Sparse Principal Component Analysis

Sparse Principal Component Analysis (SPCA) aims to identify principal components that explain data variance while simultaneously being sparse, enhancing interpretability and reducing dimensionality. Current research focuses on improving the efficiency and accuracy of SPCA algorithms, including developing novel convex relaxations, leveraging techniques like thresholding and iterative methods (e.g., projected power methods, alternating minimization), and exploring connections to other models such as state space models and coupled generator decompositions. These advancements are impacting various fields, including neuroscience (EEG/MEG data fusion), image processing (remote sensing, face recognition), and machine learning (federated learning, hyperparameter tuning), by enabling more efficient and interpretable analysis of high-dimensional data. The development of computationally efficient algorithms that overcome the inherent computational challenges of SPCA remains a key focus.