A method for combining mutual information and canonical correlation analysis

Highlights We propose a hybrid measure of relevance based on MI and KCCA. Our measure PMI weighs more the samples with predictive powers. PMI effectively eliminates the samples with no predictive contribution. We show that PMI has improved feature detection capability. Feature selection is a critical step in many artificial intelligence and pattern recognition problems. Shannon's Mutual Information (MI) is a classical and widely used measure of dependence measure that serves as a good feature selection algorithm. However, as it is a measure of mutual information in average, under-sampled classes (rare events) can be overlooked by this measure, which can cause critical false negatives (missing a relevant feature very predictive of some rare but important classes). Shannon's mutual information requires a well sampled database, which is not typical of many fields of modern science (such as biomedical), in which there are limited number of samples to learn from, or at least, not all the classes of the target function (such as certain phenotypes in biomedical) are well-sampled. On the other hand, Kernel Canonical Correlation Analysis (KCCA) is a nonlinear correlation measure effectively used to detect independence but its use for feature selection or ranking is limited due to the fact that its formulation is not intended to measure the amount of information (entropy) of the dependence. In this paper, we propose a hybrid measure of relevance, Predictive Mutual Information (PMI) based on MI, which also accounts for predictability of signals from each other in its calculation as in KCCA. We show that PMI has more improved feature detection capability than MI, especially in catching suspicious coincidences that are rare but potentially important not only for experimental studies but also for building computational models. We demonstrate the usefulness of PMI, and superiority over MI, on both toy and real datasets.