Theoretical Analysis of Dynamic Clustering

Details Theoretical Analysis of Dynamic Clustering Theoretical Analysis of Dynamic Clustering

2012-04-15

arxiv.org/abs/1204.3235v1

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A theoretical framework is derived to investigate the convergence and stability of dynamic clustering methods which transform data according to different laws of attraction to achieve autonomous partitions. On applying the conservation law, we establish partial differential equations to prescribe the successive transformations of the underlying probability densities in dynamic clustering. These partial differential equations correspond to anti-diffusion processes and are solved analytically. We show that a broad class of unsupervised shrinking or clustering methods including the mean-shift algorithm are intrinsically unstable except for independent normal densities. Theoretical results of the supervised dynamic clustering processes indicate that an effective supervision must be chosen judiciously to ensure a correct convergence since a universally optimal supervising function does not exist.

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