Optimal Dimensionality of Metric Space for Classification

For large-scale classification problems, the training samples can be clustered beforehand as a downsampling pre-process, and then only the obtained clusters are used for training. Motivated by such assumption, we proposed a classification algorithm, Support Cluster Machine (SCM), within the learning framework introduced by Vapnik. For the SCM, a compatible kernel is adopted such that a similarity measure can be handled not only between clusters in the training phase but also between a cluster and a vector in the testing phase. We also proved that the SCM is a general extension of the SVM with the RBF kernel. The experimental results confirm that the SCM is very effective for largescale classification problems due to significantly reduced computational costs for both training and testing and comparable classification accuracies. As a by-product, it provides a promising approach to dealing with privacy-preserving data mining problems.