Gaussian Process Classification Algorithm And Application Research

Gaussian process is a collection of random variable, any number of randomcombinations of variables in the collection obey a joint Gaussian distribution. Gaussianprocess deter mined by the mean function and covariance function uniquely. One Gaussianprocess corre sponds to a covariance function, which is the kernel function. How to choosethe covariance function is the key to the training process. A common method is useparameters to signify the covariance function, and adjust the parameters in the trainingprocess. The classic approachs include optimization methods, such as scalar conjugategradient method; and sampling method, such as hybrid Monte Carlo method. They are alleffective ways to get the desired covariance function.The main advantage of the Gaussianprocess model include: it is a non-parametric probability model, not only give outputprediction for the unknown in put, but also give the accuracy of the prediction parameters (iethe estimat ed variance); it can express a prior knowledge of the process in the form of a prioriprobability, thereby improving the performance of the process model; compared to neuralnetworks and support vector machine method, the parameters of Gaussian process model aresignificantly reduced, thus the parameter optimization is relatively easy and convergenceeasier.The main contents of the thesis are outlined as follows:1．Firstly, we introduce the basics knowledge about Gaussian process, and overview twoGaussian approximation algorithms for the binary classification: Laplace approximationalgorithm and expectation propagation approximation algorithm.2．We analyze the different effects of these two algorithms under the classification.Consider the different characteristics of the global nuclear functions and local kernelfunctions, we propose the Gaussian classification method combined with the combination ofkernel functions. The advantages of the combined kernel function is: learning ability andgeneralization ability of the different kernel functions have their pros and cons, so a newkernel function combined with different kernel functions can has a good learning ability andgeneralization ability.3．Based on the Gaussian binary classification, we developed on the Gaussian mulvariateclassification methods. At the same time, we compare the experiment results to the supportvector machine,4．Based on the features of the rough set and Gaussian processes, we propose a gaussianprocess classification method based on rough set. This method takes full advantage of rough set to handle the large amount of data, eliminating redundant information advantages,reducing the computation time of the Gaussian process.