Parallel non-negative matrix tri-factorization for text data co-clustering

As a novel paradigm for data mining and dimensionality reduction, Non-negative Matrix Tri-Factorization (NMTF) has attracted much attention due to its notable performance and elegant mathematical derivation, and it has been applied to a plethora of real-world applications, such as text data co-clustering. However, the existing NMTF-based methods usually involve intensive matrix multiplications, which exhibits a major limitation of high computational complexity. With the explosion at both the size and the feature dimension of texts, there is a growing need to develop a parallel and scalable NMTF-based algorithm for text data co-clustering. To this end, we first show in this paper how to theoretically derive the original optimization problem of NMTF by introducing the Lagrangian multipliers. Then, we propose to solve the Lagrange dual objective function in parallel through an efficient distributed implementation. Extensive experiments on five benchmark corpora validate the effectiveness, efficiency, and scalability of our distributed parallel update algorithm for an NMTF-based text data co-clustering method.