Fuzzy clustering of probability density functions

ABSTRACT Basing on L1-distance and representing element of cluster, the article proposes new three algorithms in Fuzzy Clustering of probability density Functions (FCF). They are hierarchical approach, non-hierarchical approach and the algorithm to determine the optimal number of clusters and the initial partition matrix to improve the qualities of established clusters in non-hierarchical approach. With proposed algorithms, FCF has more advantageous than Non-fuzzy Clustering of probability density Functions. These algorithms are applied for recognizing images from Texture and Corel database and practical problem about studying and training marks of students at an university. Many Matlab programs are established for computation in proposed algorithms. These programs are not only used to compute effectively the numerical examples of this article but also to be applied for many different realistic problems.

[1]  N. Turkkan,et al.  Bayesian Analysis in the L1-Norm of the Mixing Proportion Using Discriminant Analysis , 2006 .

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

[3]  Robin Sibson,et al.  SLINK: An Optimally Efficient Algorithm for the Single-Link Cluster Method , 1973, Comput. J..

[4]  Qinghua Hu,et al.  Large margin clustering on uncertain data by considering probability distribution similarity , 2015, Neurocomputing.

[5]  James C. Bezdek,et al.  On cluster validity for the fuzzy c-means model , 1995, IEEE Trans. Fuzzy Syst..

[6]  René Vidal,et al.  Unsupervised Riemannian Clustering of Probability Density Functions , 2008, ECML/PKDD.

[7]  Debasis Sengupta,et al.  Classification Using Kernel Density Estimates , 2006, Technometrics.

[8]  F. James Rohlf,et al.  12 Single-link clustering algorithms , 1982, Classification, Pattern Recognition and Reduction of Dimensionality.

[9]  T. Pham-Gia,et al.  Clustering probability distributions , 2010 .

[10]  Mohammad Shojafar,et al.  FR trust: a fuzzy reputation-based model for trust management in semantic P2P grids , 2014, Int. J. Grid Util. Comput..

[11]  Thu Pham-Gia,et al.  Statistical Discrimination Analysis Using the Maximum Function , 2008, Commun. Stat. Simul. Comput..

[12]  J. C. Dunn,et al.  A Fuzzy Relative of the ISODATA Process and Its Use in Detecting Compact Well-Separated Clusters , 1973 .

[13]  K. Fukunaga.  Chapter 11 – CLUSTERING , 1990 .

[14]  Pavel Pudil,et al.  Introduction to Statistical Pattern Recognition , 2006 .

[15]  Angel R. Martinez,et al.  Computational Statistics Handbook with MATLAB , 2001 .

[16]  Thu Pham-Gia,et al.  Bounds for the Bayes Error in Classification: A Bayesian Approach Using Discriminant Analysis , 2007, Stat. Methods Appl..

[17]  David W. Scott,et al.  Multivariate Density Estimation: Theory, Practice, and Visualization , 1992, Wiley Series in Probability and Statistics.

[18]  Steven Furnell,et al.  D-FICCA: A density-based fuzzy imperialist competitive clustering algorithm for intrusion detection in wireless sensor networks , 2014 .

[19]  Vilém Novák,et al.  Fuzzy Set , 2009, Encyclopedia of Database Systems.

[20]  Alex Pentland,et al.  Big Data and Management , 2014 .

[21]  Wen-Liang Hung,et al.  Automatic clustering algorithm for fuzzy data , 2015 .

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

[23]  P. J. Green,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[24]  Donald Gustafson,et al.  Fuzzy clustering with a fuzzy covariance matrix , 1978, 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes.

[25]  S. R,et al.  Data Mining with Big Data , 2017, 2017 11th International Conference on Intelligent Systems and Control (ISCO).

[26]  U. Kaymak,et al.  Compatible cluster merging for fuzzy modelling , 1995, Proceedings of 1995 IEEE International Conference on Fuzzy Systems..

[27]  Isak Gath,et al.  Unsupervised Optimal Fuzzy Clustering , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[28]  J. Wade Davis,et al.  Statistical Pattern Recognition , 2003, Technometrics.

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

[30]  N. Glick.  Separation and probability of correct classification among two or more distributions , 1973 .

[31]  Wen-Liang Hung,et al.  An automatic clustering algorithm for probability density functions , 2015 .

[32]  Raghu Krishnapuram,et al.  Fitting an unknown number of lines and planes to image data through compatible cluster merging , 1992, Pattern Recognit..

[33]  D. Defays,et al.  An Efficient Algorithm for a Complete Link Method , 1977, Comput. J..

[34]  K. Matusita.  On the notion of affinity of several distributions and some of its applications , 1967 .

[35]  Godfried T. Toussaint,et al.  Some Inequalities Between Distance Measures for Feature Evaluation , 1972, IEEE Transactions on Computers.