4.6 Article

Optimization and expansion of non-negative matrix factorization

Journal

BMC BIOINFORMATICS
Volume 21, Issue 1, Pages -

Publisher

BMC
DOI: 10.1186/s12859-019-3312-5

Keywords

Non-negative matrix factorization; Deconvolution; Imputation

Funding

  1. Ontario Institute for Cancer Research through Government of Ontario
  2. Prostate Cancer Canada
  3. Movember Foundation [RS2014-01]
  4. Terry Fox Research Institute New Investigator Award
  5. CIHR New Investigator Award
  6. Genome Canada
  7. Natural Sciences and Engineering Research Council (NSERC) of Canada
  8. Canadian Institutes of Health Research (CIHR)
  9. Canada Foundation for Innovation (CFI)
  10. Government of Canada through Genome Canada
  11. Ontario Genomics Institute [OGI-125]
  12. Discovery Frontiers: Advancing Big Data Science in Genomics Research program

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Background Non-negative matrix factorization (NMF) is a technique widely used in various fields, including artificial intelligence (AI), signal processing and bioinformatics. However existing algorithms and R packages cannot be applied to large matrices due to their slow convergence or to matrices with missing entries. Besides, most NMF research focuses only on blind decompositions: decomposition without utilizing prior knowledge. Finally, the lack of well-validated methodology for choosing the rank hyperparameters also raises concern on derived results. Results We adopt the idea of sequential coordinate-wise descent to NMF to increase the convergence rate. We demonstrate that NMF can handle missing values naturally and this property leads to a novel method to determine the rank hyperparameter. Further, we demonstrate some novel applications of NMF and show how to use masking to inject prior knowledge and desirable properties to achieve a more meaningful decomposition. Conclusions We show through complexity analysis and experiments that our implementation converges faster than well-known methods. We also show that using NMF for tumour content deconvolution can achieve results similar to existing methods like ISOpure. Our proposed missing value imputation is more accurate than conventional methods like multiple imputation and comparable to missForest while achieving significantly better computational efficiency. Finally, we argue that the suggested rank tuning method based on missing value imputation is theoretically superior to existing methods. All algorithms are implemented in the R package NNLM, which is freely available on CRAN and Github.

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