Relational co-clustering via manifold ensemble learning

Co-clustering targets on grouping the samples and features simultaneously. It takes advantage of the duality between the samples and features. In many real-world applications, the data points or features usually reside on a submanifold of the ambient Euclidean space, but it is nontrivial to estimate the intrinsic manifolds in a principled way. In this study, we focus on improving the co-clustering performance via manifold ensemble learning, which aims to maximally approximate the intrinsic manifolds of both the sample and feature spaces. To achieve this, we develop a novel co-clustering algorithm called Relational Multi-manifold Co-clustering (RMC) based on symmetric nonnegative matrix tri-factorization, which decomposes the relational data matrix into three matrices. This method considers the inter-type relationship revealed by the relational data matrix and the intra-type information reflected by the affinity matrices. Specifically, we assume the intrinsic manifold of the sample or feature space lies in a convex hull of a group of pre-defined candidate manifolds. We hope to learn an appropriate convex combination of them to approach the desired intrinsic manifold. To optimize the objective, the multiplicative rules are utilized to update the factorized matrices and the entropic mirror descent algorithm is exploited to automatically learn the manifold coefficients. Experimental results demonstrate the superiority of the proposed algorithm.