New Clustering Algorithms for the Support Vector

7 This study presents two new clustering algorithms for partition of data sam8 ples for the Support Vector Machine (SVM) based hierarchical classification. 9 A divisive (top-down) approach is considered in which a set of classes is 10 automatically separated into two smaller groups at each node of the hierar11 chy. The first algorithm splits the data samples based on a variation of the 12 Normalized Cuts (NCuts) clustering algorithm wherein the weights of adja13 cency matrix are modified to utilize class membership in the process. The 14 second algorithm also uses the NCuts clustering; however, it considers the in15 volved classes rather than the individual data samples. It uses the minimum 16 distances between the convex hulls of classes as a distance measure for deter17 mining the weights of the graph. Splits are determined for both algorithms 18 based on the eigenvector corresponding to the second smallest eigenvalue of 19 a Laplacian matrix, and it is observed that the proposed algorithms generate 20 well-separated and well-balanced clusters. Unlike other clustering methods 21 used for this purpose, the methods in the present study are found to be 22 more suitable when SVMs are used as base classifiers. As demonstrated in 23 Preprint submitted to Pattern Recognition Letters March 26, 2010 the experiments, the proposed clustering algorithms are integrated into the 24 hierarchical SVM classifiers, which results in significantly improved testing 25 times with a negligible decrease in classification accuracies as compared to 26 the traditional multi-class SVMs. 27