Kernel based Support Vector Machine via Semidefinite Programming: application to Medical Diagnosis

Support vector machine (SVM) is a well sound learning method and a robust classification procedure, Choosing a suitable kernel function in SVM is crucial for obtaining good performance; the difficulty is how to choose a suitable data transformation for the given problem. To this end, multiple kernel matrices, each of them corresponding to a given similarity measure, can be linearly combined. in this paper, the optimal kernel matrix, obtained as linear combination of known kernel matrices. is generated using a semidefinite programming approach. A suitable model formulation assures that the obtained kernel matrix is positive semidefinite and is optimal with respect to the dataset under consideration. The proposed approach has been applied to some very important medical diagnostic decision making problems and the results obtained by carrying out preliminary numerical experiments demonstrated the effectiveness of the proposed solution approach.