Zertifikatsstudium „Data Science and Big Data“

Jetzt bewerben für das Zertifikatsstudium „Data Science and Big Data“ an der Technischen Universität Dortmund 

Im Februar startet das erfolgreiche berufsbegleitende Zertifikatsstudium „Data Science and Big Data“ an der Technischen Universität Dortmund zum fünften Mal.
Renommierte Wissenschaftlerinnen und Wissenschaftlern vermitteln Ihnen die neuesten datenwissenschaftlichen Erkenntnisse und zeigen, wie dieses Wissen praxisnah im eigenen Big-Data Projekt umgesetzt werden kann.
Von der Analyse über das Management bis zur zielgerichteten Darstellung der Ergebnisse lernen Sie dabei Methoden der Disziplinen Statistik, Informatik und Journalistik kennen.

Das Zertifikatsstudium richtet sich an alle Personen, die über einen natur-  oder ingenieurwissenschaftlich/ statistische Studienhintergrund verfügen oder aufgrund ihrer mehrjährigen Berufserfahrung mit Fragestellungen zum Thema Datenanalyse vertraut sind.

Mögliche Berufsgruppen sind:

  • Data Analyst
  • Consultant/ Unternehmensberater
  • Business Analyst
  • Software-Entwickler

Das weiterbildende Studium umfasst 10 Veranstaltungstage über eine Dauer von 10 Monaten (Kursabschluss: ca. November 2021). Die Kosten betragen 6.900 € (zahlbar in 3 Raten). Bewerbungsschluss ist der 4. Dezember 2020. Weitere Informationen und Hinweise zur Anmeldung finden Sie unter: http://www.zhb.tu-dortmund.de/datascience

Bei Fragen können Sie sich gerne an den zuständigen Bildungsreferenten Daniel Neubauer wenden: daniel.neubauer@tu-dortmund.de oder 0231/755-6632.

Hinweis:

Ergänzend bieten wir einen R-Basis- und R-Vertiefungskurs an. Wenn Sie sich für das Zertifikatsstudium bewerben und für einen Kurs bzw. beide Kurse, erhalten Sie pro R-Kurs einen Rabatt von 250 €. Weitere Informationen finden Sie unter: https://dortmunder-r-kurse.de/kursangebot/

Wir behalten uns vor, das weiterbildende Studium je nach Entwicklungen der Corona-Pandemie als Online-Kurs durchzuführen

Online-Kurse zur Statistiksoftware R

R – ein unverzichtbares Werkzeug für Data Scientists. Lassen Sie sich auf den neusten Stand in der Open Source Statistiksoftware R aus der modernen Datenanalyse bringen.

Zielgruppe unserer Fortbildungen sind nicht nur Statistikerinnen und Statistiker, sondern auch Anwenderinnen und Anwender jeder Fachrichtung aus Industrie und Forschungseinrichtungen, die mit R ihre Daten effektiv analysieren möchten. Sie erwerben durch die Teilnahme Qualifikationen zur selbstständigen Analyse Ihrer eigenen Daten sowie Schlüsselkompetenzen im Umgang mit Big Data. Dafür bieten wir den R-Basiskurs und den R-Vertiefungskurs im November als Online-Veranstaltungen an.

Termine:

R-Basiskurs:  4. – 6. November (jeweils 9:00 – 13:00 Uhr) – Der Kurs richtet sich an Anfänger ohne Erfahrungen mit R sowie an Nutzer mit rudimentären oder eingerosteten R-Wissen. Entsprechend sind keine Vorkenntnisse über R notwendig. Zusätzlich zu den 3 Online-Tagen erhalten die Teilnehmenden Zugang zu 1,5 Stunden Videomaterial.

R-Vertiefungskurs: 17. – 20. November (jeweils 9:00 – 13:00 Uhr) – Der Vertiefungskurs richtet sich an fortgeschrittene R Nutzer sowie Absolventen des Basiskurses. Er ist ideal für Mitarbeiter aus Unternehmen, die ihre Analysen effizient mit R durchführen möchten.

