Sparse GCA and Thresholded Gradient Descent

• URL: http://arxiv.org/abs/2107.00371v1
• Date: Thu, 1 Jul 2021 11:15:20 GMT
• Title: Sparse GCA and Thresholded Gradient Descent
• Authors: Sheng Gao, Zongming Ma
• Abstract summary: Generalized correlation analysis (GCA) is concerned with uncovering linear relationships across datasets. We study sparse GCA when there are potentially multiple generalized correlations in data. We propose a thresholded descent algorithm for estimating GCA loading vectors and gradient matrices in high dimensions.
• Score: 9.971356146653973
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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