Research On Classification Problems Based On Support Vector Machine

Classification problem is a common problem in practical applications, as well as a basic research topic in machine-learning domain. It faces many new puzzles and challenges both in theoretical research and in practical applications on the rapidly developing information technique. Support Vector Machine (SVM) is a newly developed machine learning method based on the foundation of the Statistical Learning Theory (SLT) and the optimization theory. Now, SVM has already shown excellent learning performance in many fields.This thesis focuses on the classification problem, particularly concerns of the researches on the theoretical model as well as the practical applications of SVM. The main works of this thesis are as the following:1. The basic theories used in this thesis were introduced, including the main problems and methods in Machine Learning, Statistical Learning Theory and Support Vector Machines; then, some of the recent researches on SVM were also reviewed.2. From the viewpoint of geometric structure of the feature space, some metrics (Riemannian metric, distance metric, and angle metric) induced by the kernel function are analyzed; the geometric character of Gaussian Radius Basis kernel is discussed in detail; the relations among the mapping, the kernel and the metric are also analyzed.3. A new method to solve the imbalanced or/and cost-sensitive classification problem is proposed. Under the Riemannian metric induced in the embedded manifold, a suitable conformal mapping of kernel is applied to enlarge the spatial resolution around the support vectors of the less pattern class, such that the separability for the samples of the less class is well improved.4. The comparability of the decision functions given by the sub-classifiers with different kernel-parameters in 1-v-r method is discussed, and the positive result is obtained.5. The existance of the invalid regions in the multi-class classification problems is analyzed, and a fuzzy-output SVM is proposed to resolve the patterns within such regions for some practical problems.6. The complicacies of the ranking problem and the general classification problem are compared from the viewpoint of VC dimension, a new concept"ranking dimension"is proposed. The traditional embedded space method, which can directly transform an ordinal ranking problem into a binary classification problem, is modified to adapt the non linear-separable problem based on SVM scheme, and the performance of the new method is validated by it's application in enterprise credit risk assessment problem.