Generalization Performance Of SVMC Based On Markov Chain Samples

Support vector machine classification algorithm is one of the most widely used methods for data classification.What is more,the algorithm plays an irreplaceable role in the field of image processing and other fields related to image recognition(such as image segmentation)and has a great performance ability in the field of remote sensing image analysis which is included in the geographic remote sensing system.In addition,the support vector machine classification algorithm has a good generalization ability,which means it can solve the problem that can not be solved under some classical system: it can solve linear inseparable problem in lower-dimension-space and avoid the “curse of dimensionality” problem.The core idea of the algorithm is to map the data(data in the lower-dimension-space is linearly inseparable)from lower-dimensionspace to higher-dimension-space by using kernel function in the case where the dataset capacity is limited.Kernel function greatly reduces the difficulty of the problem and also reduces many unnecessary troubles.We chose two different kernel functions(linear kernel and Gaussian kernel)in this thesis and make the theoretical analysis and numerical experimental analysis of support vector machine algorithm based on two different kernel functions.Classical support vector machine classification problem are all based on the assumption that samples are independent and identically distributed,no matter in theoretical analysis or in practical applications,the assumption that samples are independent is very strong.In many machine learning applications,such as market prediction,system diagnosis and speech recognition,their samples are natural in nature,and they are not independent.Therefore,we can not make any hypothesis about the distribution of these samples,let alone assume the samples satisfy independent and identically distributed.Markov chain is widely used in practical issues and shows a good performace ability in many aspects.Consequently,we change the assumption that samples are independent to that samples are uniformly ergodic Markov chains,which make it convenient for us to study the generalization performance of support vector machine classification algorithms: first of all,we make the theoretical research about the generalization ability of linear kernel support vector machine classification algorithms based on uniformly ergodic Markov chains,however most of the datasets are linear inseparable,so we make theoretical research about Gaussian kernel support vector machine classification algorithms based on uniformly ergodic Markov chains;Then,we prove that the linear kernel and Gaussian kernel support vector machine classification algorithm based on uniformly ergodic Markov chains are consistent,and we present the convergence rate of linear kernel and Gaussian kernel support vector machine classification algorithm based on uniformly ergodic Markov chains,respectively.In addition to theoretical research,we also make the experimental analysis of linear kernel and Gaussian kernel support vector machine classification algorithm.In practice,we find that learning algorithm is time-consuming in the case where the datasets are infinty.Inspired by Markov chain Monte Carlo method,we introduce a new Markov sampling algorithm which enables us to obtain the uniformly ergodic Markov chains that we needed for classification.Secondly,we make a numerical experiment of learning performance of support vector machine classification algorithm based on the uniformly ergodic markov chains,and then make comparison with the algorithm based on independent and identically distributed.