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Stochastic gradient descent estimation of generalized matrix factorization models with application to single-cell RNA

Cristian Castiglione¹, Alexandre Segers^2,3, Lieven Clement²

¹Institute for Data Science and Analytics, Bocconi University, Via Röntgen 1, Milan 20136, Italy.

Biostatistics (Oxford, England)

|May 5, 2026

Summary

This study introduces a generalized matrix factorization model and a scalable algorithm for dimensionality reduction in single-cell RNA sequencing data. The new method efficiently analyzes millions of cells, outperforming existing techniques for improved biological insights.

Keywords:

RNA-seq dimension reduction generalized linear models matrix factorization single-cell stochastic optimization

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Area of Science:

Computational Biology
Genomics
Bioinformatics

Background:

Single-cell RNA sequencing (scRNA-seq) enables gene expression quantification at the single-cell level, crucial for studying cellular heterogeneity.
Dimensionality reduction is essential for visualizing and analyzing complex scRNA-seq data but is computationally challenging due to data size.
Existing methods like principal component analysis struggle with large-scale scRNA-seq datasets.

Purpose of the Study:

To develop a generalized matrix factorization model for scRNA-seq data analysis.
To propose a scalable algorithm for efficient dimensionality reduction on large single-cell datasets.
To provide a robust and accurate method for analyzing cellular heterogeneity and gene expression dynamics.

Main Methods:

A generalized matrix factorization model based on exponential dispersion family distributions was developed.
A scalable adaptive stochastic gradient descent algorithm was designed for efficient model estimation.
The proposed method was benchmarked against state-of-the-art techniques using numerical experiments and real-world biological data.

Main Results:

The generalized matrix factorization model encompasses many existing dimensionality reduction approaches.
The stochastic gradient descent algorithm enables efficient analysis of datasets containing millions of cells.
The proposed method demonstrated superior performance in execution time, memory usage, and reconstruction accuracy compared to existing methods.
The method successfully scaled to analyze large single-cell datasets, facilitating dimensionality reduction.

Conclusions:

The novel generalized matrix factorization model and scalable algorithm offer significant advancements in single-cell data analysis.
The method provides a powerful tool for researchers to explore cellular heterogeneity and gene expression dynamics in large scRNA-seq datasets.
An open-source R package, sgdGMF, is available for implementing the discussed methods.