This thesis provides a new approach of designing support vector machines (SVMs) with Gaussian kernel functions for multicategory classification: for the given training samples of multicategory classification, methodologies of how support vectors can be selected among training samples and how discriminant functions can be constructed for classifying the data, are suggested. A short background about generalization bound describing the relationship between the general and empirical risks of SVMs, is also described. For the classification problem, the SVM constructs the discriminant function representing the separating hyperplane in the sense of the structural risk minimization (SRM) principle, that is, optimizing the structure of SVM in the sense of minimizing the general risk. One weak point in this approach is that the SVM is intrinsically linear. For the nonlinear decision boundary, the SVM employs nonlinear kernel such as Gaussian kernel function instead of linear units. However, in this case, there is no systematic way of determining the kernel parameters using the SVM algorithm. In this sense, a new approach of determining the parameters of kernel functions in the sense of minimizing mean square error (MSE) after selecting the support vectors, is considered. The suggested algorithm is composed of two parts: 1) the first part is selecting support vectors among training samples using the optimization technique for a quadratic function defined by the summation of decision error and regularization term such as norm square of weight parameters of an estimation network, and 2) the second part is estimating the parameters of SVM with kernel functions using the minimization algorithm of mean square error. To show the effectiveness of suggested approach, the simulation for the classification of various benchmark data from UCI machine learning group is
performed.
이 논문은 SVM을 기본으로 새로운 분류방법을 연구하였습니다.
우선, 이차함수의 최적화 방법을 이용해서 학습자료에서 support vetor들을 선택하였고, 그리고나서 kernel을 이용한 SVM에서의 변수들을 평균제곱오차 알고리즘의 최소화방법을 이용해 최적화시켰습니다. 우리는 이러한 방법으로 UCI 기계학습그룹에서 얻은 다양한 benchmark 자료들을 분류하여 그 효율성을 살펴보았습니다. 이 시뮬레이션 결과는 제시된 방법이 분류 수행에 있어서 효과적임을 보여주고 있습니다. 하지만, 선택되어진 support vetor들간에 결정적인 역할을 하는 support vector를 찾는 문제와 최적의 수행을 함에 있어서의 판별함수를 만들기위해서 support vector들을 어떻게 조합해야 하는지가 우리들의 과제로 남아있습니다.
