Fast approximation of orthogonal matrices and application to PCA

Orthogonal projections are a standard technique of dimensionality reduction in machine learning applications. We study the problem approximating orthogonal matrices so that their application is numerically fast and yet accurate. find an approximation by solving optimization over set structured matrices, we call extended Givens transformations, including rotations as special case. propose efficient greedy algorithm to solve such show it strikes balance between accuracy speed computation. The approach relevant spectral methods illustrate its PCA.