Integer Low Rank Approximation of Integer matrices

TL;DR

This paper introduces a novel block coordinate descent method for integer low rank approximation of integer matrices, effectively handling discrete data and outperforming existing methods in accuracy.

Contribution

It develops a new algorithm based on integer least squares estimation specifically for integer matrices, addressing a gap in existing real-number techniques.

Findings

Method achieves more accurate solutions than existing continuous data methods.

Numerical experiments demonstrate effectiveness on association analysis and random integer matrices.

Algorithm successfully preserves the integer nature of data during approximation.

Abstract

Integer data sets frequently appear in many applications in sciences and technology. To analyze these, integer low rank approximation has received much attention due to its capacity of representing the results in integers preserving the meaning of the original data sets. To our knowledge, none of previously proposed techniques developed for real numbers can be successfully applied, since integers are discrete in nature. In this work, we start with a thorough review of algorithms for solving integer least squares problems, {and} then develop a block coordinate descent method based on the integer least squares estimation to obtain the integer low rank approximation of integer matrices. The numerical application on association analysis and numerical experiments on random integer matrices are presented. Our computed results seem to suggest that our method can find a more accurate solution than other existing methods for continuous data sets.