Statistics and Its Interface

Volume 9 (2016)

Number 2

Convergence and stability analysis of mean-shift algorithm on large data sets

Pages: 159 – 170

DOI: http://dx.doi.org/10.4310/SII.2016.v9.n2.a4

Authors

Xiaogang Wang (Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada)

Weiliang Qiu (Channing Division of Network Medicine, Brigham and Women’s Hospital, Harvard Medical School, Boston, Massachusetts, U.S.A.)

Jianhong Wu (Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada)

Abstract

We present theoretical convergent analysis of mean-shift type of clustering methods for large data sets. It is proved that correct convergence for unsupervised mean shift type of algorithms relies on its ability to successfully transform data points to be clustered into data patterns of a multivariate normal distribution. Our analytical stability analysis suggests that a judiciously chosen supervision mechanism might be essential for correct convergence in dynamical clustering. The proposed theoretical framework could be used to study other dynamical clustering methods.

Keywords

anti-diffusion, convergence, conservation law, dynamic clustering, entropy, partial differential equations

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