Four algorithms to solve symmetric multi-type non-negative matrix tri-factorization problem

Multi-Task Clustering using Constrained Symmetric Non-Negative Matrix Factorization

Researchers have attempted to improve the quality of clustering solutions through various mechanisms. A promising new approach to improve clustering quality is to combine data from multiple related datasets (tasks) and apply multi-task clustering. In this paper, we present a novel framework that can simultaneously cluster multiple tasks through balanced Intra-Task (within-task) and Inter-Task (...

CG-type algorithms to solve symmetric matrix equations

The global FOM and GMRES are among the effective algorithms to solve linear system of equations with multiple right-hand sides. In this paper, we study these algorithms in the case that the coefficient matrix is symmetric and extract two CGtype algorithms for solving symmetric linear systems of equations with multiple right– hand sides. Then, we compare the numerical performance of the new algo...

Algorithms for Non-negative Matrix Factorization

Non-negative matrix factorization (NMF) has previously been shown to be a useful decomposition for multivariate data. Two different multiplicative algorithms for NMF are analyzed. They differ only slightly in the multiplicative factor used in the update rules. One algorithm can be shown to minimize the conventional least squares error while the other minimizes the generalized Kullback-Leibler d...

Scalable non-negative matrix tri-factorization: Supplementary material

We provide further details on performance analysis for our block-wise matrix tri-factorization. In particular, we include analysis of orthogonal matrix tri-factorization that is discussed in our manuscript but whose results, due to conceptual similarity with non-orthogonal factorization were not included in there. We also present the impact of communication overhead on both non-orthogonal and o...

Non-negative matrix factorization