Abstract
Robustness, which is the ability of learning algorithms to resist data disturbance and irrelevant data variations, is very critical for most visual learning systems. One usually has to collect a large number of examples in order to train a model that is robust against different kinds of data disturbance or variations. On the other hand, because the distribution of data is often highly nonlinear in the input space, a robust learning solution can be achieved by using nonlinear learning methods. Kernel methods have been extensively applied to many visual learning applications. In this dissertation, we develop five different robust kernels that can be used in conjunction with kernel learning machines, and consequently improve the robustness for resolving several image-related problems. By putting special attention in the kernel design, the proposed kernels can robustly provide image similarity in noisy environments. For the first kernel, it is a weighted linear combination of a robust ρ-function and a Radial Basis Function (RBF). For the second kernel, we incorporate a learned image appearance model with a robust ρ-function, and design a kernel which suppresses the influence of data elements too far away from a regular appearance model. For the third kernel, it is designed by incorporating the notions of robust error function and tangent distance. This kernel is insensitive to some irrelevant data deformations and noise disturbances. The fourth kernel is a robust image kernel especially designed for pedestrian identification problem for video surveillance. It can be used over unordered feature sets, and it allows us to represent a target image in a hierarchical structure. Finally, we propose a framework to learn novel facial expression kernels, which can be applied to estimate the facial expression intensity and recognize facial expressions. It performs robustly against inter-personal variations based on using the intra-person expression flow. The expression kernel involves determining a weighting mask for the facial optical flows by solving a constrained quadratic optimization problem for each expression. From the theoretical point of view, these kernels are proved to satisfy the Mercer's condition, so they are valid to be used in a class of kernel-based learning algorithms to enhance their robustness. From a practical point of view, these kernels are shown to significantly improve the robustness of the machine learning algorithms for many visual learning applications.