L0-norm Sparse Graph-regularized SVD for Biclustering

TL;DR

This paper introduces a novel sparse graph-regularized SVD method with L0-norm penalties for biclustering high-dimensional data, effectively capturing structural sparsity and prior graph information to improve interpretability.

Contribution

It develops a new biclustering approach combining L0-norm and graph-regularized penalties, solved via an efficient iterative algorithm, advancing structural sparsity and interpretability in high-dimensional data analysis.

Findings

Effective in capturing natural blocking structures in simulated data

Outperforms existing methods in real gene expression datasets

Enhances interpretability through structural sparsity

Abstract

Learning the "blocking" structure is a central challenge for high dimensional data (e.g., gene expression data). Recently, a sparse singular value decomposition (SVD) has been used as a biclustering tool to achieve this goal. However, this model ignores the structural information between variables (e.g., gene interaction graph). Although typical graph-regularized norm can incorporate such prior graph information to get accurate discovery and better interpretability, it fails to consider the opposite effect of variables with different signs. Motivated by the development of sparse coding and graph-regularized norm, we propose a novel sparse graph-regularized SVD as a powerful biclustering tool for analyzing high-dimensional data. The key of this method is to impose two penalties including a novel graph-regularized norm ($|\pmb{u}|\pmb{L}|\pmb{u}|$) and $L_0$-norm ($\|\pmb{u}\|_0$) on singular vectors to induce structural sparsity and enhance interpretability. We design an efficient Alternating Iterative Sparse Projection (AISP) algorithm to solve it. Finally, we apply our method and related ones to simulated and real data to show its efficiency in capturing natural blocking structures.