Robust Blockwise Random Pivoting: Fast and Accurate Adaptive Interpolative Decomposition

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Bibliographische Detailangaben
Veröffentlicht in:	arXiv.org (Dec 19, 2024), p. n/a
1. Verfasser:	Dong, Yijun
Weitere Verfasser:	Chen, Chao, Martinsson, Per-Gunnar, Pearce, Katherine
Veröffentlicht:	Cornell University Library, arXiv.org
Schlagworte:	Parallel processing Tolerances Mathematical analysis Matrices (mathematics) Interpolation Optimization Approximation Algorithms Asymptotic properties Robustness (mathematics) Complexity Error detection Decomposition
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Beschreibung
Abstract:	The interpolative decomposition (ID) aims to construct a low-rank approximation formed by a basis consisting of row/column skeletons in the original matrix and a corresponding interpolation matrix. This work explores fast and accurate ID algorithms from comprehensive perspectives for empirical performance, including accuracy in both skeleton selection and interpolation matrix construction, efficiency in terms of asymptotic complexity and hardware efficiency, as well as rank adaptiveness. While many algorithms have been developed to optimize some of these aspects, practical ID algorithms proficient in all aspects remain absent. To fill in the gap, we introduce robust blockwise random pivoting (RBRP) that is asymptotically fast, hardware-efficient, and rank-adaptive, providing accurate skeletons and interpolation matrices comparable to the best existing ID algorithms in practice. Through extensive numerical experiments on various synthetic and natural datasets, we demonstrate the appealing empirical performance of RBRP from the aforementioned perspectives, as well as the robustness of RBRP to adversarial inputs.
ISSN:	2331-8422
Quelle:	Engineering Database