2021/07/01 by Sheng Gao, Gao, Sheng, Zongming Ma +1
Engineering · Mathematics · #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Random Matrices and Applications #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2107.00371
openalex publication_date 2021/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Generalized correlation analysis (GCA) is concerned with uncovering linear relationships across multiple datasets. It generalizes canonical correlation analysis that is designed for two datasets. We study sparse GCA when there are potentially multiple generalized correlation tuples in data and the loading matrix has a small number of nonzero rows. It includes sparse CCA and sparse PCA of correlation matrices as special cases. We first formulate sparse GCA as generalized eigenvalue problems at both population and sample levels via a careful choice of normalization constraints. Based on a Lagrangian form of the sample optimization problem, we propose a thresholded gradient descent algorithm for estimating GCA loading vectors and matrices in high dimensions. We derive tight estimation error bounds for estimators generated by the algorithm with proper initialization. We also demonstrate the prowess of the algorithm on a number of synthetic datasets.