Sparse group principal component analysis via double thresholding with application to multi-cellular programs

2026-02-04

AI Summary

This study addresses the computational inefficiency and limited statistical power of existing methods for estimating multicellular programs (MCPs). To overcome these challenges, the authors propose Sparse Group Principal Component Analysis (SGPCA), which incorporates a dual-thresholding strategy within power iteration: first selecting relevant gene sets and then identifying active cell types. This approach efficiently enforces both group-wise and individual sparsity in MCP estimation, achieving linear time complexity and stronger theoretical guarantees. Extensive simulations demonstrate that SGPCA substantially improves estimation accuracy and detection power compared to current methods. Applied to lupus research, SGPCA successfully identifies key differential MCPs that distinguish patients from healthy individuals, highlighting its practical utility in uncovering biologically meaningful cellular interactions.

Technology Category

• Machine Learning: Kernel Methods
• Reasoning under Uncertainty: Probabilistic Programming
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Large-scale security measurements

Abstract

Multi-cellular programs (MCPs) are coordinated patterns of gene expression across interacting cell types that collectively drive complex biological processes such as tissue development and immune responses. While MCPs are typically estimated from high-dimensional gene expression data using methods like sparse principal component analysis or latent factor models, these approaches often suffer from high computational costs and limited statistical power. In this work, we propose Sparse Group Principal Component Analysis (SGPCA) to estimate MCPs by leveraging their inherent group and individual sparsity. We introduce an efficient double-thresholding algorithm based on power iteration. In each iteration, a group thresholding step first identifies relevant gene groups, followed by an individual thresholding step to select active cell types. This algorithm achieves a linear computational complexity of $O(np)$, making it highly efficient and scalable for large-scale genomic analyses. We establish theoretical guarantees for SGPCA, including statistical consistency and a convergence rate that surpasses competing methods. Through extensive simulations, we demonstrate that SGPCA achieves superior estimation accuracy and improved statistical power for signal detection. Furthermore, We apply SGPCA to a Lupus study, discovering differentially expressed MCPs distinguishing Lupus patients from normal subjects.

Problem

• multi-cellular programs
• sparse principal component analysis
• high-dimensional gene expression
• statistical power
• computational efficiency

Innovation

• Sparse Group PCA
• Double Thresholding
• Multi-cellular Programs
• Power Iteration
• Group Sparsity