A Unified Framework for Kernelization: The Empirical Kernel Feature Space

In this paper, we propose to kernelize linear learning machines, e.g., PCA and LDA, in the empirical kernel feature space, a finite-dimensional embedding space, in which the distances of the data in the kernel feature space are preserved. The empirical kernel feature space provides a unified framework for the kernelization of all kinds of linear machines: performing a linear machine in the finite-dimensional empirical feature space, its nonlinear kernel machine is then established in the original input data space. This method is different from the conventional kernel-trick based kernelization, and more importantly, the final nonlinear kernel machines, called empirical kernel machines, are shown to be more efficient in many real-world applications, such as face recognition and facial expression recognition, than the kernel-trick based kernel machines.