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The microarray technology allows for the simultaneous monitoring of thousands of genes for each sample. The high-dimensional gene expression data can be used to study similarities of gene expression profiles across different samples to form a gene clustering. The clusters may be indicative of genetic pathways. Parallel to gene clustering is the important application of sample classification based on all or selected gene expressions. The gene clustering and sample classification are often undertaken separately, or in a directional manner (one as an aid for the other). However, such separation of these two tasks may occlude informative structure in the data. Here we present an algorithm for the simultaneous clustering of genes and subset selection of gene clusters for sample classification. We develop a new model selection criterion based on Rissanen's MDL (minimum description length) principle. For the first time, an MDL code length is given for both explanatory variables (genes) and response variables (sample class labels). The final output of the proposed algorithm is a sparse and interpretable classification rule based on cluster centroids or the closest genes to the centroids.

Simultaneous gene clustering and subset selection for sample classification via MDL