Isometry pursuit

TL;DR

Isometry pursuit is a convex algorithm that identifies orthonormal submatrices, aiding in discovering isometric embeddings within interpretable dictionaries, with theoretical and experimental validation.

Contribution

The paper introduces a novel convex normalization and pursuit method for identifying orthonormal submatrices, providing a new approach for coordinate selection tasks.

Findings

The method effectively identifies isometric embeddings from Jacobians.

It outperforms greedy and brute-force methods in coordinate selection.

Theoretical analysis supports its convergence and accuracy.

Abstract

Isometry pursuit is a convex algorithm for identifying orthonormal column-submatrices of wide matrices. It consists of a novel normalization method followed by multitask basis pursuit. Applied to Jacobians of putative coordinate functions, it helps identity isometric embeddings from within interpretable dictionaries. We provide theoretical and experimental results justifying this method. For problems involving coordinate selection and diversification, it offers a synergistic alternative to greedy and brute force search.