Trace Lasso Regularization for Adaptive Sparse Canonical Correlation Analysis via Manifold Optimization Approach

doi:10.1007/s40305-022-00449-x

Journal of the Operations Research Society of China ›› 2024, Vol. 12 ›› Issue (3): 573-599.doi: 10.1007/s40305-022-00449-x

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Trace Lasso Regularization for Adaptive Sparse Canonical Correlation Analysis via Manifold Optimization Approach

Kang-Kang Deng¹, Zheng Peng²

1 Beijing International Center for Mathematical Research, Peking University, Beijing 100871, China;
2 School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China

Received:2021-06-04 Revised:2022-09-24 Online:2024-09-30 Published:2024-08-15
Contact: Zheng Peng, Kang-Kang Deng E-mail:pzheng@xtu.edu.cn;freedeng1208@gmail.com
Supported by:
This research was supported by the National Science Foundation of China (No. 12071398), the Natural Science Foundation of Hunan Province (No. 2020JJ4567) and the Key Scientific Research Found of Hunan Education Department (Nos. 20A097 and 18A351).

Abstract

Abstract: Canonical correlation analysis (CCA) describes the relationship between two sets of variables by finding a linear combination that maximizes the correlation coefficient. However, in high-dimensional settings where the number of variables exceeds sample size, or in the case that the variables are highly correlated, the traditional CCA is no longer appropriate. In this paper, a new matrix regularization is introduced, which is an extension of the trace Lasso in the vector case. Then we propose an adaptive sparse version of CCA (ASCCA) to overcome these disadvantages by utilizing the trace Lasso regularization. The adaptability of ASCCA is that the sparsity regularization of canonical vectors depends on the sample data, which is more realistic in practical applications. The ASCCA model is further reformulated to an optimization problem on the Riemannian manifold. Then we adopt a manifold inexact augmented Lagrangian method to solve the resulting optimization problem. The performance of the ASCCA model is compared with some existing sparse CCA techniques in different simulation settings and real datasets.

Key words: Canonical correlation analysis, Sparsity of canonical vectors, Trace Lasso regularization, Manifold optimization

CLC Number:

Kang-Kang Deng, Zheng Peng. Trace Lasso Regularization for Adaptive Sparse Canonical Correlation Analysis via Manifold Optimization Approach[J]. Journal of the Operations Research Society of China, 2024, 12(3): 573-599.

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Trace Lasso Regularization for Adaptive Sparse Canonical Correlation Analysis via Manifold Optimization Approach

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