Truncated SVD (2023)

Meaningful decompositions have got to be my favorite subject in linear algebra, and SVD is the king of these. Another location this pops up is "eigenfaces", an early form of compression (and correlation) of images of faces.

Years ago I did a write up of how the SVD relates to singularities of a robotic manipulator:

https://akintokinematics.com/notebooks/singular_value_decomp...

If you want a truncated SVD, there’s a decent chance you will be happy with a randomized SVD.

The paper “Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions” (Halko, Martinsson, and Tropp) is on arxiv. It is generally pretty accessible (although a little mathy), but also has great pseudocode for a number of common use-cases.

Some years ago, I was dabbling with PCA and was reading up a bit on the internet forums.

As soon as I saw that animation in the blog post, I knew that was from the user “amoeba” in stats stack exchange. Quite random, but turned out my memory was accurate: https://stats.stackexchange.com/a/140579