Isometry pursuit

Samson J Koelle

Keywords: Manifold learning, interpretability, sparse coding

TL;DR: Isometry pursuit is a convex algorithm for identifying orthonormal column-submatrices of wide matrices.

Abstract:

Isometry pursuit is a convex algorithm for identifying orthonormal column-submatrices of wide matrices.
It consists of a vector normalization followed by multitask basis pursuit.
Applied to Jacobians of putative coordinate functions, it helps identify locally isometric embeddings from within interpretable dictionaries.
We provide theoretical and experimental results justifying this method, including a proof with realistic assumptions that such isometric submatrices, should they exist, are contained within the obtained support.
For problems involving coordinate selection and diversification, it offers a synergistic alternative to greedy and brute force search.

Primary Area: Optimization (e.g., convex and non-convex, stochastic, robust)

Submission Number: 18296