Integer Matrix Approximation and Its Applications

Abstract

The integer low-rank approximation of integer matrices (ILA) has received attention recently due to its capacity of naturally representing parts of integer data sets. Different from the general low-rank approximations, the integer approximation is naturally discrete, therefore, the conventional techniques for matrix approximation, such as SVD and non-negative matrix approximation, are inappropriate and unable to solve this problem. To the best of our knowledge, a numerical method for finding a low-rank integer approximation of an integer matrix has not been proposed in the literature earlier. In this talk, we want to propose a block coordinate descent method to obtain the integer low-rank approximation of integer matrices. This method consists of recursively finding integer solutions of integer least square problems. Applications on the real world problems such as the market basket transactions, association rule mining, cluster analysis, and pattern extraction will be given. Numerically, we show that our ILA method can find a more accurate solution than any other existing methods designed for continuous data sets.