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Fast approximation of orthogonal matrices and application to PCA (1907.08697v5)
Published 18 Jul 2019 in math.NA, cs.LG, cs.NA, eess.SP, and stat.ML
Abstract: 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.