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Study On The Theory And Application Of Support Vector Machines

Posted on:2007-08-09Degree:DoctorType:Dissertation
Country:ChinaCandidate:S Q RenFull Text:PDF
GTID:1118360215970514Subject:Information and Communication Engineering
Abstract/Summary:PDF Full Text Request
Statistical learning theory (SLT) is a new statistical theory framework established from small samples, and support vector machines (SVM) is a novel powerful machines learning method based on VC dimension theory and structural risk minimization (RSM) principle, which are the important foundation in SLT. SVM has good generalization capability, and also has solved some practical problems such as small samples, nonlinearity, over learning, high dimension and local minimum point etc, which exit in most of the traditional machines learning method.Although, SLT and SVM have very stabile theory foundation and good development foreground, but there still are some problems in SVM which have not been well solved. For example, the kernel fimction adaptive construction and selection, fast training arithmetic, multi-class SVM model and expanding the application field etc.To deal with the above-mentioned problems, this dissertation has carefully studied the pattern recognition theory and application based on SLT and SVM, the main work andnovel results in this thesis are shown as followed.(1) To the binary and multi-class objects classification problem, the thesis differently gives out the strict definition and the distinguishable condition for separating the features by linear classification hyper surface in the feature space. Especially, when the Gram matrix of kernel function is strict positive, then the samples must be linear distinguishable in the feature space which is induced by the kernel function. The results are help to feature selection, kernel function construction and classifiers design.(2) To the binary and multi-class pattern recognition problem, in this thesis, the efficiency rate of features are defined by the contribution to classes margin of each feature, and a novel feature selection algorithm is put forward based on the feature efficiency rate. Because the new feature selection arithmetic is foundation on the RSM, so it can make good compromise between the classification capability and generalized capability, the performance of the new feature selection method, such as classification capability and generalized capability are improved obviously in contrast to the classical Relief method.(3) In this dissertation, a novel kernel function adaptive construction algorithm is put forward, which is based on the feature linear distinguishable condition, the function approaching theory and the properties of kernel function. This new kernel functions include the adaptive polynomial model and the B-Spline model, and the model parameters estimation method are also offered. The two kernel functions have the linear distinguishable and good generalized capability.(4) In this thesis, a new multi-class SVM model called Half-Versus-Half (H-V-H) method is put forward, which is based on increasing the dimension of decision space through extending the classes labels binary code. The new model can be sequentially solved and effectively improve the computational velocity, and it hasn't the region which is unable to test. In a addition, this dissertation has analyzed the generalized capability of H-V-H method.(5) A novel piecewise support vector machines (PSVM) model is provided in this thesis. The PSVM has decreased the complexity of pattern recognition, and improved the computational velocity some times by partitioning the feature space into several subspaces, and it can provide the ability to classify the samples with very complex distribution. Furthermore, this dissertation has analyzed the generalized capability of PSVM model.(6) In the dissertation, the nonlinear curve of autocorrelation coefficients is derived, and the generalized correlated K-distributed clutter simulation principle and the flow diagram are presented in the paper, then a novel model parameters estimation algorithm is also put forward through the parameter decoupling technology. Additional, this dissertation has applied SVM to detect the objects in generalized correlated K-distributed radar clutter.The problems needed further research and some personal ideas for developing SVM are pointed out in conclusion part.
Keywords/Search Tags:statistical learning theory, support vector machines, VC dimension, structural risk minimization, feature separability, kernel function, feature selection, multi-class SVM, piecewise SVM, generalized correlated K-distributed, signal detection
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