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Fast approximation of orthogonal matrices and application to PCA
lib:eb604eda803b1b89 (v1.0.0)
Authors: Cristian Rusu,Lorenzo Rosasco
ArXiv: 1907.08697
Document: PDF DOI
Abstract URL: https://arxiv.org/abs/1907.08697v4
We study the problem of approximating orthogonal matrices so that their application is numerically fast and yet accurate. We find an approximation by solving an optimization problem over a set of structured matrices, that we call extended orthogonal Givens transformations, including Givens rotations as a special case. We propose an efficient greedy algorithm to solve such a problem and show that it strikes a balance between approximation accuracy and speed of computation. The approach is relevant to spectral methods and we illustrate its application to PCA.
ArXiv: 1907.08697
Document: PDF DOI
Abstract URL: https://arxiv.org/abs/1907.08697v4
We study the problem of approximating orthogonal matrices so that their application is numerically fast and yet accurate. We find an approximation by solving an optimization problem over a set of structured matrices, that we call extended orthogonal Givens transformations, including Givens rotations as a special case. We propose an efficient greedy algorithm to solve such a problem and show that it strikes a balance between approximation accuracy and speed of computation. The approach is relevant to spectral methods and we illustrate its application to PCA.
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