NVE: A Separability and Coverage-Aware Internal Validation Metric for Biclustering

2026-08-29

AI Summary

论文提出了一种新的双聚类内部验证指标NVE及其变体NVE_cov，通过引入分离性和覆盖性概念来评估双聚类的质量，解决了现有指标无法有效衡量双聚类间差异性和数据解释能力的问题。

Abstract

Biclustering, or co-clustering, aims to discover coherent submatrices by grouping rows and columns of a data matrix simultaneously. This local two-dimensional structure makes validation more difficult than in ordinary clustering, where internal indices usually rely on compactness and separation in a single shared feature space. Existing popular internal biclustering measures such as Mean Squared Residue (MSR), and Virtual Error (VE) mainly evaluate within-bicluster coherence. Although useful, these measures do not directly assess whether the extracted biclusters are mutually distinct or whether they explain a meaningful portion of the data matrix. This paper investigates Normalised Virtual Error (NVE), an internal validation metric that extends VE using a super-bicluster normalization strategy. By comparing the VE of each bicluster with the VE obtained after merging it with other biclusters, NVE introduces a relative notion of separability and redundancy. We also study a coverage-adjusted variant, NVE\textsubscript{cov}, which penalizes solutions that obtain low error by selecting only very small submatrices. Through controlled synthetic benchmarks and yeast gene-expression datasets, we examine whether NVE and NVE\textsubscript{cov} provide information beyond standard coherence-based metrics. The results show that NVE is sensitive to redundant and poorly separated biclusters, while NVE\textsubscript{cov} changes solution rankings when low-error biclusters cover only a negligible part of the matrix. These findings suggest that NVE-based measures are useful complementary criteria for internal co-clustering validation, especially when coherence, separability, and coverage must be considered jointly.

Problem

• biclustering
• separability
• coverage

Innovation

• Normalized Virtual Error
• Separability
• Coverage
• Biclustering Validation
• Super-bicluster Normalization