Fast optimization of non-negative matrix tri-factorization

Statistical Optimization of Non-Negative Matrix Factorization

Non-Negative Matrix Factorization (NMF) is a dimensionality reduction method that has been shown to be very useful for a variety of tasks in machine learning and data mining. One of the fastest algorithms for NMF is the Block Principal Pivoting method (BPP) of [6], which follows a block coordinate descent approach. The optimization in each iteration involves solving a large number of expensive ...

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

Fast Bayesian Non-Negative Matrix Factorisation and Tri-Factorisation

Nonnegative matrix factorisation and tri-factorisation Nonnegative matrix factorisation (NMF) and tri-factorisation (NMTF) methods decompose a given matrix R into two or three smaller matrices so that R ≈ UV T or R ≈ FSG , respectively. Schmidt, Winther and Hansen (2009) introduced a Bayesian version of nonnegative matrix factorisation (left), which we extend to matrix tri-factorisation (right)...

Non-negative Matrix Tri-Factorization for co-clustering: An analysis of the block matrix

Article history: Received 22 April 2014 Received in revised form 7 December 2014 Accepted 31 December 2014 Available online 9 January 2015