Tag Archives: 3D

Illustration of principal component analysis (PCA)

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Why (a) PCA?

3d

3D model of ellipsoid and its three principal components

A principal component analysis is a way to reduce dimensionality of a data set consisting of numeric vectors to a lower dimensionality. Then it is possible to visualize the data set in three or less dimensions. Have a look at this use case. I’ll try to explain the motivation using a simple example.

Think of a very flat square (e.g. 1x1x.05) in a three dimensional space. What you see of this cuboid when looking at it from a specific angle while assuming perspectivic visual indicators away is basically a 2 dimensional projection of it. From one angle it looks like a rhombus, looking straight from the edge side all you see is a line-like shape. So obviously the representation offering the most information about this cuboid is the one you see when looking at it perpendicular to the main surface. Continue reading →

Visualization of voting behaviour in the 17th German Bundestag

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votings

Click to get to the interactive 3D scatter plot with labels (PCA plot)

(Attention: The calculations and analysis are not biased by my political views – but the interpretation of the results might be and their verbal formulation certainly is … ;)

About a week ago I came across an article titled “How divided is the Senate?” by Vik Paruchuri where he uses a method called principal component analysis (PCA) to visualize the closeness of votings given by senators of the 113th Congress of the USA. I immediately fell in love with the idea behind this article as well as the method applied – which was a great opportunity to revise some statistics and alebra basics. And because (pretending) transparency is a major foundation of a modern democracy, full detailed word by word protocols of every meeting of the Bundestag are published as PDFs and text files on their website. So I downloaded all those protocols for the 17th Bundestag, extracted the votings and loaded the votes into a data frame. That was quite a drag because judging from typos (Sevim Dadelen, Sevim Dagelen, Sevim Dagdelen, …), different name versions (Erwin Josef Rüddel, Erwin Rüddel) and line breaks within the longer names like Dr. Karl-Theodor Freiherr von und zu Guttenberg (his title is gone, so the name became a tad handier by now) those text files where manually sanitized PDF convertions of live transcripts. I’ll spare you the details – but getting the data finally right took quite some effort.

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