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- Copyright © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
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- 1573-7497
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- 10.1007/s10489-023-04666-6
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Abstract
Generalized canonical correlation analysis (GCCA) has been widely used for classification and regression problems. The key idea of GCCA is to map the data from different views into a common space with the minimum reconstruction error. However, GCCA employs the squared Frobenius norm as a distance metric to find a latent correlated space without a specific strategy to cope with outliers, thus misguiding the GCCA’s training task in real-world applications and leading to suboptimal performance. This inspires us to propose a novel robust formulation for GCCA, namely, GCCA with the p-order (0<p≤2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$0<p\le 2$$\end{document}) of Frobenius norm minimization (called RGCCA). It is difficult to solve the RGCCA involving the nonsmooth and nonconvex p-order of F-norm terms. Therefore, an efficient iterative algorithm is developed to solve RGCCA, theoretically analyzing its convergence property. In addition, the parameters of RGCCA nicely trade-off between accuracy and training time, a property especially useful for larger samples. Empirical experiments and theoretical analysis prove the effectiveness and robustness of RGCCA on both noiseless and noisy datasets.
Journal
Applied Intelligence – Springer Journals
Published: Sep 1, 2023
Keywords: Outliers and noise; p-order of Frobenius norm; Robust RGCCA; Squared Frobenius norm