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.
Abstract (translated)
等距追踪是一种凸优化算法，用于识别宽矩阵中的正交列子矩阵。该方法包括一种新颖的归一化技术，随后进行多任务基追踪。当应用于假设坐标函数的雅可比矩阵时，它有助于从可解释字典中识别等距嵌入。我们提供了理论和实验结果来证明这种方法的有效性。对于涉及坐标选择和多样化的难题，该方法提供了一种协同替代方案，相比于贪心算法和暴力搜索更为优越。
URL
https://arxiv.org/abs/2411.18502
