Identification of clusters in tissue samples in gene expression data with Principal Component Analysis based on relative variance matrix

Principal Component Analysis (PCA) has been in use as a preprocessing step to clustering for long. We have focused on the clustering of tissue samples in gene expression data. Different clustering techniques and algorithm are available in literature on gene expression data but with the existing ambiguity on the number of clusters, apart from relying on biologically known groups. A consensus is needed to reach on the number of clusters in the wide variety of existing clustering techniques based on different similarity or dissimilarity metrics. The conventional usage of PCA for clustering is either by forcing the unit variance to each variable or the high magnitude of variance of an individual variable is allowed to dominate the entire results of PCA. We propose the use of relative variance covariance method in PCA, so as to give due consideration to the joint and individual variances in the dataset and identify clusters with principal component loadings. We emphasize empirically that the proposed approach of PCA is conclusively more informative than the available approaches to identify cluster structure in tissue samples (sample expression profiles). Clusters formed are valid with the existing results on the data set under study and with valid biological background.