Agglomerative hierarchical kernel spectral data clustering

Abstract

In this paper we extend the agglomerative hierarchical kernel spectral clustering (AH-KSC [1]) technique from networks to datasets and images. The kernel spectral clustering (KSC) technique builds a clustering model in a primal-dual optimization framework. The dual solution leads to an eigen-decomposition. The clustering model consists of kernel evaluations, projections onto the eigenvectors and a powerful out-of-sample extension property. We first estimate the optimal model parameters using the balanced angular fitting (BAF) [2] criterion. We then exploit the eigen-projections corresponding to these parameters to automatically identify a set of increasing distance thresholds. These distance thresholds provide the clusters at different levels of hierarchy in the dataset which are merged in an agglomerative fashion as shown in [1], [4]. We showcase the effectiveness of the AH-KSC method on several datasets and real world images. We compare the AH-KSC method with several agglomerative hierarchical clustering techniques and overcome the issues of hierarchical KSC technique proposed in [5].