Research On Robustness With Noises Of Fuzzy Support Vector Machine

A support vector machine(SVM) is a binary classification model which has been widely used in many fields. But there are still some problems in its application. One problem is that, when mislabeled noises exist in the training set, because of overfitting, support vector machine is very sensitive to them.Based on the support vector machine, and introducing fuzzy membership degrees to make different samples in the training set have different impact s on the training of the classifier, the fuzzy support vector machine(FSVM) is obtained. In order to make FSVM robust to the training noises, the key is to set proper memberships for its training set, through which noises get small memberships and thus have little impacts on the training process.For the setting of memberships for FSVM, two methods are studied in this paper. Based on the C-means clustering method, introduing memberships as variables to be optimized, and adding a noise term to the objective function, a robust C-means algorithm is obtained. The clustering can be implemented in the high-dimension space through a kernel function, which is called the kernel robust C-means algorithm. For the two clustering methods, discrete and continuous method to solve the problem are separately introduced. Apply one of the two clusteri ng methods to the two classes separately, and assign the memberships obtained by the clustering method to the corresponding training samples,then a fuzzy training set is obtained, which is used to train the FSVM. This is a useful way to improve the the learning capacity of the FSVM from noise polluted training set.Based on the fuzzified representation of the C-means algorithm, using K-L information as a regularization term to control the fuzziness of the clustering, and choose the Mahalanobis distance metric, the regularied fuzzy C-means algorithm is derived. Adding a extra noises cluster, a robust regularized fuzzy C-means algorithm is obtained. Given the training set, clustering are implemented for the two classes separately. The membership for each training sample is set as the maximum of its memberships towards all the non-noise clusters, which is used for the training of FSVM. The experiment shows that, the FSVM classifier obtained in this way has a higher classification accuracy for the test set than the standard SVM classifier.Finally, the FSVM based on the kernel robust C-means algorithm is used to the lung CT image segmentation. The experiment shows that, when wrong segmentation is involved in the training CT, compared with the standard SVM, FSVM can get a better segmentation for the test CT image.