One-class problem includes one-class description and one-class classification. Given a dataset without label, the former means how to describe the intrinsic information (opposite to abnormal information or noise information) of the dataset, and the latter means that if we thought the data in the dataset as target samples, then how to divide them with all the outlying samples (includes outliers). It is significant to study one-class problem not only to pattern recognition but also to Information science. The main contents involved in the thesis are the following: (1) Firstly we give the contents and significance about the research of one-class problem, and then divide the one-class problem into one-class description and one-class classification. We show the potential applications of the one-class problem at last. (2) We present a model to solve the problem of one-class description: Variance-based Information Decomposing Model (VIDM), and introduce algorithms based on the Principal Component Analysis and the Principal Curves to the VIDM. (3) Making experiments on abnormal returns detection and feature extraction of speaker recognition to show the practicality of the VIDM and its algorithms. (4) One-class classification and outlier problems are investigated by using the idea of SVM. Based on regarding a one-class problem as the one to estimate a function, the generalization error is defined for the first time. The linear separability, margin and optimal linear classifier are then defined and the regular SVM is reformulated into that for one-class problems. (5) Through integrating the idea of semi-supervised learning into the problem of one-class classification, a kind of semi-one-class classification algorithm is presented (Semi-v-SVM). This algorithm is verified by the experiment of merchandise classification in auction website of"eachnet" (www.eachnet.com).
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