Convexity dependent anisotropic diffusion for mode detection in cluster analysis

In cluster analysis, regions of high local density of data points, which might correspond to significant clusters, can be found from the modes of the underlying probability density function (pdf). However, due to irregularities in the data distribution, the modes and the valleys of the pdf are often ill defined so that mode detection can lead to poor results. In this paper, an anisotropic diffusion process is proposed in order to reinforce the smoothing of the pdf in the modal regions where it is concave and in the valleys where it is convex, while preserving the boundaries between them. This adaptive smoothing procedure is combined with a strategy which consists in applying a forward diffusion when the pdf is concave and a backward diffusion when it is convex. Iterations of this convexity dependent anisotropic diffusion tend to enhance the modes and to deepen the valleys of the underlying pdf, so that mode detection becomes trivial. Experiment and comparative results with some well-known clustering algorithms over simulated datasets show the effectiveness of the proposed clustering method.