Presentation Information
[A-2-05]Speeding up of computing matrix approximation using CUR factorization with singular value decay
◎Haruto Ishizaki1, Takafumi Miyata1 (1. Fukuoka institute Technology)
Keywords:
CUR factorization,Low-rank matrix approximation,Singular value decomposition
CUR factorization is the algorithm for approximating a large-scale data matrix to a small-scale low-rank one.Since the small matrices obtained from CUR factorization involve columns and rows of original matrix, it is possible to keep the structures of original matrix such as sparsity and nonnegativity.Selecting the columns and rows from an original matrix is needed to compute CUR factorization, and these selections are done by using singular vectors.Since these selections affect the accuracy of the matrix approximation, the number of the selection is dynamically adjusted by the decay pattern of singular values, and thus the computation of singular value decomposition is required iteratively.To speed up the algorithm, we consider computing a partial singular value decomposition, which is only necessary part for the selections.Numerical experiments show that our approach can reduce the computational time of the algorithm while keeping the accuracy of the matrix approximation.