Integer Low Rank Approximation of Integer matrices
For researchers analyzing integer data sets, this work provides a tailored approximation method that preserves integer meaning, though the improvement is incremental over existing techniques.
The paper addresses integer low rank approximation for integer matrices, proposing a block coordinate descent method based on integer least squares estimation. Numerical experiments show the method achieves more accurate solutions than existing continuous methods.
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.