In this paper, I proposed a method to classify multi-class problem. To achieve that goal I proposed a modified SOM(Self-Organizing Map), so called K-SOM(Kernel Self-Organizing Map), and how to use the result of SOM to combine it with Support Vector Machine. SOM is an approach to extract a topological relationship among data. And SVM is the newest method for classification. However, SVM deals data not on the original data space but on the transformed kernel space. In this case, transformed kernel space has much higher or infinite dimension than original data space. If we select proper kernel function and then on kernel space transformed data distribution is well formed and linearly separable-like, SVM can provide much better classification accuracy than on original data space. To combine SOM with SVM, space matching is necessary. That is, SOM is also analyzed on the kernel space. It is more reasonable and guarantee much better clustering performance than conventional Kohonen SOM.
From the SOM result, I constructed a hierarchical decision tree by using scattering measure. SVM can solve only binary classification problem. Therefore we need to original problem to the combination of binary sub-problems. In this process, allowing overlapping between groups can provide a chance to correct the misclassified data again. Because SOM result represent the relationship among class, applying a proper measure on this result can give hierarchical decision tree easily. Most of errors on classification problem are occurred on the confusing area. By allowing overlapping same class between two groups, hierarchical SVM scheme provide a better performance and from the structural properties of tree H-SVM give a better speed to classify data.
