Kernel-based convolution expansion for facial expression recognition

Abstract

The ever-growing depth and width of Convolutional Neural Networks (CNNs) drastically increases the number of their parameters and requires more powerful devices to train and deploy. In this paper, we propose a new architecture that outperforms the classical linear convolution function by expanding the latter to a higher degree kernel function without additional weights. We opt for Taylor Series Kernel which maps input data to a higher-dimensional Reproducing Kernel Hilbert Space (RKHS). Mapping features to a higher-order RKHS is performed in both implicit and explicit ways. For the former way, we compute several polynomial kernels of different degrees leveraging the kernel trick. Whereas, the latter way is achieved by concatenating the result of these polynomial kernels. The proposed Taylor Series Kernelized Convolution (TSKC) is able to learn more complex patterns than the linear convolution kernel and thus be more discriminative. The experiments conducted on Facial Expression Recognition (FER) datasets demonstrate that TSKC outperforms the ordinary convolution layer without additional parameters.