Fast approximation of orthogonal matrices and application to PCA
This work addresses computational efficiency in spectral methods like PCA, but it appears incremental as it builds on existing Givens transformations.
The paper tackles the problem of approximating orthogonal matrices for fast and accurate computation, proposing a greedy algorithm that balances accuracy and speed, and demonstrates its application to PCA.
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.