Large-Scale Sparse Kernel Canonical Correlation Analysis

This paper presents gradKCCA, a large-scale sparse non-linear canonical correlation method. Like Kernel Canonical Correlation Analysis (KCCA), our method finds non-linear correlations through kernel functions, but unlike KCCA, our method does not incorporate 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 pre-images 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 $\ell_1$ norm of the pre-images 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.