Sparse data embedding and prediction by tropical matrix factorization

Background Matrix factorization methods are linear models, with limited capability to model complex relations. In our work, we use tropical semiring to introduce non-linearity into matrix factorization models. We propose a method called Sparse Tropical Matrix Factorization ( STMF ) for the estimatio...

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Veröffentlicht in:BMC bioinformatics Jg. 22; H. 1; S. 89 - 18
Hauptverfasser: Omanović, Amra, Kazan, Hilal, Oblak, Polona, Curk, Tomaž
Format: Journal Article
Sprache:Englisch
Veröffentlicht: London BioMed Central 25.02.2021
BioMed Central Ltd
Springer Nature B.V
BMC
Schlagworte:
Algorithms
Analysis
Bioinformatics
Biomedical and Life Sciences
Cancer
Computational Biology/Bioinformatics
Computer Appl. in Life Sciences
Data embedding
Deep learning
Embedding
Extreme values
Factorization
Gene Expression
Genetic research
Genomes
Humans
Life Sciences
Linear algebra
Linear models (Statistics)
Linear regression models
Linearity
Machine learning
Mathematical analysis
Matrix completion
Matrix factorization
Matrix methods
Methods
Microarrays
Missing observations (Statistics)
Motion pictures
Neoplasms - genetics
Neural networks
Normal distribution
Recommender systems
Research Article
Rings (mathematics)
Sparse data
Support vector machines
Tropical factorization
Tropical semiring
Slovenia
Data embedding
Sparse data
Tropical semiring
Matrix factorization
Tropical factorization
Matrix completion
ISSN:1471-2105, 1471-2105
Online-Zugang:Volltext
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Zusammenfassung:Background Matrix factorization methods are linear models, with limited capability to model complex relations. In our work, we use tropical semiring to introduce non-linearity into matrix factorization models. We propose a method called Sparse Tropical Matrix Factorization ( STMF ) for the estimation of missing (unknown) values in sparse data. Results We evaluate the efficiency of the STMF method on both synthetic data and biological data in the form of gene expression measurements downloaded from The Cancer Genome Atlas (TCGA) database. Tests on unique synthetic data showed that STMF approximation achieves a higher correlation than non-negative matrix factorization ( NMF ), which is unable to recover patterns effectively. On real data, STMF outperforms NMF on six out of nine gene expression datasets. While NMF assumes normal distribution and tends toward the mean value, STMF can better fit to extreme values and distributions. Conclusion STMF is the first work that uses tropical semiring on sparse data. We show that in certain cases semirings are useful because they consider the structure, which is different and simpler to understand than it is with standard linear algebra.
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ISSN:1471-2105
1471-2105
DOI:10.1186/s12859-021-04023-9