Weitere Informationen zu den Inhalten und zur Anmeldung finden Sie unter: https://dortmunder-r-kurse.de/kursangebot/

Bei Fragen können Sie sich gerne an den zuständigen Bildungsreferenten Daniel Neubauer wenden: daniel.neubauer@tu-dortmund.de oder 0231/755-6632.

Die führende Fachkonferenz für Machine Learning

Seien Sie dabei, wenn sich am 16. bis 17. November 2020 Anwender, Entscheider und Experten von Predictive Analytics und Machine Learning in Berlin treffen, um sich über die neuesten Erkenntnisse und Fortschritte zu informieren.

Vom Data Lab zu Data Ops

Die Zeit des Experimentierens ist vorbei. Unternehmen erwarten, dass ihre Data Labs das liefern, was ihnen der KI-Hype versprochen hat: mehr Kunden, höhere Umsätze, effizientere Prozesse und vieles mehr. Doch viele Projekte stecken in der PoC-Falle fest: sie funktionieren als Prototyp – aber nicht im realen Betrieb. Aus der Data Science muss eine Data Industry werden: wir müssen selbst lernen, effizienter und effektiver zu werden – und zwar darin die wirklich kritischen Herausforderungen im Unternehmen zu identifizieren, die passenden Lösungsideen zu entwickeln, die Ideen schnell in funktionierende Modelle zu übersetzen, aus den Modellen skalierbare Lösungen zu entwickeln und schließlich dafür zu sorgen, dass diese Lösungen von den Fachbereichen gewinnbringend genutzt werden. Dies verlangt ein neues Selbstverständnis: wir sind nicht das Experimentierlabor der Unternehmen – sondern deren Maschinenraum: Data Ops statt Data Labs.

Predictive Analytics für die Finanz- & Versicherungsbranche

Auf der diesjährigen Konferenz starten wir ein neues Format: eine Vortragsreihe für angewandte Predictive Analytics in der Finanz- und Versicherungsbranche. Dieser eintägige Track zeigt Ihnen die wichtigsten Anwendungsfälle von Machine & Deep Learning für Banken, Versicherungen, Investoren und Fonds auf, indem er Ihnen reale Projekte von bekannten Unternehmen vorstellt. Sie erfahren, wie Sie Datenschutz- und Regulierungsprobleme lösen, Ihre Datenbestände mit Data Governance und Datenstrategie verwalten und verwerten sowie mit Data Science & Analytics erfolgreiche Datenprodukte entwickeln und betreiben.

Lassen Sie sich wertvolle Tipps und Tricks von erfahrenen Experten aus namhaften Unternehmen nicht entgehen!

Mit dem Code “DATASCIENCEPAW” bekommen Sie zusätzliche 15 Prozent Rabatt auf Ihre Buchung.

Connections Between Data Science & Finance

Image Source: pixabay.com

The world of finance is changing at an unprecedented rate. Data science has completely altered the face of traditional finance management. Though data has long been a critical component to finances, the introduction of big data and artificial intelligence have created new tools that are strengthening the predictive ability of many financial institutions.

These changes have led to a rapid increase in the need for financial professionals with data science skills. Nearly every sector in finances is converting to greater use of data science and management from the stock market and retirement accounts to credit score calculation. A greater understanding of the interplay between data and finance is a key skill gap.

Likewise, they have opened many doors for those that are interested in analyzing their personal finances. More and more people are taking their finances into their own hands and using the data tools available to make the best decisions for them. In today’s world, the sky’s the limit for financial analysis and management!

The Rise of the Financial Analyst

Financial analysts are the professionals who are responsible for the general management of money and investments both in an industrial and personal finance realm. Typically a financial analyst will spend time reviewing and understanding the overall stock portfolio and financial standing of a client including:

  • Stocks
  • Bonds
  • Retirement accounts
  • Financial history
  • Current financial statements and reports
  • Overarching business and industry trends

From there, the analyst will provide a recommendation with data-backed findings to the client on how they should manage their finances going into the future.

