Scalable non-negative matrix tri-factorization

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

Identifying target genes of transcription factors (TFs) is crucial to understand transcriptional regulation. However, our understanding of genome-wide TF targeting profile is limited due to the cost of large-scale experiments and intrinsic complexity of gene regulation. Thus, computational prediction methods are useful to predict unobserved TF-gene associations. Here, we develop a new Weighted Imputed Neighborhood-regularized Tri-Factorization one-class collaborative filtering algorithm, WINTF. It predicts unobserved target genes for TFs using known but noisy, incomplete, and biased TF-gene associations and protein-protein interaction networks. Our benchmark study shows that WINTF significantly outperforms its counterpart matrix factorization-based algorithms and tri-factorization methods that do not include weight, imputation, and neighbor-regularization, for TF-gene association prediction. When evaluated by independent datasets, accuracy is 37.8 percent on the top 495 predicted associations, an enrichment factor of 4.19 compared with random guess. Furthermore, many predicted novel associations are supported by literature evidence. Although we only use canonical TF-gene interaction data, WINTF can directly be applied to tissue-specific data when available. Thus, WINTF provides a potentially useful framework to integrate multiple omics data for further improvement of TF-gene prediction and applications to other sparse and noisy biological data. The benchmark dataset and source code are freely available at https://github.com/XieResearchGroup/WINTF.

Fast optimization of non-negative matrix tri-factorization

Non-negative matrix tri-factorization (NMTF) is a popular technique for learning low-dimensional feature representation of relational data. Currently, NMTF learns a representation of a dataset through an optimization procedure that typically uses multiplicative update rules. This procedure has had limited success, and its failure cases have not been well understood. We here perform an empirical study involving six large datasets comparing multiplicative update rules with three alternative optimization methods, including alternating least squares, projected gradients, and coordinate descent. We find that methods based on projected gradients and coordinate descent converge up to twenty-four times faster than multiplicative update rules. Furthermore, alternating least squares method can quickly train NMTF models on sparse datasets but often fails on dense datasets. Coordinate descent-based NMTF converges up to sixteen times faster compared to well-established methods.

Scalable non-negative matrix tri-factorization

Background

Matrix 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.

Results

We 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.

Conclusions

A 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.