Compactly supported graph building for spectral clustering

In spectral clustering approaches is of great importance how is built the graph representation over a data set, being reflected in the achieved clustering performance. In this work is introduced a methodology to build a graph representation of a given data, based on compactly supported radial basis functions which enables to highlight relevant pair-wise sample relationships. To tune such functions, an objective function is proposed, which aims to find a trade-off between a similarity and a sparsity measure, allowing to achieve a suitable local and global data structure representation. Synthetic and real-world data sets are tested. Results shows how proposed method improves clustering results, specially for an image segmentation task.