As you can imagine, with all of this data to analyze, the need for financial analysts to have a background or understanding of data science has never been higher! Finance jobs requiring skills such as artificial intelligence and big data increased by over 60% in the last year. Though these new jobs are typically rooted in computer science and data analytics, most professionals still need a background in financial management as well.

The unique skills required for a position like this means there is a huge (and growing) skills gap in the financial sector. Those professionals that are qualified and able to rise to fill the need are seeing substantial pay increases and hundreds of job opportunities across the nation and the globe.

A Credit Score Example

But where does all of this data science and professional financial account management come back to impact the everyday person making financial decisions? Surprisingly, pretty much in every facet of their lives. From things like retirement accounts to faster response times in financial analysis to credit scores — data science in the financial industry is like a cloaked hand pulling the strings in the background.

Take, for example, your credit score. It is one of the single most important numbers in your life, for better or worse. A high credit score can open all sorts of financial doors and get you better interest rates on the things you need loans for. A bad score can limit the amount lenders willing to qualify you for a loan and increase the interest rate substantially, meaning you will end up paying far more money in the end.

Your credit score is calculated by several things — though we understand the basic outline of what goes into the formula, the finer points are somewhat of a mystery. We know the big factors are:

  • Personal financial history
  • Debit-credit ratio
  • Length of credit history
  • Number of new credit hits or applications

All of this data and number crunching can have a real impact on your life, just one example of how data in the financial world is relevant.

Using Data Science in Personal Finance

Given all this information, you might be thinking to yourself that what you really need is a certificate in data science. Certainly, that will open a number of career doors for you in a multitude of realms, not just the finance industry. Data science is quickly becoming a cornerstone of how most major industries do business.

However, that isn’t necessarily required to get ahead on managing your personal finances. Just a little information about programs such as Excel can get you a long way. Some may even argue that Excel is the original online data management tool as it can be used to do things like:

  • Create schedules
  • Manage budgets
  • Visualize data in charts and graphs
  • Track revenues and expenses
  • Conditionally format information
  • Manage inventory
  • Identify trends in large data sets

There are even several tools and guides out there that will help you to get started!

***

Data analysis and management is here to stay, especially when it comes to the financial industry. The tools are likely to continue to become more important and skills in their use will increase in value. Though there are a lot of professional skills using big data to manage finances, there are still a lot of tools out there that are making it easier than ever to glean insights into your personal finances and make informed financial decisions.

K Nearest Neighbour For Supervised Learning

K-Nearest Neighbour (KNN) Algorithms is an easy-to-implement & advanced level supervised machine learning algorithm used for both – classification as well as regression problems. However, you can see a wide of its applications in classification problems across various industries.

If you’ve been shopping a lot in e-commerce sites like Amazon, Flipkart, Myntra, or love watching web series over Netflix and Amazon Prime, one common thing you’ve always noticed, and that is recommendations.

Are you wondering how they recommend you following your choice? They use KNN Supervised Learning to find out what you may need the next when you’re buying and recommend you with a few more products.

Imagine you’re looking for an iPhone to purchase. When you scroll down a little, you see some iPhone cases, tempered glasses – saying, “People who purchased an iPhone have also purchased these items. The same applies to Netflix and Amazon Prime. When you finished a show or a series, they give you recommendations of the same genre. And do it all using KNN supervised learning and classify the items for the best user experience.

Advantages Of KNN

  • Quickest Calculation Time
  • Simple Algorithms
  • High Accuracy
  • Versatile – best use for Regression and Classification.
  • Doesn’t make any assumptions about data.

Where KNN Are Mostly Used

  • Simple Recommendation Models
  • Image Recognition Technology
  • Decision-Making Models
  • Calculating Credit Rating

Choosing The Right Value For K

 To choose the right value of K, you have to run KNN algorithms several times with different values of K and select the value of K, which reduces the number of errors you’ve come across and come out as the most stable value for K.

