Isometry pursuit
This provides a synergistic alternative to greedy and brute force search for problems involving coordinate selection and diversification, though it appears incremental as it builds on existing convex optimization methods.
The paper tackles the problem of identifying orthonormal column-submatrices in wide matrices, proposing a convex algorithm called isometry pursuit that combines a novel normalization method with multitask basis pursuit, and it shows theoretical and experimental results for applications like coordinate selection and diversification.
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.