A New Method to Address Singularity Problem in Multimodal Data Analysis

In general, the ‘small sample (n)-large feature ( )’ problem of bioinformatics, image analysis, high throughput molecular screening, astronomy, and other high dimensional applications makes the features highly collinear. In this context, the paper presents a new feature extraction algorithm to address this ‘large small n’ issue associated with multimodal data sets. The proposed algorithm judiciously integrates the concept of both regularization and shrinkage with canonical correlation analysis to extract important features. To deal with the singularity problem, the proposed method increases the diagonal elements of covariance matrices by using regularization parameters, while the off-diagonal elements are decreased by shrinkage coefficients. The concept of hypercuboid equivalence partition matrix of rough hypercuboid approach is used to compute both significance and relevance measures of a feature. The importance of the proposed algorithm over other existing methods is established extensively on real life multimodal omics data set.