Exemplar Selection via Leave-One-Out Kernel Averaged Gradient Descent and Subtractive Clustering

Scalable data mining and machine learning require data abstractions. This work presents a scheme for automatic selection of representative real data points as exemplars. Currently few algorithms can select representative exemplars from the data. K-medoids and Affinity Propagation are such algorithms. K-medoids requires the number of exemplars to be given in advance, as well as a dissimilarity matrix in memory. Affinity propagation automatically finds exemplars as well as their k number but it requires a similarity matrix in memory. A fast algorithm, which works without the need of any matrix in memory, is Subtractive Clustering, but it requires user-defined bandwidth parameters. The essence of the proposed solution relies on a leave-one-out kernel averaged gradient descent that automatically estimates a suitable bandwidth parameter from the data in conjunction with Subtractive Clustering algorithm that further uses this bandwidth for extracting the most representative exemplars, without initial knowledge of their number. Experimental simulations and comparisons of the proposed solution with Affinity propagation exemplar selection on various benchmark datasets seem promising.