Non-negative Matrix Factorization (NMF) Applied to Cell Clustering of scRNAseq

Non-negative Matrix Factorization (NMF) is a matrix decomposition technique used to decompose a data matrix into the product of two or more smaller matrices, where the elements of these smaller matrices are all non-negative. NMF is particularly suitable for data mining and feature extraction as it can retain the structure and interpretability of the data.

scRNA-seq data is typically represented by a high-dimensional matrix, where each row corresponds to a gene, and each column corresponds to a single cell's gene expression profile. When applied to scRNA-seq data, the goal of NMF is to decompose the original gene expression matrix into two matrices: the gene factor matrix and the cell coefficient matrix. The gene factor matrix represents gene sets that may correspond to biological processes or cell states, while the cell coefficient matrix describes the activity level of each cell on these gene sets.

By performing cluster analysis on the cell coefficient matrix, researchers can identify cells with similar expression patterns, i.e., cell subpopulations, which is crucial for understanding cellular heterogeneity within tissues and discovering new cell types.

Since NMF only produces non-negative components, this characteristic makes it especially useful for handling gene expression data, as gene expression data is naturally non-negative. Additionally, another advantage of NMF is that its results are easily interpretable, since the gene sets can be seen as the fundamental building blocks of cell expression profiles.

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