Minimum Sum-Squared Residue Co-clustering of Gene Expression Data

Abstract

Microarray experiments have been extensively used for simultaneously measuring DNA expression levels of thousands of genes in genome research. A key step in the analysis of gene expression data is the clustering of genes into groups that show similar expression values over a range of conditions. Since only a small subset of the genes participate in any cellular process of interest, by focusing on subsets of genes and conditions, we can lower the noise induced by other genes and conditions -a co-cluster characterizes such a subset of interest. Cheng and Church [3] introduced an effective measure of co-cluster quality based on mean squared residue. In this paper, we use two similar squared residue measures and propose two fast k-means like co-clustering algorithms corresponding to the two residue measures. Our algorithms discover k row clusters and l column clusters simultaneously while monotonically decreasing the respective squared residues. Our co-clustering algorithms inherit the simplicity, efficiency and wide applicability of the k-means algorithm. Minimizing the residues may also be formulated as trace optimization problems that allow us to obtain a spectral relaxation that we use for a principled initialization for our iterative algorithms. We further enhance our algorithms by an incremental local search strategy that helps avoid empty clusters and escape poor local minima. We illustrate co-clustering results on a yeast cell cycle dataset and a human B-cell lymphoma dataset. Our experiments show that our co-clustering algorithms are efficient and are able to discover coherent co-clusters.

Parameter-less co-clustering for star-structured heterogeneous data

“…Co-clustering has been studied in many different application contexts including text mining [11], gene expression analysis [8,27] and graph mining [5] where these methods have yielded an impressive improvement in performance over traditional clustering techniques. The methods differ primarily by the criterion they optimize, such as minimum loss in mutual information [11], sum-squared distance [8], minimum description length (MDL) [5], Bregman divergence [2] and non-parametric association measures [29,17].…”

“…The methods differ primarily by the criterion they optimize, such as minimum loss in mutual information [11], sum-squared distance [8], minimum description length (MDL) [5], Bregman divergence [2] and non-parametric association measures [29,17]. Among these approaches, only those ones based on MDL and association measure are claimed to be parameter-free [19].…”

A Clustering Model Based on Matrix Approximation with Applications to Cluster System Log Files

“…Similar ideas have been explored in for gene expression data in [4]. Here we illustrated in our clustering model.…”

DisCo: Distributed Co-clustering with Map-Reduce: A Case Study towards Petabyte-Scale End-to-End Mining

“…Various co-clustering algorithms have adopted different error functions, such as minimum mutual information [15], sum-squared distance [9], and code length [6]. A general co-clustering framework based on Bregman divergence [4] has been proposed, which covers the entire exponential family.…”