STMF

STMF applies tropical semiring-based matrix factorization to embed and predict sparse biological datasets such as gene expression matrices.

Key Features:

• Non-Linearity via Tropical Semiring: STMF uses tropical semiring operations to introduce non-linear dynamics into matrix factorization.
• Sparse Data Handling: The method is tailored for sparse data and estimates missing or unknown values with improved accuracy compared to Non-negative Matrix Factorization (NMF).
• Enhanced Pattern Recovery: STMF demonstrates superior pattern recovery on synthetic and real biological datasets, achieving higher correlation than NMF on synthetic tests.
• Performance on TCGA Gene Expression: When applied to gene expression measurements from The Cancer Genome Atlas (TCGA), STMF outperformed NMF in six of nine datasets.
• Extreme-value and Distribution Robustness: STMF better accommodates extreme values and non-standard distributions rather than averaging toward mean values as in NMF.

Scientific Applications:

• Gene Expression Profiling: Embedding and pattern recovery of gene expression matrices, including TCGA datasets, for downstream analysis.
• Missing Value Estimation: Imputing missing or unknown entries in high-dimensional sparse biological matrices.
• Embedding and Prediction of Sparse Datasets: Producing low-dimensional embeddings for prediction and downstream analyses in genomics and other life sciences.

Methodology:

STMF applies tropical semiring operations within matrix factorization to introduce non-linearity and favor fitting extreme values and diverse distributions rather than averaging as in NMF.