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Study on the Method of Non-linear Classification Base on the Contraction of the Closed Convex Hull

Author: LiuYongQiang
Tutor: ChenZengZhao
School: Central China Normal University
Course: Pattern Recognition and Image Processing
Keywords: Statistical Learning Theory Support Vector Machine Nuclear thinking Feature space Closed convex hull Bisects the nearest point Decision Tree Multi - class classification
CLC: TP181
Type: Master's thesis
Year: 2009
Downloads: 39
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Abstract

Support Vector Machine is a new machine learning method based on statistical learning theory developed to solve the problem in the case of small sample statistical learning, so it has good generalization capability and promote performance. Learning machine, the core part of the support vector machine, kernel function derived mode analysis of nuclear methods, through the construction of a nuclear function, support vector machine is also a kind of linear methods to solve nonlinear problems become nonlinear learning powerful mathematical foundation of the problem and research platform, nuclear thought to reduce the complexity for the nonlinear learning, so that the study of the non-linear learning problems is directly converted into a linear learning problems, whereby, pattern analysis nuclear guide researchers to study the methodology of nonlinear learning problems. In-depth study of this paper support vector machines and nuclear thinking, as well as the comparative analysis of the multi-class classification method of support vector machine to do the work of the following aspects: First, the the linear two types of classification method - bisects the nearest point thought to promote the use of nuclear and chemical, into non-linear classification methods. Bisects the the recent point method and support vector machine have the same classification performance and generalization ability are two ways to get the optimal classification surface is the same for the same two types of data, but split the nearest point of law has a simple geometric features and more low computational complexity. Linearly inseparable closed convex package contraction principle promotion into nonlinear data processing methods. Closed convex package contraction principle is a data pretreatment mathematical means, through two types of data with respect to the respective mean center contraction, so the two types of data into a separable data, closed convex package contraction principle was originally used solve linear problems, through nuclear thinking its marketing application to nonlinear problems. Support Vector Machine for nonseparable problems through the soft margin ideas to solve a relaxation of constraints to enhance the performance of the classifier. The bisector of the particularity of the nearest point of law, the paper combines closed convex hull of the contraction principle to solve the problem of non-separable closed convex package contraction principle by selecting the appropriate shrinkage learning machine training misclassification rate is reduced to zero, so a high level of superiority and practicality. Third, the proposed feature space to determine whether the two types of data overlap separation metric methods for multi-class problem to construct a separation metric matrix separation measure, given the new relatively simple to determine the condition of the contraction coefficient. What sorter for different classification problems, but also to determine the corresponding data distribution, most of the existing classification method, however, did not advance this make judgments, and therefore has a certain blindness. In this paper, the separation metric method by constructing a separation metric matrix to determine whether overlapping samples also can know the depth of the overlapping between the various categories. Such a priori information extraction can reduce the sorter blindness, can also improve the existing multi-class classification method to improve the performance of their classification. Fourth, the use of the closed convex hull of the contraction principle and features of the spatial separation metric method improved decision tree multi-class classification algorithm. Classification performance of the decision tree multi-class classification method with the decision tree structure, especially the choice of decision tree root node close contact, the decision tree classification method does not do certain restrictions on the selection of the root node, and therefore relatively blind , the decision tree classification has not been significantly improved. By separation metric matrix construct multiple categories, unified for all categories of data in accordance with the maximum depth of the cross contraction, select the most likely segmentation subclass as the upper nodes of the classification tree, the decision tree in turn, thereby reducing the training time of wrong fraction to improve the classification performance of the classification tree. Fifth, this paper to the handwritten digital and handwritten Chinese characters as the object of study, testing and comparison of several multi-class support vector machine classification method and the proposed method, the results prove that the proposed method has higher relative to other methods classification accuracy and classification performance.

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