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Mathematical Problems in Engineering
Volume 2017 (2017), Article ID 3696850, 11 pages
Research Article

A Clustering Method for Data in Cylindrical Coordinates

1University of Electro-Communications, 1-5-1 Chofugaoka, Chofu, Tokyo 182-8585, Japan
2Department of Computer and Information Engineering, National Institute of Technology, Tsuyama College, 654-1 Numa, Tsuyama, Okayama 708-8506, Japan

Correspondence should be addressed to Kazuhisa Fujita

Received 7 April 2017; Revised 18 July 2017; Accepted 16 August 2017; Published 27 September 2017

Academic Editor: Ivan Giorgio

Copyright © 2017 Kazuhisa Fujita. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We propose a new clustering method for data in cylindrical coordinates based on the -means. The goal of the -means family is to maximize an optimization function, which requires a similarity. Thus, we need a new similarity to obtain the new clustering method for data in cylindrical coordinates. In this study, we first derive a new similarity for the new clustering method by assuming a particular probabilistic model. A data point in cylindrical coordinates has radius, azimuth, and height. We assume that the azimuth is sampled from a von Mises distribution and the radius and the height are independently generated from isotropic Gaussian distributions. We derive the new similarity from the log likelihood of the assumed probability distribution. Our experiments demonstrate that the proposed method using the new similarity can appropriately partition synthetic data defined in cylindrical coordinates. Furthermore, we apply the proposed method to color image quantization and show that the methods successfully quantize a color image with respect to the hue element.