因所收集到的資料常具有不同程度的差異性與雜訊干擾，機器學習演算法的強健度一直是個相當重要的課題。為使演算法更具有強健性，我們往往需要蒐集大量的訓練資料以涵蓋所有可能的資料變化。而在原始的資料空間裡，資料的分佈通常是非線性的，因此應用非線性的演算法將可以得到較好的結果。對視覺學習問題而言，核心方法（kernel methods）在近年來得到了相當大的進展。這篇論文即發展了五個可供核心演算法使用的強健核心（kernel function），意欲在面對不同影像相關問題時改善核心演算法的強健度。藉著特別的設計，我們定義的核心函數可以在高度雜訊的環境裡合理估測影像關聯性。第一個核心主要是由一個基礎於rho函數與RBF函數所加權構成。藉著估測影像模型，第二個核心可以減輕不合理的資料元素所帶來的影響。第三個核心結合了切線距離與rho函數，使其對變形影像及雜訊均具有不錯的強健性。第四個核心是特別為了視訊監控中的行人辨識應用所設計的。它允許我們使用未排序的特徵集合來描述一張影像，並進一步將其組織為階層式架構。最後，我們提出了一個最佳化方法來學習核心函數，應用在表情強度估測以及表情辨識這兩種問題上。從理論角度而言，這些核心函數均滿足Mercer's condition，所以他們可以被應用在許多核心演算法上以提升強健性。從實用角度而言，藉著許多在不同應用上的實驗結果，我們也驗證了這些核心函數確實可以改善核心演算法的強健度。

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.

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