Research On Fuzzy Least Squares Support Vector Machine Based On Kernel Fuzzy C-means

Support vector machine is a machine learning method developed on the basis of statistical learning theory. It has solid theoretical basis and visualized geometric interpretation. Support vector machine aims to seek the maximum margin, the support planes are related to a few support vector, so the algorithm has the property of sparsity, but at the same time it lose the consideration of the data structure. There are many noises and outliers in real data, we introduce the fuzziness to overcome this situation. We set small fuzzy membership to the noises and outliers, so that we can reduce the influence to the training.To take the structure of the data into consideration, the within class scatter is brought into the least squares support vector machine. At the same time, we introduce the method of kernel fuzzy c-means to set the fuzziness in the penalty term. The main innovation is as follow:(1)Proposed the least squares support vector machine based on the within class scatter. We bring the within class scatter in Fisher discriminant analysis into the least squares support vector machine, and form the algorithm of the least squares support vector machine based on the within class scatter(WCSLS-SVM). And the dual problem and solution was given. The traditional SVM aims to seek the maximum margin, compared to the traditional algorithms, this new algorithm take the data structure into consideration. The experimental result shows the algorithm has higher accuracy in some data classification.(2)Proposed the KFCM based on linear combination of feature mapping. The feature maps which generate the global and local kernel function are orthogonally processed in the feature space, and then form a new feature map. The solutions to the fuzziness and the weight of the kernel function in the feature space are also given.(3)Proposed the fuzzy WCSLS-SVM based on the KFCM. In order to reduce the influence of the noises and outliers, the fuzzy membership is added to the penalty term, the method of the KFCM based on linear combination of feature mapping in section 4 is applied in the fuzzy WCSLS-SVM. The experiment shows the accuracy is improved, the algorithm is robust for classification problems with noises and outliers.