Your Step-By-Step Guide For Choosing The Value Of K

  • As you decrease the value of K to 1 (K = 1), you’ll reach a query point, where you get to see many elements from class A (-) and class B (+) where (-) is the only nearest neighbor. Reasonably, you would think about the query point to be most likely the red one. As K =1, which has a blue color, KNN incorrectly predicts the wrong color blue.
  • As you increase the value of K to 2 (K=2), you get to see two elements, (-) and (+) are the only nearest neighbor. As you have two values, which are of Class A and Class B, KNN incorrectly predicts the wrong values (Blue and Red).
  • As you increase the value of K to 3 (K=3), you get to see three elements (-) and (+), (+) are the only nearest neighbor. And this time, you got three values, one from blue and two from red. As your assumption is red, KNN correctly predicts the right value (Blue and Red, Red). Your answer is more stable this time compared to previous ones.

Conclusion

KNN works by finding the nearest distance between a query and all the elements in the database. By choosing the value for K, we get the closest to the query. And then, KNN algorithms look for the most frequent labels in classification and averages of labels in regression.

Spiky cubes, Pac-Man walking, empty M&M’s chocolate: curse of dimensionality

This is the first article of the article series Illustrative introductions on dimension reduction.

“Curse of dimensionality” means the difficulties of machine learning which arise when the dimension of data is higher. In short if the data have too many features like “weight,” “height,” “width,” “strength,” “temperature”…., that can undermine the performances of machine learning. The fact might be contrary to your image which you get from the terms “big” data or “deep” learning. You might assume that the more hints you have, the better the performances of machine learning are. There are some reasons for curse of dimensionality, and in this article I am going to introduce two major reasons below.

  1. High dimensional data usually have rich expressiveness, but usually training data are too poor for that.
  2. The behaviors of data points in high dimensional space are totally different from our common sense.

Through these topics, you will see that you always have to think about which features to use considering the number of data points.

*From now on I am going to talk about only Euclidean distance. If you are not sure what Euclidean distance means, please just keep it in mind that it is the type of distance most people wold have learnt in normal compulsory education.

1. Number of samples and degree of dimension

The most straightforward demerit of adding many features, or increasing dimensions of data, is the growth of computational costs. More importantly, however, you always have to think about the degree of dimensions in relation of the number of data points you have. Let me take a simple example in a book “Pattern Recognition and Machine Learning” by C. M. Bishop (PRML). This is an example of measurements of a pipeline. The figure below shows a comparison plot of 3 classes (red, green and blue), with parameter x_7 plotted against parameter x_6 out of 12 parameters.

* The meaning of data is not important in this article. If you are interested please refer to the appendix in PRML.

Assume that we are interested in classifying the cross in black into one of the three classes. One of the most naive ideas of this classification is dividing the graph into grids and labeling each grid depending on the number of samples in the classes (which are colored at the right side of the figure). And you can classify the test sample, the cross in black, into the class of the grid where the test sample is in. Thereby the cross is classified to the class in red.

Source: C.M. Bishop, “Pattern Recognition and Machine Learning,” (2006), Springer, pp. 34-35

As I mentioned in the figure above, we used only two features out of 12 features in total. When the total number of data points is fixed and you add remaining ten axes/features one after another, what would happen? Let’s see what “adding axes/features” means. If you are talking about 1, 2, or 3 dimensional grids, you can visualize them. And as you can see from the figure below, if you make each 10^1, 10^2, 100^3 grids respectively in 1, 2, 3 dimensional spaces, the number of the small regions in the grids are respectively 10, 100, 1000. Even though you cannot visualize it anymore, you can make grids for more than 3 dimensional data. If you continue increasing the degree of dimension, the number of grids increases exponentially, and that can soon surpass the number of training data points. That means there would be a lot of empty spaces in such high dimensional grids. And the classifying method above: coloring each grid and classifying unknown samples depending on the colors of the grids, does not work out anymore because there would be a lot of empty grids.

