Sparse principal component analysis via double thresholding with applications in pseudo-bulk expression data

Music City Center 

We study the problem of principal component estimation in high-dimensional settings, where the leading principal components exhibit both group and individual sparsity. This simultaneous sparsity structure is commonly observed in multi-cell-type gene expression data, where the same genes are often expressed across related cell subtypes in biological processes. To incorporate this structure into PCA, we propose a double-thresholding algorithm that first filters out group-level signals via group thresholding, then applies individual thresholding within each selected group to enforce individual sparsity. Our algorithm is computationally efficient and scalable, making it well-suited for high-dimensional gene expression analysis. Furthermore, we establish the consistency and convergence rate of the resulting estimator. Experiments on both simulated and real datasets demonstrate the effectiveness of our approach.