Nonnegative Decompositions with Resampling for Improving Gene Expression Data Biclustering Stability

The small sample sizes and high dimensionality of gene expression datasets pose significant problems for unsupervised subgroup discovery. While the stability of unidimensional clustering algorithms has been previously addressed, generalizing existing approaches to biclustering has proved extremely difficult. Despite these difficulties, developing a stable biclustering algorithm is essential for analyzing gene expression data, where genes tend to be co-expressed only for subsets of samples, in certain specific biological contexts, so that both gene and sample dimensions have to be taken into account simultaneously. In this paper, we describe an elegant approach for ensuring bicluster stability that combines three ideas. A slight modification of nonnegative matrix factorization that allows intercepts for genes has proved to be superior to other biclustering methods and is used for base-level clustering. A continuous-weight resampling method for samples is employed to generate slight perturbations of the dataset without sacrificing data and a positive tensor factorization is used to extract the biclusters that are common to the various runs. Finally, we present an application to a large colon cancer dataset for which we find 5 stable subclasses.