* If you are still puzzled by the idea of “more than 3 dimensional grids,” you should not think too much about that now. It is enough if you can get some understandings on high dimensional data after reading the whole article of this.

Source: Goodfellow and Yoshua Bengio and Aaron Courville, Deep Learning, (2016), MIT Press, p. 153

I said the method above is the most naive way, but other classical classification methods , for example k-nearest neighbors algorithm, are more or less base on a similar idea. Many of classical machine learning algorithms are based on the idea of smoothness prior, or local constancy prior. In short in classical ways, you  do not expect data to change so much in a small region, so you can expect unknown samples to be similar to data in vicinity. But that soon turns out to be problematic when the dimension of data is bigger because training data would be sparse because the area of multidimensional space grows exponentially as I mentioned above. And sometimes you would not be able to find training data around test data. Plus, in high dimensional data, you cannot treat distance in the same as you do in lower dimensional space. The ideas of “close,” “nearby,” or “vicinity” get more obscure in high dimensional data. That point is related to the next topic: the intuition have cultivated in normal life is not applicable to higher dimensional data.

2. Bizarre characteristics of high dimensional data

We form our sense of recognition in 3-dimensional ways in our normal life. Even though we can visualize only 1, 2, or 3 dimensional data, we can actually generalize the ideas in 1, 2, or 3 dimensional ideas to higher dimensions. For example 4 dimensional cubes, 100 dimensional spheres, or orthogonality in 255 dimensional space. Again, you cannot exactly visualize those ideas, and for many people, such high dimensional phenomenon are just imaginary matters on blackboards. Those high dimensional ideas are designed to retain some conditions just as well as 1, 2, or 3 dimensional space. Let’s take an example of spheres in several dimensional spaces. General spheres in any D-dimensional space can be defined as a set of any \boldsymbol{x}, such that |\boldsymbol{x} - \boldsymbol{c}| = r, where \boldsymbol{c} is the center point and r is length of radius. When \boldsymbol{x} is 2-dimensional, the spheres are called “circles.” When \boldsymbol{x} is 3-dimensional, the spheres are called “spheres” in our normal life, unless it is used in a conversation in a college cafeteria, by some students in mathematics department. And when \boldsymbol{x} is D-dimensional, they are called D-ball, and again, this is just a imaginary phenomenon on blackboard.

* Vectors and points are almost the same because all the vectors are denoted as “arrows” from the an origin point to sample data points.  The only difference is that when you use vectors, you have to consider their directions.

* “D-ball” is usually called “n-ball,” and in such context it is a sphere in a n-dimensional space. But please let me use the term “D-ball” in this article.

Not only spheres, but only many other ideas have been generalized to D-dimensional space, and many of them are indispensable also for data science. But there is one severe problem: the behaviors of data in high dimensional field is quite different from those in two or three dimensional space. To be concrete, in high dimensional field, cubes are spiky, you have to move like Pac-Man, and M & M’s Chocolate looks empty inside but tastes normal.

2.1: spiky cubes
Let’s take a look at an elementary-school-level example of geometry first. Assume that you have several unit squares or unit cubes like below. In each of them a circle or sphere with diameter 1 is inscribed. The length of a diagonal line in each square is \sqrt{2}, and that in each cube is \sqrt{3}.

If you stack the squares or cubes as below, what are the length of diameters of the blue circle or sphere, circumscribing all the 4 orange circles or the 8 orange spheres?

The answers are, the diameter of the blue circle is \sqrt{2} - 1, and the diameter of the blue sphere is \sqrt{3} - 1.

