just one metric but the journey to calculate this metric involves answering some really important questions which can be crucial for the business. Metrics and questions like:

  1. Number of sales
  2. Average number of times a customer buys
  3. Full Customer journey
  4. How many marketing channels were involved in one purchase?
  5. When the purchase was made?
  6. Customer retention rate
  7. Marketing cost
  8. Cost of acquiring a new customer

and so on are somehow associated with the calculation of CLV and exploring these questions can be quite insightful. Lately, a lot of companies have started to use this metric and shift their focuses in order to make more profit. Amazon is the perfect example for this, in 2013, a study by Consumers Intelligence Research Partners found out that prime members spends more than a non-prime member. So Amazon started focusing on Prime members to increase their profit over the past few years. The whole article can be found here.

How to calculate CLV?

There are several methods to calculate CLV and few of them are listed below.

Method 1: By calculating average revenue per customer


Figure 1: Using average revenue per customer


Let’s suppose three customers brought 745€ as profit to a company over a period of 2 months then:

CLV (2 months) = Total Profit over a period of time / Number of Customers over a period of time

CLV (2 months) = 745 / 3 = 248 €

Now the company can use this to calculate CLV for an year however, this is a naive approach and works only if the preferences of the customer are same for the same period of time. So let’s explore other approaches.

Method 2

This method requires to first calculate KPI’s like retention rate and discount rate.


CLV = Gross margin per lifespan ( Retention rate per month / 1 + Discount rate – Retention rate per month)


Retention rate = Customer at the end of the month – Customer during the month / Customer at the beginning of the month ) * 100

Method 3

This method will allow us to look at other metrics also and can be calculated in following steps:

  1. Calculate average number of transactions per month (T)
  2. Calculate average order value (OV)
  3. Calculate average gross margin (GM)
  4. Calculate customer lifespan in months (ALS)

After calculating these metrics CLV can be calculated as:


CLV = T*OV*GM*ALS / No. of Clients for the period


Transactions (T) = Total transactions / Period

Average order value (OV) = Total revenue / Total orders

Gross margin (GM) = (Total revenue – Cost of sales/ Total revenue) * 100 [but how you calculate cost of sales is debatable]

Customer lifespan in months (ALS) = 1 / Churn Rate %


CLV can be calculated using any of the above mentioned methods depending upon how robust your company wants the analysis to be. Some companies are also using Machine learning models to predict CLV, maybe not directly but they use ML models to predict customer churn rate, retention rate and other marketing KPI’s. Some companies take advantage of all the methods by taking an average at the end.

Matrix search: Finding the blocks of neighboring fields in a matrix with Python


In this article we will look at a solution in python to the following grid search task:

Find the biggest block of adjoining elements of the same kind and into how many blocks the matrix is divided. As adjoining blocks, we will consider field touching by the sides and not the corners.

Input data

For the ease of the explanation, we will be looking at a simple 3×4 matrix with elements of three different kinds, 0, 1 and 2 (see above). To test the code, we will simulate data to achieve different matrix sizes and a varied number of element types. It will also allow testing edge cases like, where all elements are the same or all elements are different.

To simulate some test data for later, we can use the numpy randint() method:

The code

How the code works

In summary, the algorithm loops through all fields of the matrix looking for unseen fields that will serve as a starting point for a local exploration of each block of color – the find_blocks() function. The local exploration is done by looking at the neighboring fields and if they are within the same kind, moving to them to explore further fields – the explore_block() function. The fields that have already been seen and counted are stored in the visited list.

find_blocks() function:

  1. Finds a starting point of a new block
  2. Runs a the explore_block() function for local exploration of the block
  3. Appends the size of the explored block
  4. Updates the list of visited points
  5. Returns the result, once all fields of the matrix have been visited.

explore_block() function:

  1. Takes the coordinates of the starting field for a new block and the list of visited points
  2. Creates the queue set with the starting point
  3. Sets the size of the current block (field_count) to 1
  4. Starts a while loop that is executed for as long as the queue is not empty
    1. Takes an element of the queue and uses its coordinates as the current location for further exploration
    2. Adds the current field to the visited list
    3. Explores the neighboring fields and if they belong to the same block, they are added to the queue
    4. The fields are taken off the queue for further exploration one by one until the queue is empty
  5. Returns the field_count of the explored block and the updated list of visited fields

Execute the function

The returned result is biggest block: 4, number of blocks: 4.

Run the test matrices:


The matrices for the article were visualized with the seaborn heatmap() method.