Balance Support Vector Machines Locally Using the Structural Similarity Kernel

A structural similarity kernel is presented in this paper for SVM learning, especially for learning with imbalanced datasets. Kernels in SVM are usually pairwise, comparing the similarity of two examples only using their feature vectors. By building a neighborhood graph (kNN graph) using the training examples, we propose to utilize the similarity of linking structures of two nodes as an additional similarity measure. The structural similarity measure is proven to form a positive definite kernel and is shown to be equivalent to a regularization term that encourages balanced weights in all local neighborhoods. Analogous to the unsupervised HITS algorithm, the structural similarity kernel turns hub scores into signed authority scores, and is particularly effective in dealing with imbalanced learning problems. Experimental results on several benchmark datasets show that structural similarity can help the linear and the histogram intersection kernel to match or surpass the performance of the RBF kernel in SVM learning, and can significantly improve imbalanced learning results.