2015/12/12 by Qiaoya Zhang, Zhang, Qiaoya, Yiyuan She +1
Computer Science · Engineering · Mathematics · #Algorithm #Artificial intelligence #Blind Source Separation Techniques #Computation (stat.CO) #Computer science #Dimensionality reduction #Estimator #FOS: Computer and information sciences #Face and Expression Recognition #Gaussian #Interpretability #Lasso (programming language) #Machine Learning (stat.ML) #Mathematical optimization #Mathematics #Principal component analysis #Regularization (linguistics) #Scalability #Sparse and Compressive Sensing Techniques #Statistics #stat.CO #stat.ML
paper · pdf · doi:10.48550/arxiv.1512.03883
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2015/12/12 · arxiv created 2016/01/28 · arxiv updated 2016/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Principal Component Analysis (PCA) is a dimension reduction technique. It produces inconsistent estimators when the dimensionality is moderate to high, which is often the problem in modern large-scale applications where algorithm scalability and model interpretability are difficult to achieve, not to mention the prevalence of missing values. While existing sparse PCA methods alleviate inconsistency, they are constrained to the Gaussian assumption of classical PCA and fail to address algorithm scalability issues. We generalize sparse PCA to the broad exponential family distributions under high-dimensional setup, with built-in treatment for missing values. Meanwhile we propose a family of iterative sparse generalized PCA (SG-PCA) algorithms such that despite the non-convexity and non-smoothness of the optimization task, the loss function decreases in every iteration. In terms of ease and intuitive parameter tuning, our sparsity-inducing regularization is far superior to the popular Lasso. Furthermore, to promote overall scalability, accelerated gradient is integrated for fast convergence, while a progressive screening technique gradually squeezes out nuisance dimensions of a large-scale problem for feasible optimization. High-dimensional simulation and real data experiments demonstrate the efficiency and efficacy of SG-PCA.