Support Vector Data Description And Support Vector Machine And Their Applications

The presented study focuses on such issues as the improvement of support vector data description (SVDD) and its applications, the applications of support vector machine (SVM) to functional magnetic resonance imaging (fMRI) and the solutions of matrix inverse problem and its optimal approximation problem over R-symmetry and R-skew symmetric matrices.As an important method of data description, SVDD can be used to outlier detection or classification, which can give the target data set a spherically shaped description. In real life the target data set often contains more than one class of objects and each class of objects need to be described and distinguished simultaneously. When the target data set contains two classes of objects, SVDD can only give a description for the target data set, regardless of the differences among different target classes in the target data set, that is, SVDD can not give a description for each class of objects in the target data set. To solve the above problem, an improved support vector data description method without considering negative examples is presented, which is named normal two-class SVDD(NTC-SVDD). The proposed method can give each class of objects in the target data set a hypersphere-shaped description simultaneously if the target data set contains two classes of objects. The characteristics of the improved support vector data description are discussed. The results of the proposed approach on artificial and actual data show that the proposed method works better on the 3-class classification problem with one object class being undersampled severely than other normal multi-class classifiers.To overcome the shortcomings that NTC-SVDD could not contain the information of negative examples, we proposed a two-class SVDD with negative examples, termed two-class support vector data description (TC-SVDD). The characteristics of the improved support vector data description are discussed. The TC-SVDD is applied to the classification of the UCI data sets.A density-induced SVDD (D-SVDD) is an improved SVDD. Note that the dual optimization problem of the D-SVDD is not such a simple optimization problem as the quadratic programming problem. In fact there has not an effectively solution for the dual optimization problem of the D-SVDD, which makes the D-SVDD be not an easy data description method. To solve the above problem, we proposed an improved data description method called a general density-induced SVDD (GD-SVDD) both with and without negative examples. GD-SVDD not only improved the D-SVDD, but also generalized the SVDD. Both the parameters and the ROC error curve of the GD-SVDD are discussed. The results of different data description methods on all UCI datasets show that the performance of the GD-SVDD is much better than that of the K-NNDD with K=3 and the SVDD with Gaussian kernel.As one of the most important supervised learning methods, the SVM has been applied to fMRI data in a large number of literatures. Firstly, a linear SVM with different inputs including the average volume within a task block and a single volume of a task block was used to explore the asymmetrical cortical activity in motor areas based on a vivo fMRI data of hand-griped experiment. Mour?o-Miranda et al.[22] proposed an SVM approach, termed a spatial–temporal SVM, to obtain a dynamic discrimination map. However, based on multi-subject level, this method could not be adapted to fMRI data of a single object. To overcome this limitation, in the present paper, a SVM-based imaging method was proposed to investigate discriminative brain functional activations dynamically between different tasks of a hand-grasp experiment on a single-subject level. Then the proposed method was applied to a vivo fMRI data of a hand-grasp task, The proposed method can deal with the fMRI data with only of a single subject.A matrix inverse problem is an important type of inverse problem. A large number of results on matrix inverse problem and its optimal approximation problem for different kind of matrices are present. We first studied some properties of R-skew conjugate matrices and anti-Hermitian R-symmetric matrices, then the solutions of the matrix inverse problem and the corresponding optimal approximation problem over R- symmetric and R-skew symmetric matrices.