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.
|Title of host publication||36th International Conference on Machine Learning, ICML 2019|
|Number of pages||9|
|Publication status||Published - 2019|
|MoE publication type||A4 Article in a conference publication|
|Event||International Conference on Machine Learning - Long Beach, United States|
Duration: 9 Jun 2019 → 15 Jun 2019
Conference number: 36
|Name||Proceedings of Machine Learning Research|
|Conference||International Conference on Machine Learning|
|Period||09/06/2019 → 15/06/2019|
Uurtio, V., Bhadra, S., & Rousu, J. (2019). Large-Scale Sparse Kernel Canonical Correlation Analysis. In 36th International Conference on Machine Learning, ICML 2019 (pp. 6383-6391). (Proceedings of Machine Learning Research; Vol. 97).