Locally-scaled spectral clustering using empty region graphs

Authors:
Carlos D. Correa;Peter Lindstrom
Affiliations:
Lawrence Livermore National Laboratory, Livermore, CA, USA;Lawrence Livermore National Laboratory, Livermore, CA, USA
Venue:
Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
Year:
2012

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Abstract

This paper introduces a new method for estimating the local neighborhood and scale of data points to improve the robustness of spectral clustering algorithms. We employ a subset of empty region graphs - the β-skeleton - and non-linear diffusion to define a locally-adapted affinity matrix, which, as we demonstrate, provides higher quality clustering than conventional approaches based on κ nearest neighbors or global scale parameters. Moreover, we show that the clustering quality is far less sensitive to the choice of β and other algorithm parameters, and to transformations such as geometric distortion and random perturbation. We summarize the results of an empirical study that applies our method to a number of 2D synthetic data sets, consisting of clusters of arbitrary shape and scale, and to real multi-dimensional classification examples from benchmarks, including image segmentation.