On the bias of H-scores for comparing biclusters, and how to correct it

Cheng and Churchs algorithm has 2400 citations to date, 597 since 2015, and 179 in 2018-19 alone. It was the first to be applied to gene microarray data, and it is one of the main tools available in biclustering packages (e.g., the biclust R library) as well as in gene expression data analysis packages (e.g., IRIS-EDA, Monier et al. 2019). In addition, it is widely used as a benchmark: almost all published biclustering algorithms include a comparison with it. The role of the H-score in a biclustering algorithm is to allow validation and comparisons of biclusters, which may have different numbers of rows and columns. Our findings document a bias that can distort biclustering results. We prove, both analytically and by simulation, that the average H-score increases with the number of rows/columns in a bicluster - even in the ideal (and simplest) case of a single bicluster generated by an additive model plus a white noise. This biases the H-score, and hence all H-score based algorithms, towards small biclusters. Importantly, our analytical proof provides a straightforward way to correct this bias.