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[2509.15429] Random Matrix Theory-guided sparse PCA for single-cell RNA-seq data
Summary
This paper presents a Random Matrix Theory-guided approach to sparse PCA for single-cell RNA-seq data, enhancing dimensionality reduction and cell-type classification accuracy.
Why It Matters
Single-cell RNA-seq data is crucial for understanding cellular heterogeneity, but its analysis is complicated by noise. This research offers a novel method that improves data interpretation and classification, which can significantly impact biological research and clinical applications.
Key Takeaways
- Introduces a biwhitening algorithm to estimate transcriptomic noise in single cells.
- Utilizes Random Matrix Theory to enhance sparse PCA, making it nearly parameter-free.
- Demonstrates improved performance over traditional PCA and other methods in cell-type classification tasks.
Computer Science > Machine Learning arXiv:2509.15429 (cs) [Submitted on 18 Sep 2025 (v1), last revised 26 Feb 2026 (this version, v2)] Title:Random Matrix Theory-guided sparse PCA for single-cell RNA-seq data Authors:Victor Chardès View a PDF of the paper titled Random Matrix Theory-guided sparse PCA for single-cell RNA-seq data, by Victor Chard\`es View PDF HTML (experimental) Abstract:Single-cell RNA-seq provides detailed molecular snapshots of individual cells but is notoriously noisy. Variability stems from biological differences and technical factors, such as amplification bias and limited RNA capture efficiency, making it challenging to adapt computational pipelines to heterogeneous datasets or evolving technologies. As a result, most studies still rely on principal component analysis (PCA) for dimensionality reduction, valued for its interpretability and robustness, in spite of its known bias in high dimensions. Here, we improve upon PCA with a Random Matrix Theory (RMT)-based approach that guides the inference of sparse principal components using existing sparse PCA algorithms. We first introduce a novel biwhitening algorithm which self-consistently estimates the magnitude of transcriptomic noise affecting each gene in individual cells, without assuming a specific noise distribution. This enables the use of an RMT-based criterion to automatically select the sparsity level, rendering sparse PCA nearly parameter-free. Our mathematically grounded approach retains the ...
