Similarity is a basic problem of pattern recognition, and the performances of many algorithms greatly rely on the goodness of the underlying similarity, such as ranking, nearest neighbor classification, clustering and various graph-based semi-supervised learning algorithms. Moreover, the kernel function in the kernel method is also a special similarity measure. Similarity is also an important issue in computer vision, which is closely related to pattern recognition. However, the similarity in computer vision should integrate the domain knowledge, and should be consistent with human perception. How to design the similarity measures which meet the two requirements is an important open question in computer vision. Upholding these two requirements as guiding principles, the thesis investigates the similarity measures for general visual feature vector and histogram, respectively, proposes several new distances and a kernel function, and also proposes a classification scheme which utilizes multiple similarity measures on different kinds of features. The main contributions are as follows. 1. It is proved that Kernel Principal Component Analysis (KPCA) consists of two independent steps, and Multiple Similarity Principal Component Analysis (MSPCA) is proposed as a nonlinear dimensionality reduction algorithm. The two steps of KPCA are kernel feature vector extraction and Principal Component Analysis (PCA). The kernel feature vector consists of the kernel values between the sample and the training set. MSPCA uses multiple kernels to measure the similarities on different kinds of features respectively, and therefore extends the kernel feature vector to the kernel feature matrix. It then utilizes previously proposed Two-Dimensional Principal Component Analysis (2DPCA) to reduce the dimensionality of the kernel feature matrix. MSPCA’s performance is superior to other classic subspace methods since it utilizes the similarities on different kinds of features respectively. 2. The Dynamic Similarity Kernel (DSK) is proposed. The similarity theories in cognitive psychology show that human infers the overall similarity based on the similar aspects among the compared items. Inspired by this evidence, DSK dynamically selects the dimensions with the smallest distances among the compared feature vectors, and computes the kernel value based on them. It improves the accuracies of image classification and face recognition significantly, especially for face recognition with oc...
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