Next let’s think about the same situation in higher dimensional space. Assume that there are some unit D-dimensional hypercubes stacked, in each of which a D-ball with diameter 1 is inscribed, touching all the surfaces inside. Then what is the length of the diameter of  a D-ball circumscribing all the unit D-ball in the hypercubes ? Given the results above, it ca be predicted that its diameter is \sqrt{D}  -1. If that is true, there is one strange point: \sqrt{D} - 1 can soon surpass 2: that means in the chart above the blue sphere will stick out of the stacked cubes. That sounds like a paradox, but with one hypothesis, the phenomenon makes sense: cubes become more spiky as the degree of dimension grows. This hypothesis is a natural deduction because diagonal lines of hyper cubes get longer, and the the center of each surface of hypercubes still touches the unit D-ball with diameter 1, inscribing inscribing inside each unit hypercube.

If you stack 4 hypercubes, the blue sphere circumscribing them will not stick out of the stacked hypercubes anymore like the figure below.

*Of course you cannot visualize what is going on in D-dimensional space, so the figure below is just a pseudo simulation of D-dimensional space in our 3-dimensional sense. I guess you have to stack more than four hyper cubes in higher dimensional data, but you cannot easily imagine what will go on in such space anymore.

 

*You can confirm the fact that hypercube gets more spiky as the degree of dimension growth, by comparing the volume of the hypercube and the volume of the D-ball inscribed inside the hypercube. Thereby you can prove that the volume of hypercube concentrates on the corners of the hypercube. Plus, as I mentioned the longest diagonal distance of hypercube gets longer as dimension degree increases. That is why hypercube is said to be spiky. For mathematical proof, please check the Exercise 1.19 of PRML.

2.2: Pac-Man walking

Next intriguing phenomenon in high dimensional field is that most of pairs of vectors in high dimensional space are orthogonal. In other words, if you select two random vectors in high dimensional space, the angle between them are mostly close to 90^\circ. Let’s see the general meaning of angle between two vectors in any dimensional spaces. Assume that the angle between two vectors \boldsymbol{u}, and \boldsymbol{v} is \theta, then cos\theta is calculated as cos\theta = \frac{<\boldsymbol{u}, \boldsymbol{v}>}{|\boldsymbol{u}||\boldsymbol{v}|}. In 1, 2, or 3 dimensional space, you can actually see the angle, but again you can define higher dimensional angle, which you cannot visualize anymore. And angles are sometimes used as similarity of two vectors.

* <\boldsymbol{u}, \boldsymbol{v}> is the inner product of \boldsymbol{u}, and \boldsymbol{v}.

Assume that you generate a pair of two points inside a D-dimensional unit sphere and make two vectors \boldsymbol{u}, and \boldsymbol{v} by connecting the origin point and those two points respectively. When D is 2, I mean spheres are circles in this case, any \theta are equally generated as in the chart below. The fact might be the same as your intuition.   How about in 3-dimensional space? In fact the distribution of \theta is not uniform. \theta = 90^\circ is the most likely to be generated. As I explain in the figure below, if you compare the area of cross section of a hemisphere and the area of a cone whose vertex is the center point of the sphere, you can see why.

I generated 10000 random pairs of points in side a D-dimensional unit sphere, and calculated the angle between them. In other words I just randomly generated two D-dimensional vectors \boldsymbol{u} and \boldsymbol{v}, whose elements are randomly generated values between -1 and 1, and calculated the angle between them, repeating this process 10000 times. The chart below are the histograms of angle between pairs of generated vectors in respectively 2, 3, 50, and 100 dimensional space.

As I explained above, in 2-dimensional space, the distribution of \theta is almost uniform. However the distribution concentrates a little around 90^\circ in 3-dimensional space. You can see that the bigger the degree of dimension is, the more the angles of generated vectors concentrate around 90^\circ. That means most pairs of vectors in high dimensional space are close to orthogonal. Movements are also sequence of vectors, so when most pairs of movement vectors are orthogonal, that means you can only move like Pac-Man in such space.

