Abstract
A common goal in data-analysis is to sift through a large data-matrix and detect any significant submatrices (i.e., biclusters) that have a low numerical rank. We present a simple algorithm for tackling this biclustering problem. Our algorithm accumulates information about 2-by-2 submatrices (i.e., ‘loops’) within the data-matrix, and focuses on rows and columns of the data-matrix that participate in an abundance of low-rank loops. We demonstrate, through analysis and numerical-experiments, that this loop-counting method performs well in a variety of scenarios, outperforming simple spectral methods in many situations of interest. Another important feature of our method is that it can easily be modified to account for aspects of experimental design which commonly arise in practice. For example, our algorithm can be modified to correct for controls, categorical- and continuous-covariates, as well as sparsity within the data. We demonstrate these practical features with two examples; the first drawn from gene-expression analysis and the second drawn from a much larger genome-wide-association-study (GWAS).
Highlights
Many applications in data-analysis involve some form of ‘biclustering’— referred to as coclustering, two-mode clustering, two-way clustering, block clustering, and coupled two-way clustering, to name a few
An important problem in genomics is how to detect the genetic signatures associated with disease
In this paper we present a new biclustering method which can scale up efficiently to handle large genomic data sets, such as GWAS-data
Summary
Many applications in data-analysis involve some form of ‘biclustering’— referred to as coclustering, two-mode clustering, two-way clustering, block clustering, and coupled two-way clustering, to name a few (see, e.g., [1,2,3,4,5]). The goal of biclustering is to search through a large data-array and reveal components that have special structure. These structured components involve only a subset of the rows and columns in the data-array, and finding them can be rather difficult (i.e., biclustering is NP-complete [6]). Because this problem is so general, it should come as no surprise that there are many different kinds of biclustering algorithms developed for a variety of applications, ranging from political science to neuroscience [7, 8]. We demonstrate the efficacy of our loop-counting method by applying it to a gene-expression data-set and a GWAS data-set, using gene-enrichment analysis as a form of validation
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