Deep Kernel Coherence Encoder

Haitao Liu, Randy C. Paffenroth, Louis Scharf, Fangzheng Sun

Abstract: Here we propose a non-linear generalization of Kernel Canonical Correlation Analysis (KCCA) using deep neural networks, which we call a Deep Kernel Coherence Encoder (DKCE). While classic KCCA only provides a few parameters that can be trained using data, DKCE works by optimizing over many parameters encoded in a combination of a radial basis function kernel and a deep neural network. This novel structure simultaneously provides a large number of parameters, through the deep neural network, and an infinite dimensional feature space, by way of the radial basis function kernel and Mercer's theorem. Moreover, we provide an efficient computational back-propagation method based on entry-wise coherence maximization that can be used in high-dimensional settings and implemented using standard software libraries. Lastly, we provide preliminary, but suggestive, results of our proposed method on the MNIST and Fashion MNIST data sets, and provide directions for future research.