Scalable non-negative matrix tri-factorization

Abstract

BackgroundMatrix factorization is a well established pattern discovery tool that has seen numerous applications in biomedical data analytics, such as gene expression co-clustering, patient stratification, and gene-disease association mining. Matrix factorization learns a latent data model that takes a data matrix and transforms it into a latent feature space enabling generalization, noise removal and feature discovery. However, factorization algorithms are numerically intensive, and hence there is a pressing challenge to scale current algorithms to work with large datasets. Our focus in this paper is matrix tri-factorization, a popular method that is not limited by the assumption of standard matrix factorization about data residing in one latent space. Matrix tri-factorization solves this by inferring a separate latent space for each dimension in a data matrix, and a latent mapping of interactions between the inferred spaces, making the approach particularly suitable for biomedical data mining.ResultsWe developed a block-wise approach for latent factor learning in matrix tri-factorization. The approach partitions a data matrix into disjoint submatrices that are treated independently and fed into a parallel factorization system. An appealing property of the proposed approach is its mathematical equivalence with serial matrix tri-factorization. In a study on large biomedical datasets we show that our approach scales well on multi-processor and multi-GPU architectures. On a four-GPU system we demonstrate that our approach can be more than 100-times faster than its single-processor counterpart.ConclusionsA general approach for scaling non-negative matrix tri-factorization is proposed. The approach is especially useful parallel matrix factorization implemented in a multi-GPU environment. We expect the new approach will be useful in emerging procedures for latent factor analysis, notably for data integration, where many large data matrices need to be collectively factorized.Electronic supplementary materialThe online version of this article (doi:10.1186/s13040-017-0160-6) contains supplementary material, which is available to authorized users.

A New Weighted Imputed Neighborhood-Regularized Tri-Factorization One-Class Collaborative Filtering Algorithm: Application to Target Gene Prediction of Transcription Factors

“…While the output clusters may be used for certain ranking tasks, these methods require prior knowledge in the number of clusters and correct cluster labels in addition to the inputs for M(T)F-based ranking methods. The matrix tri-factorization has been applied to gene function prediction, patient stratification, and disease module detection [44], [45].…”

“…-We develop a new algorithm WINTF, which for the first time incorporates sample weight, imputation, and side information into the existing tri-factorization frameworks [44], [45], making it better handle noisy and sparse data. -We develop an efficient optimization algorithm based on the multiplicative update rule.…”

Fast optimization of non-negative matrix tri-factorization

“…Such an iterative update involves multiplying the current approximation with the gradient of the objective function, which captures the discrepancy between the input data matrix and its latent-based reconstruction. Several studies improved the performance of multiplicative update rules, for example, by using parallelization [16, 17]. A significant limitation of multiplicative update rules is that the method is slow to converge [13].…”