Source: https://edition.cnn.com/style/article/pac-man-40-anniversary-history/index.html

* Of course I am talking about arcade Mac-Man game. Not Pac-Man in Super Smash Bros.  Retro RPG video games might have more similar playability, but in high dimensional space it is also difficult to turn back. At any rate, I think you have understood it is even difficult to move smoothly in high dimensional space, just like the first notorious Resident Evil on the first PS console also had terrible playability .

2.3: empty M & M’s chocolate

Let’s think about the proportion of the volume of the outermost \epsilon surface of general spheres with radius r. First, in 2 two dimensional space, spheres are circles. The area of the brown part of the circle below is \pi r^2. In order calculate the are of \epsilon \cdot r thick surface of the circle, you have only to subtract the area of \pi \{ (1 - \epsilon)\cdot r\} ^2. When \epsilon = 0.01, the area of outer most surface is \pi r^2 - \pi (0.99\cdot r)^2, and its proportion to the area of the whole circle is \frac{\pi r^2 - \pi (0.99\cdot r)^2}{\pi r^2} = 0.0199.

In case of 3-dimensional space, the value of a sphere with radius r is \frac{4}{3} \pi r^2, so the proportion of the \epsilon surface is calculated in the same way: \frac{\frac{4}{3} \pi r^3 -\frac{4}{3} \pi (0.99\cdot r)^2}{\frac{4}{3}\pi r^2} = 0.0297. Compared to the case in 2 dimensional space, the proportion is a little bigger.

How about in D-dimensional space? We have seen that even in  D-dimensional space the surface of a sphere, I mean D-ball, can be defined as a set of any points whose distance from the center point is all r. And it is known that the volume of D-ball is defined as below.

\Gamma () is called gamma function, but in this article it is not so important. The most important point now is, if you discuss any D-ball, their volume only depends on their radius r. That meas the proportion of outer \epsilon surface of D-ball is calculated as \frac{\pi r^2 - \pi \{ (1 - \epsilon)\cdot r\} ^2}{\pi r^2}. When \epsilon is 0.01, the proportion of the 1% surface of D-ball changes like in the chart below.

* And of course when D is 2,  \frac{\pi ^{(\frac{D}{2})}}{\Gamma (\frac{D}{2} + 1)} = \pi, and when D is 3 ,  \frac{\pi ^{(\frac{D}{2})}}{\Gamma (\frac{D}{2} + 1)} = \frac{4}{3} \pi

You can see that when D is over 400, around 90% of volume is concentrated in the very thin 1% surface of D-ball. That is why, in high dimensional space, M & M’s chocolate look empty but tastes normal: all the chocolate are concentrated beneath the sugar coating.

More interestingly, even if you choose any points as a central point of a sphere with radius r, the other points are squashed to the surface of the sphere, even if all the data points are uniformly distributed. This situation is problematic for classical machine learning algorithms, which are often based on the Euclidean distances between pairs of two sample data points: if you go from the central point to another sample point, the possibility of finding the point within (1 - \epsilon)\cdot r radius of the center is almost zero. But if you reach the outermost \epsilon part of the surface of the sphere, most data points are there. However, for one of the data points in the surface, any other data points are distant in the same way.

Inside M & M’s chocolate is a mysterious world.

Source: https://hipwallpaper.com/mms-wallpapers/

You have seen that using high dimensional data can be problematic in many ways. Data science and machine learning are largely based on one idea: you can find a lower dimensional meaningful and easier structure in data. In the next articles I am going to introduce some famous dimension reduction algorithms. And hopefully I would like to give some deeper insights in to these algorithms, in straightforward ways.

* I could not explain the relationships of variance and bias of data. This is also a very important factor when you think about dimensionality of data. I hope I can write about this topic someday. You can also look it up if you are interested.

* 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.

Illustrative introductions on dimension reduction

“What is your image on dimensions?”

….That might be a cheesy question to ask to reader of Data Science Blog, but most people, with no scientific background, would answer “One dimension is a line, and two dimension is a plain, and we live in three-dimensional world.” After that if you ask “How about the fourth dimension?” many people would answer “Time?”

