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

TL;DR

Multi-cellular programs (MCPs) are coordinated gene expression patterns across cell types that drive complex biology. This paper introduces Sparse Group Principal Component Analysis (SGPCA), a scalable method that enforces both group-level and within-group sparsity via a double-thresholding extension of power iteration, achieving $O(np)$ per-iteration cost and theoretical guarantees of consistency and accelerated convergence. A stability-based tuning procedure selects thresholds, enhancing variable selection for MCP discovery. Through simulations, SGPCA demonstrates superior estimation accuracy and power for MCP detection; applied to a Lupus study, it identifies MCPs that differentiate patients from controls and yields biologically meaningful insights into immune processes.

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.

Figures (5)

• Figure 1: An illustrative example of gene co-expression pattern across three cell types. In this example, gene 1 is expressed across all cell types; gene 2 is expressed across cell types 1 and 3; gene 3 is expressed only in cell type 2. All other genes are not expressed in all cell types. Gray blocks indicate non-expression, colored blocks indicate active expression and varying transparency signifies different expression levels.
• Figure 2: Simulation results for three settings. Top row: alignment. Bottom row: Type I error.
• Figure 3: Estimation results for PC1. Upper left panel: a upset plot which exhibits the number of genes co-expressed across different cell subtypes. Lower left panel: Top 20 genes with the largest magnitude of loadings across subtypes in the first PC. Right panel: Top 10 biological processes enriched in the first PC.
• Figure 4: Histograms of scores on the 4 identified PCs. Vertical lines are score means by group. P-values are returned by debiasing test of PC scores.
• Figure 5: Upset plots of identified genes in each PC and differentially expressed genes identified by GCATE method, by cell subtypes.

Theorems & Definitions (5)

• Lemma 3.1
• Remark 3.1
• Theorem 3.1
• Remark 3.2: Reduction to the individual-sparsity case
• Remark 3.3: Comparison with SDP-based approaches