提出新指标NVE,同时评估biclustering的分离度与覆盖范围。
NVE: A Separability and Coverage-Aware Internal Validation Metric for Biclustering

- 基于虚拟误差改进,通过合并对比衡量biclustter间分离性。
- 能识别冗余和重叠严重的聚类结果,避免小区域过拟合。
- 适合需兼顾一致性、独立性和覆盖性的生物数据挖掘场景。
Biclustering旨在同时对数据矩阵的行和列进行分组,发现一致的子矩阵。与传统聚类不同,其二维结构使验证更复杂。现有主流内部指标如均方残差(MSR)和虚拟误差(VE)主要评估组内一致性,但未直接衡量组间独立性或覆盖程度。本文提出归一化虚拟误差(NVE),通过超bicluster归一化策略扩展VE,比较单个bicluster与其与其他bicluster合并后的VE,引入相对分离度与冗余判断。还提出覆盖调整版本NVE_cov,惩罚仅覆盖极小矩阵区域却得低误差的解。在合成数据和酵母基因表达数据集上的实验表明,NVE对冗余和分离度差的bicluster敏感,而NVE_cov在低覆盖率解中改变排名。结果表明,基于NVE的指标可作为内部共聚类验证的有效补充,尤其适用于需联合考虑一致性、分离度和覆盖性的场景。
原文摘要 · Abstract (English)
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.
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