Structured sparse PCA to identify miRNA co-regulatory modules

This paper presents a new mathematical formulation and the corresponding algorithms for structured sparse principal component analysis (PCA). We introduce a new concept of support matrices with structured prior based on Markov Random Field (MRF). Both the support matrices and principal components are regularized by the L₁ norm to be integrated in a coupled objective function to recover the structured sparsity from the given data. Block coordinate descent and subgradient-based optimization methods are utilized to search for proper local minima for the formulated non-convex optimization problem. We implement the proposed methods to jointly analyze micro-RNA (miRNA) and gene interaction data to identify miRNA-gene co-regulatory modules (co-modules). Our preliminary experiments demonstrate that our structured sparse PCA has the potential to identify meaningful co-regulatory modules with enriched cellular functionalities.