An Algorigtm for Singular Value Decomposition of Matrices in Blocks

TL;DR

This paper introduces two block matrix decomposition methods similar to SVD, designed to handle large matrices by processing smaller blocks, demonstrated on a large document-term matrix.

Contribution

It presents novel block matrix decomposition algorithms that avoid large matrix handling, suitable for size-limited computational environments.

Findings

Effective decomposition of large matrices into blocks

Applicable to document-term matrices with size constraints

Achieved economy and full decompositions on test data

Abstract

Two methods to decompose block matrices analogous to Singular Matrix Decomposition are proposed, one yielding the so called economy decomposition, and other yielding the full decomposition. This method is devised to avoid handling matrices bigger than the biggest blocks, so it is particularly appropriate when a limitation on the size of matrices exists. The method is tested on a document-term matrix (17780x3204) divided in 4 blocks, the upper-left corner being 215x215.