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 l...

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Bibliographic Details
Published in:PloS one 2019-06, Vol.14 (6), p.e0217994
Main Authors: Čopar, Andrej, Zupan, Blaž, Zitnik, Marinka
Format: Article
Language:English
Subjects:
Algorithms
Analysis
Artificial intelligence
Bioinformatics
Computer and Information Sciences
Convergence
Data types
Databases, Factual
Datasets
Descent
Factorization
Gene expression
Least squares method
Matrices (Mathematics)
Methods
Models, Theoretical
Mutation
Natural language processing
Optimization
Optimization theory
Physical Sciences
Representations
Research and Analysis Methods
Signal processing
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Summary: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.
ISSN:1932-6203
1932-6203
DOI:10.1371/journal.pone.0217994