Fast approximation of orthogonal matrices and application to PCA

18 Jul 2019  ·  Cristian Rusu, Lorenzo Rosasco ·

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. read more

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