Singular Value Decomposition

Alexander Alexandrov
Saturday, March 12, 2016

SVD Overview

SVD Illustration

Visualization of the SVD of a two-dimensional, real shearing matrix M. The SVD decomposes M into three simple transformations.

  1. Rotation V*
  2. Scaling Σ
  3. Rotation U

Random Data

Let's generate some random data 40x10. Then add some pattern. So most of the rows from 5 up to 10 column are shifted by some value.

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Hierarchical Clustering

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Pattern injected into the random data is not evident.

Hierarchical Clustering + SVD

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First singular vectors have catched most of the variance and pattern has become evident.