Clustering-based Low Rank Approximation Method

TL;DR

This paper introduces a hybrid clustering-based low rank approximation method that combines generalized low rank approximation and cluster analysis to improve matrix data compression and numerical precision.

Contribution

It presents a novel hybrid algorithm that generalizes GLRAM and clustering, enhancing low rank approximation for matrix-structured data.

Findings

Improved numerical precision in low-rank approximation

Effective clustering-based matrix compression demonstrated

Theoretical and experimental validation of the method

Abstract

We propose a clustering-based generalized low rank approximation method, which takes advantage of appealing features from both the generalized low rank approximation of matrices (GLRAM) and cluster analysis. It exploits a more general form of clustering generators and similarity metrics so that it is more suitable for matrix-structured data relative to conventional partitioning methods. In our approach, we first pre-classify the initial matrix collection into several small subset clusters and then sequentially compress the matrices within the clusters. This strategy enhances the numerical precision of the low-rank approximation. In essence, we combine the ideas of GLRAM and clustering into a hybrid algorithm for dimensionality reduction. The proposed algorithm can be viewed as the generalization of both techniques. Theoretical analysis and numerical experiments are established to validate the feasibility and effectiveness of the proposed algorithm.