Data Transformation for Sum Squared Residue

Abstract

The sum squared residue has been popularly used as a clustering and co-clustering quality measure, however little research on its detail properties has been performed. Recent research articulates that the residue is useful to discover shifting patterns but inappropriate to find scaling patterns. To remedy this weakness, we propose to take specific data transformations that can adjust latent scaling factors and eventually lead to lower the residue. First, we consider data matrix models with varied shifting and scaling factors. Then, we formally analyze the effect of several data transformations on the residue. Finally, we empirically validate the analysis with publicly-available human cancer gene expression datasets. Both the analytical and experimental results reveal column standard deviation normalization and column Z-score transformation are effective for the residue to handle scaling factors, through which we are able to achieve better tissue sample clustering accuracy.