ArticleMathematics (Basel, Switzerland)2021
Assessing Methods for Evaluating the Number of Components in Non-Negative Matrix Factorization.
Article in Mathematics (Basel, Switzerland), 2021. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 13 papers.
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13 citing papers in PubMed.
- Scalable joint non-negative matrix factorization for paired single cell gene expression and chromatin accessibility data.NAR genomics and bioinformatics · 2026Article
- A spectrum of gut microbiota signatures predicts long-term health status.Bioinformatics (Oxford, England) · 2026Article
- Detecting signatures underlying the composition of biological data.Nucleic acids research · 2025Article
- Understanding rheumatic disease through continuous cell state analysis.Nature reviews. Rheumatology · 2025Review
- Distinguishing isotropic and anisotropic signals for X-ray total scattering using machine learning.Acta crystallographica. Section A, Foundations and advances · 2025Article
- Leveraging principal component analysis to uncover urban pedestrian dynamics.Journal of geographical systems · 2025Article
- Normal tissue transcriptional signatures for tumor-type-agnostic phenotype prediction.Scientific reports · 2024Article
- Integration of Pan-Cancer Cell Line and Single-Cell Transcriptomic Profiles Enables Inference of Therapeutic Vulnerabilities in Heterogeneous Tumors.Cancer research · 2024Article
- Functional transcriptional signatures for tumor-type-agnostic phenotype prediction.bioRxiv : the preprint server for biology · 2024Article
- Accurate image derived input function in [EJNMMI physics · 2023Article
- Inferring therapeutic vulnerability within tumors through integration of pan-cancer cell line and single-cell transcriptomic profiles.bioRxiv : the preprint server for biology · 2023Article
- Decision of the Optimal Rank of a Nonnegative Matrix Factorization Model for Gene Expression Data Sets Utilizing the Unit Invariant Knee Method: Development and Evaluation of the Elbow Method for Rank Selection.JMIR bioinformatics and biotechnology · 2023Article
- Clustering single-cell multimodal omics data with jrSiCKLSNMF.Frontiers in genetics · 2023Article
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6 authors.
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Abstract
Non-negative matrix factorization is a relatively new method of matrix decomposition which factors an m×n data matrix X into an m×k matrix W and a k×n matrix H, so that X≈W×H. Importantly, all values in X, W, and H are constrained to be non-negative. NMF can be used for dimensionality reduction, since the k columns of W can be considered components into which X has been decomposed. The question arises: how does one choose k? In this paper, we first assess methods for estimating k in the context of NMF in synthetic data. Second, we examine the effect of normalization on this estimate's accuracy in empirical data. In synthetic data with orthogonal underlying components, methods based on PCA and Brunet's Cophenetic Correlation Coefficient achieved the highest accuracy. When evaluated on a well-known real dataset, normalization had an unpredictable effect on the estimate. For any given normalization method, the methods for estimating k gave widely varying results. We conclude that when estimating k, it is best not to apply normalization. If underlying components are known to be orthogonal, then Velicer's MAP or Minka's Laplace-PCA method might be best. However, when orthogonality of the underlying components is unknown, none of the methods seemed preferable.
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