Bidimensional linked matrix factorization for pan-omics pan-cancer analysis
Open accessAbstract
Several modern applications require the integration of multiple large data matrices that have shared rows and/or columns. For example, cancer studies that integrate multiple omics platforms across multiple types of cancer, pan-omics pan-cancer analysis, have extended our knowledge of molecular heterogeneity beyond what was observed in single tumor and single platform studies. However, these studies have been limited by available statistical methodology. We propose a flexible approach to the simultaneous factorization and decomposition of variation across such bidimensionally linked matrices, BIDIFAC+. BIDIFAC+ decomposes variation into a series of low-rank components that may be shared across any number of row sets (e.g., omics platforms) or column sets (e.g., cancer types). This builds on a growing literature for the factorization and decomposition of linked matrices which has primarily focused on multiple matrices that are linked in one dimension (rows or columns) only. Our objective function extends nuclear norm penalization, is motivated by random matrix theory, gives a unique decomposition under relatively mild conditions, and can be shown to give the mode of a Bayesian posterior distribution. We apply BIDIFAC+ to pan-omics pan-cancer data from TCGA, identifying shared and specific modes of variability across four different omics platforms and 29 different cancer types.
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For BIDIFAC, for column-missingness, imputation error is smallest for stronger joint-signal strength.
“For column-missingness, where entries for an entire ‘omic are missing across all samples, imputation error is smallest for stronger joint-signal strength.”
From Missing data in multi-omics integration: Recent advances through artificial intelligence (2023) · cites this paper as Lock et al., 2022
For BIDIFAC, simulation studies indicate that for entry-level missingness, imputation error is smallest for stronger signals.
“Simulation studies assessing the performance of BIDIFAC across different types of missingness (entry, column, and block) and signal strength indicate that for entry-level missingness, imputation error is smallest when for stronger signals.”
From Missing data in multi-omics integration: Recent advances through artificial intelligence (2023) · cites this paper as Lock et al., 2022
For BIDIFAC, a similar trend of smallest imputation error for stronger signal is observed for block-level missingness.
“A similar trend is observed for block-level missingness, which is the type of missingness where several omics (columns) are missing across a set of samples (rows).”
From Missing data in multi-omics integration: Recent advances through artificial intelligence (2023) · cites this paper as Lock et al., 2022
BIDIFAC+ assumes that shared structures are present across the integrated matrices, an assumption that may be violated in practice.
“However, Lock et al. (2022) note that BIDIFAC+ assumes that shared structures are present across the integrated matrices, an assumption that may be violated in practice.”
From Missing data in multi-omics integration: Recent advances through artificial intelligence (2023) · cites this paper as Lock et al., 2022
BIDIFAC+ took nearly 24 hours to reach convergence when fitted to a combined TCGA dataset, and thus may not scale well with larger aggregations of datasets.
“As well, they noted that BIDIFAC+ took nearly 24 h to reach convergence when fitted to a combined TCGA dataset, and thus the method may not scale well with larger aggregations of datasets.”
From Missing data in multi-omics integration: Recent advances through artificial intelligence (2023) · cites this paper as Lock et al., 2022
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References 41 · Cited by 19
Research works printed but not linked: 1
- Lock EF, Park JY and Hoadley KA (2022). Supplement to “Bidimensional linked matrix factorization for pan-omics pan-cancer analysis.” 10.1214/21-AOAS1495SUPPA,, PMC9060567 35505906 · DOI
- Authors
- Lock, E. F., Park, J. Y., & Hoadley, K. A.
- Affiliations
- University of Minnesota (US)
- University of Toronto (CA)
- University of North Carolina at Chapel Hill (US)
- Corresponding author
- Lock, Eric F.
- Park, Jun Young
- Hoadley, Katherine A.
- Venue
- The Annals of Applied Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 2022-03-01
- Volume
- 16
- Issue
- 1
- Pages
- 193-215
- ISSN
- 1932-6157 (ISSN-L)
- 1941-7330
- PMC
- PMC9060567
- OpenAlex
- W3004464823
- Cited by
- 19
- References
- 41
- Citations by year
- 2026: 1 · 2025: 4 · 2024: 5 · 2023: 3 · 2022: 5 · 2021: 1
- FWCI
- 2.04
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- The Annals of Applied Statistics (publishedVersion)
- PubMed (publishedVersion)
- PubMed Central (acceptedVersion)
- Funders
- National Cancer Institute (R21CA231214)
- National Institute of General Medical Sciences (R01GM130622)
- Topics
- Physical Sciences › Mathematics › Computational Mathematics › Tensor decomposition and applications
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Gene expression and cancer classification
- Keywords
- multi-omics integration, low-rank decomposition, random matrix theory, TCGA
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