Design And Application Of Relevance Vector Machine Classifier Based On Probit Model

Support Vector Machine (SVM) and Relevance Vector Machine (RVM) are twokinds of popular classifiers, which are usually utilized now. SVM, which is originallyproposed by Cortes and Vapnik in1995, has the special advantages in dealing withsmall-size, non-linear and high dimensional data. RVM, whose model function is sameas that of SVM, is first introduced by Tipping in2001based on Bayesian framework.Compared with SVM, RVM can derive accurate prediction models, while offering anumber of additional advantages. These include the benefits of absent estimation oferror parameter, probabilistic output value about each class, and the facility to utilizekernel functions which are not need to satisfy Mercer’s condition.SVM and RVM were originally designed for the binary classification problem.Unfortunately, in the real application we often meet multiclass classification problem.How to effectively extend them for multiclass classification is still an open researchissue. Several methods have been proposed to construct a multiclass classifier bycombining several binary classifiers. Based on previous work, this thesis modifies thetraditional RVM classifier based on Probit model with applications to binaryclassification and multiclass classification. The main content of this dissertation issummarized as follows:Bayesian learning theory is described in the second chapter, including the Bayesiantheory and the Variational Bayesian (VB) theory.In the third chapter, we introduce the realization of the binary RVM classifier. Theconventional RVM classifier is firstly presented. Then we develop the binary RVMclassifier based on Probit model, where the solution of posterior parameters and theprediction distribution are deduced based on VB theory. Finally their performances arecompared based on synthetic data, benchmark UCI data, and measured radar data,respectively.We do research on the multiclass RVM classifier in the forth chapter. At thebeginning, the conventional multiclass RVM classifier is introduced. Then themulticlass RVM classifier is implemented based on Probit model, where the solution ofposterior parameters and the prediction distribution are also deduced based on VBtheory. Finally, their performances are also compared based on synthetic data,benchmark UCI data, and measured radar data, respectively.For the convenience of the usage of the proposed RVM classifer, we compile a RVM classifier software based on Visual C++and MATLAB hybrid programming. Thebasic programming theory and functions of the software is introduced in the fifthchapter. This software, which only need to load data and set some parameters of theclassifier, can directly export the classification and rejection results.