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In this chapter we present the decomposition approach to the analysis of large gene expression profile data sets. We address the problem of analysis of transient time-course data of expression profiles. We accept the assumption that co-expression of genes can be related to their belonging to the same Gaussian component. We assume that parameters of Gaussian components, means and variances, can differ between time instants. However, the gene composition of components is unchanged between time instants. For such problem formulations we derive the appropriate version of expectation-maximization algorithm recursions for the estimation of model parameters.We apply the derived method to the data on gene expression profiles of human K562 erythroleukemic cells and we discuss the obtained gene clustering.

The analysis of gene expression profiles of cells and tissues, performed by DNA microarray technology, strongly relies on proper bioinformatical methods of data analysis. Due to the large number of analyzed variables (genes) and the usually low number of cases (arrays) in one experiment, limited by the high cost of the technology, the biological reasoning is difficult without previous analysis, leading to a reduction of the problem dimensionality. A wide variety of methods have been developed; the most useful, from a biological point of view, are methods of supervised gene selection withestimation of false discovery rate. However, supervised gene selection is not always satisfying for the user of microarray technology, as the complexity of biological systems analyzed by microarrays rarely can be explained by one variable. Among unsupervised methods of analysis, hierarchical clustering and principal component analysis (PCA) have gained wide biological application. In our opinion, singular value decomposition (SVD) analysis, which is similar to PCA, has additional advantages that are very essential for the interpretation of the biological data. In this chapter we shall present how to apply SVD to unsupervised analysis of transcriptome data obtained by oligonucleotide microarrays. These results have been derived from several experiments, carried out at the DNA oligonucleotide microarray Laboratory at the Institute of Oncology, Gliwice, and are currently analyzed from a biological point of view.