Mean shift-based clustering

In this paper, a mean shift-based clustering algorithm is proposed. The mean shift is a kernel-type weighted mean procedure. Herein, we first discuss three classes of Gaussian, Cauchy and generalized Epanechnikov kernels with their shadows. The robust properties of the mean shift based on these three kernels are then investigated. According to the mountain function concepts, we propose a graphical method of correlation comparisons as an estimation of defined stabilization parameters. The proposed method can solve these bandwidth selection problems from a different point of view. Some numerical examples and comparisons demonstrate the superiority of the proposed method including those of computational complexity, cluster validity and improvements of mean shift in large continuous, discrete data sets. We finally apply the mean shift-based clustering algorithm to image segmentation.

[1]  Dorin Comaniciu,et al.  An Algorithm for Data-Driven Bandwidth Selection , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

[2]  Miin-Shen Yang,et al.  A cluster validity index for fuzzy clustering , 2005, Pattern Recognit. Lett..

[3]  B. Ripley,et al.  Robust Statistics , 2018, Encyclopedia of Mathematical Geosciences.

[4]  C. D. Kemp,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[5]  Keinosuke Fukunaga,et al.  Introduction to statistical pattern recognition (2nd ed.) , 1990 .

[6]  Hichem Frigui,et al.  Clustering by competitive agglomeration , 1997, Pattern Recognit..

[7]  Zhi Liu,et al.  Mean shift blob tracking with kernel histogram filtering and hypothesis testing , 2005, Pattern Recognit. Lett..

[8]  Jun Liu,et al.  Unsupervised texture segmentation with one-step mean shift and boundary Markov random fields , 2001, Pattern Recognit. Lett..

[9]  Miin-Shen Yang,et al.  A modified mountain clustering algorithm , 2005, Pattern Analysis and Applications.

[10]  James C. Bezdek,et al.  Pattern Recognition with Fuzzy Objective Function Algorithms , 1981, Advanced Applications in Pattern Recognition.

[11]  Jin Hyung Kim,et al.  Texture-Based Approach for Text Detection in Images Using Support Vector Machines and Continuously Adaptive Mean Shift Algorithm , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

[12]  Mark A. Girolami,et al.  Mercer kernel-based clustering in feature space , 2002, IEEE Trans. Neural Networks.

[13]  Nello Cristianini,et al.  An Introduction to Support Vector Machines and Other Kernel-based Learning Methods , 2000 .

[14]  Yizong Cheng,et al.  Mean Shift, Mode Seeking, and Clustering , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[15]  James M. Keller,et al.  A possibilistic approach to clustering , 1993, IEEE Trans. Fuzzy Syst..

[16]  Nikhil R. Pal,et al.  Mountain and subtractive clustering method: Improvements and generalizations , 2000 .

[17]  Vladimir Vapnik,et al.  Statistical learning theory , 1998 .

[18]  Gunnar Rätsch,et al.  An introduction to kernel-based learning algorithms , 2001, IEEE Trans. Neural Networks.

[19]  Rajesh N. Davé,et al.  Robust clustering methods: a unified view , 1997, IEEE Trans. Fuzzy Syst..

[20]  Philippe Van Ham,et al.  Tracking of migrating cells under phase-contrast video microscopy with combined mean-shift processes , 2005, IEEE Transactions on Medical Imaging.

[21]  Keinosuke Fukunaga,et al.  Introduction to Statistical Pattern Recognition , 1972 .

[22]  Peng Zhang,et al.  A Highly Robust Estimator Through Partially Likelihood Function Modeling and Its Application in Computer Vision , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[23]  Hichem Frigui,et al.  Fuzzy and possibilistic shell clustering algorithms and their application to boundary detection and surface approximation. II , 1995, IEEE Trans. Fuzzy Syst..

[24]  Haifeng Chen,et al.  Robust Fusion of Uncertain Information , 2003, 2003 Conference on Computer Vision and Pattern Recognition Workshop.

[25]  Dorin Comaniciu,et al.  Kernel-Based Object Tracking , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

[26]  Aly A. Farag,et al.  A modified fuzzy c-means algorithm for bias field estimation and segmentation of MRI data , 2002, IEEE Transactions on Medical Imaging.

[27]  Gerardo Beni,et al.  A Validity Measure for Fuzzy Clustering , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[28]  R. Yager,et al.  Approximate Clustering Via the Mountain Method , 1994, IEEE Trans. Syst. Man Cybern. Syst..

[29]  Xiaomin Liu,et al.  A Least Biased Fuzzy Clustering Method , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[30]  Lawrence O. Hall,et al.  An investigation of mountain method clustering for large data sets , 1997, Pattern Recognit..

[31]  Catherine Blake,et al.  UCI Repository of machine learning databases , 1998 .

[32]  Miin-Shen Yang,et al.  Alternative c-means clustering algorithms , 2002, Pattern Recognit..

[33]  Larry D. Hostetler,et al.  The estimation of the gradient of a density function, with applications in pattern recognition , 1975, IEEE Trans. Inf. Theory.

[34]  Hichem Frigui,et al.  A Robust Competitive Clustering Algorithm With Applications in Computer Vision , 1999, IEEE Trans. Pattern Anal. Mach. Intell..

[35]  Nello Cristianini,et al.  An introduction to Support Vector Machines , 2000 .

[36]  Francesco Camastra,et al.  A Novel Kernel Method for Clustering , 2005, IEEE Trans. Pattern Anal. Mach. Intell..

[37]  Y. Fukuyama,et al.  A new method of choosing the number of clusters for the fuzzy c-mean method , 1989 .

[38]  J. Bezdek.  Cluster Validity with Fuzzy Sets , 1973 .

[39]  Miin-Shen Yang,et al.  A similarity-based robust clustering method , 2004, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[40]  Stephen L. Chiu,et al.  Fuzzy Model Identification Based on Cluster Estimation , 1994, J. Intell. Fuzzy Syst..

[41]  Daoqiang Zhang,et al.  Robust image segmentation using FCM with spatial constraints based on new kernel-induced distance measure , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[42]  Geoffrey C. Fox,et al.  A deterministic annealing approach to clustering , 1990, Pattern Recognit. Lett..

[43]  Rose,et al.  Statistical mechanics and phase transitions in clustering. , 1990, Physical review letters.

[44]  Dorin Comaniciu,et al.  Mean Shift: A Robust Approach Toward Feature Space Analysis , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[45]  Carlo Tomasi,et al.  Mean shift is a bound optimization , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[46]  Charles V. Stewart,et al.  MINPRAN: A New Robust Estimator for Computer Vision , 1995, IEEE Trans. Pattern Anal. Mach. Intell..