An information theoretic divergence for microarray data clustering

The Kullback-Leibler (KL) divergence used in conjunction with the unsupervised Self-Organizing Map (SOM) algorithm has been previously shown to be effective for the gene clustering problem: the patterns of the gene clusters obtained were found to be superior to those obtained by the hierarchical clustering algorithm using the uncentered Pearson correlation measure. Motivated by this initial finding, in this research we study the effectiveness of the KL-divergence in a more general setting where the data points are not necessarily projected to the unit simplex but to a parallel simplex in the positive orthant. Two novel hard and soft clustering algorithms based on the so-called generalized KL-divergence are proposed. We tested the algorithms on both gene and sample clustering problems. Experimental results on real microarray datasets with known class labels (for genes or samples) show that the generalized KL-divergence based algorithms produce comparable or better results to those obtained by similar algorithms based on popular distance measures for microarray data clustering, such as the squared Euclidean distance and the Pearson correlation. Two validation indices, namely the Adjusted Rand Index and the newly developed Variation of Information metric, have been used to validate the results.