You can find books or writings about dimensions in various field. And you can use the word “dimension” in normal conversations, in many contexts.

*In Japanese, if you say “He likes two dimension.” that means he prefers anime characters to real women, as is often the case with Japanese computer science students.

The meanings of “dimensions” depend on the context, but in data science dimension is usually the number of rows of your Excel data.

When you study data science or machine learning, usually you should start with understanding the algorithms with 2 or 3 dimensional data, and you can apply those ideas to any D dimensional data. But of course you cannot visualize D dimensional data anymore, and you always have to be careful of what happens if you expand degree of dimension.

Conversely it is also important to reduce dimension to understand abstract high dimensional stuff in 2 or 3 dimensional space, which are close to our everyday sense. That means dimension reduction is one powerful way of data visualization.

In this blog series I am going to explain meanings of dimension itself in machine learning context and algorithms for dimension reductions, such as PCA, LDA, and t-SNE, with 2 or 3 dimensional visible data. Along with that, I am going to delve into the meaning of calculations so that you can understand them in more like everyday-life sense.

This article series is going to be roughly divided into the contents below.

  1. Curse of Dimensionality
  2. PCA, LDA (to be published soon)
  3. Rethinking eigen vectors (to be published soon)
  4. KL expansion and subspace method (to be published soon)
  5. Autoencoder as dimension reduction (to be published soon)
  6. t-SNE (to be published soon)

I hope you could see that reducing dimension is one of the fundamental approaches in data science or machine learning.

Grenzenloses Machine Learning und Digital Analytics Wissen auf der Data Driven Business Berlin 2020

2 Konferenzen, 2 Tage & unbegrenztes Networking unter einem Dach

Vom 16. – 17. November 2020 trifft sich die Machine Learning & Digital Analytics-Szene in Berlin, um die neuesten und wichtigsten Entwicklungen zu diskutieren.

Sichern Sie sich grenzenloses Machine Learning und Digital Analytics Wissen auf der Data Driven Business – zwei Konferenzen, gemeinsam oder separat buchbar. In hochkarätigen Sessions werden Inhalte vermittelt, die besonders fortgeschrittene Nutzer ansprechen, aber auch für Anfänger einen guten Einstieg bieten.

Lassen Sie sich Case Studies, Deep Dives und Keynotes von erfahrenen Experten aus namhaften Unternehmen nicht entgehen.

Zwei Tage lang dreht sich alles um die Themen Digital Analytics und den Einsatz von Machine Learning. Hier gibt es umsetzbare Inhalte statt Buzzwords, 100%ige Tool- & Service-Neutralität sowie die besten Networkingmöglichkeiten mit nationalen und internationalen Experten. Inspiration bei den Keynotes, umsetzbare Taktiken zu spezifischen Themen in den Sessions oder Deep Dives mit hochtechnischem Fokus – Sie haben die Wahl und stellen so aus unterschiedlichen Tracks Ihr eigenes, für Sie relevantes Programm zusammen. Holen Sie das bestmögliche aus Ihrer Zeit auf der Data Driven Business in Berlin!

Zwei Konferenzen unter einem Dach

– gemeinsam oder separat buchbar:

  1. Marketing Analytics Summit
    ist DIE Konferenz für Digital Analysts. Optimieren Sie den Einsatz von Daten für Ihr Marketing! Das Konferenzformat besteht aus Vorträgen, Teilnehmerdiskussionen und -aktionen. Hier treffen Sie Kollegen und Experten, die den Unterschied machen.
  2. Predictive Analytics World
    ist die führende anbieterunabhängige Fachkonferenz für Machine Learning. Anwender, Entscheider und Experten von Predictive Analytics und Machine Learning treffen sich hier, um sich über die neuesten Erkenntnisse und Fortschritte zu informieren.

Mit dem Code „DATASCIENCEPAW“ bekommen Sie zusätzliche 15 Prozent Rabatt auf Ihre Buchung.