Separability, SVD and low-rank approximation of 2D image processing filters

Here’s a relevant recent lecture from Alex Townsend, as part of Gil Strang’s 18.065 course, “Rapidly Decreasing Singular Values” https://www.youtube.com/watch?v=9BYsNpTCZGg

Good stuff. A lot of clustering methods can be viewed as matrix factorization (see, e.g., https://arxiv.org/abs/1512.07548) so it would be interesting to see if you could spend more computation on the creating the low dimensional approximation to achieve a better result. E.g. perhaps optimizing the absolute error (L1 norm) would be better than the squared error (L2 norm)?

Very nice writeup. It's fun to see linear algebra out in the wild.