Use of SVD-based probit transformation in clustering gene expression profiles

The mixture-Gaussian model-based clustering method has received much attention in clustering gene expression profiles in the literature of bioinformatics. However, this method suffers from two difficulties in applications. The first one is on the parameter estimation, which becomes difficult when the dimension of the data is high or the size of a cluster is small. The second one is on the normality assumption for gene expression levels, which is seldom satisfied by real data. In this paper, we propose to overcome these two difficulties by the probit transformation in conjunction with the singular value decomposition (SVD). SVD reduces the dimensionality of the data, and the probit transformation converts the scaled eigensamples, which can be interpreted as correlation coefficients as explained in the text, into Gaussian random variables. Our numerical results show that the SVD-based probit transformation enhances the ability of the mixture-Gaussian model-based clustering method for identifying prominent patterns of the data. As a by-product, we show that the SVD-based probit transformation also improves the performance of the model-free clustering methods, such as hierarchical, KK-means and self-organizing maps (SOM), for the data sets containing scattered genes. In this paper, we also propose a run test-based rule for selection of eigensamples used for clustering.