Large-Scale Sparse Kernel Canonical Correlation Analysis

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Conference article in proceedings
Date
2019
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Language
en
Pages
9
6383-6391
Series
Proceedings of the 36th International Conference on Machine Learning, Proceedings of Machine Learning Research, Volume 97
Abstract
This paper presents gradKCCA, a large-scale sparse non-linear canonical correlation method. Like Kernel Canonical Correlation Analysis (KCCA), our method finds non-linear relations through kernel functions, but it does not rely on a kernel matrix, a known bottleneck for scaling up kernel methods. gradKCCA corresponds to solving KCCA with the additional constraint that the canonical projection directions in the kernel-induced feature space have preimages in the original data space. Firstly, this modification allows us to very efficiently maximize kernel canonical correlation through an alternating projected gradient algorithm working in the original data space. Secondly, we can control the sparsity of the projection directions by constraining the ℓ1 norm of the preimages of the projection directions, facilitating the interpretation of the discovered patterns, which is not available through KCCA. Our empirical experiments demonstrate that gradKCCA outperforms state-of-the-art CCA methods in terms of speed and robustness to noise both in simulated and real-world datasets.
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Uurtio , V , Bhadra , S & Rousu , J 2019 , Large-Scale Sparse Kernel Canonical Correlation Analysis . in 36th International Conference on Machine Learning, ICML 2019 . Proceedings of Machine Learning Research , vol. 97 , JMLR , pp. 6383-6391 , International Conference on Machine Learning , Long Beach , California , United States , 09/06/2019 . < http://proceedings.mlr.press/v97/uurtio19a.html >