fclust: An R Package for Fuzzy Clustering

Fuzzy clustering methods discover fuzzy partitions where observations can be softly assigned to more than one cluster. The package fclust is a toolbox for fuzzy clustering in the R programming language. It not only implements the widely used fuzzy k-means (FkM) algorithm, but also many FkM variants. Fuzzy cluster similarity measures, cluster validity indices and cluster visualization tools are also offered. In the current version, all the functions are rewritten in the C++ language allowing their application in large-size problems. Moreover, new fuzzy relational clustering algorithms for partitioning qualitative/mixed data are provided together with an improved version of the so-called Gustafson-Kessel algorithm to avoid singularity in the cluster covariance matrices. Finally, it is now possible to automatically select the number of clusters by means of the available fuzzy cluster validity indices.

[1]  J. Gower A General Coefficient of Similarity and Some of Its Properties , 1971 .

[2]  William M. Rand,et al.  Objective Criteria for the Evaluation of Clustering Methods , 1971 .

[3]  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.

[4]  Dirk Eddelbuettel,et al.  Seamless R and C++ Integration with Rcpp , 2013 .

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

[6]  Wei Pan,et al.  Measuring Mathematics Anxiety: Psychometric Analysis of a Bidimensional Affective Scale , 2009 .

[7]  P. Jaccard,et al.  Etude comparative de la distribution florale dans une portion des Alpes et des Jura , 1901 .

[8]  Sadaaki Miyamoto,et al.  Spherical k-Means++ Clustering , 2015, MDAI.

[9]  J. Kruskal Nonmetric multidimensional scaling: A numerical method , 1964 .

[10]  Rui-Ping Li,et al.  A maximum-entropy approach to fuzzy clustering , 1995, Proceedings of 1995 IEEE International Conference on Fuzzy Systems..

[11]  M. Cugmas,et al.  On comparing partitions , 2015 .

[12]  Conrad Sanderson,et al.  RcppArmadillo: Accelerating R with high-performance C++ linear algebra , 2014, Comput. Stat. Data Anal..

[13]  Ricardo J. G. B. Campello,et al.  A fuzzy extension of the Rand index and other related indexes for clustering and classification assessment , 2007, Pattern Recognit. Lett..

[14]  Luca Scrucca,et al.  mclust 5: Clustering, Classification and Density Estimation Using Gaussian Finite Mixture Models , 2016, R J..

[15]  Kurt Hornik,et al.  A CLUE for CLUster Ensembles , 2005 .

[16]  Frank Klawonn,et al.  Fuzzy Cluster Analysis of Larger Data Sets , 2009, Scalable Fuzzy Algorithms for Data Management and Analysis.

[17]  Rajesh N. Davé,et al.  Robust fuzzy clustering of relational data , 2002, IEEE Trans. Fuzzy Syst..

[18]  Christina Gloeckner,et al.  Modern Applied Statistics With S , 2003 .

[19]  Anupam Joshi,et al.  Low-complexity fuzzy relational clustering algorithms for Web mining , 2001, IEEE Trans. Fuzzy Syst..

[20]  Rajesh N. Davé,et al.  Validating fuzzy partitions obtained through c-shells clustering , 1996, Pattern Recognit. Lett..

[21]  Rajesh N. Davé,et al.  Characterization and detection of noise in clustering , 1991, Pattern Recognit. Lett..

[22]  J. C. Schlimmer,et al.  Concept acquisition through representational adjustment , 1987 .

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

[24]  Masao Mukaidono,et al.  Gaussian clustering method based on maximum-fuzzy-entropy interpretation , 1999, Fuzzy Sets Syst..

[25]  Ricardo J. G. B. Campello,et al.  A fuzzy extension of the silhouette width criterion for cluster analysis , 2006, Fuzzy Sets Syst..

[26]  R. Abelson,et al.  Multidimensional scaling of facial expressions. , 1962, Journal of experimental psychology.

[27]  Enrique H. Ruspini,et al.  Numerical methods for fuzzy clustering , 1970, Inf. Sci..

[28]  Uzay Kaymak,et al.  Improved covariance estimation for Gustafson-Kessel clustering , 2002, 2002 IEEE World Congress on Computational Intelligence. 2002 IEEE International Conference on Fuzzy Systems. FUZZ-IEEE'02. Proceedings (Cat. No.02CH37291).

[29]  Xavier Font,et al.  The management of vegetation classifications with fuzzy clustering , 2010 .

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

[31]  Frank Klawonn,et al.  Fuzzy clustering with polynomial fuzzifier function in connection with m-estimators , 2011 .

[32]  Michalis Vazirgiannis,et al.  c ○ 2001 Kluwer Academic Publishers. Manufactured in The Netherlands. On Clustering Validation Techniques , 2022 .

[33]  Sadaaki Miyamoto,et al.  Fuzzy c-means as a regularization and maximum entropy approach , 1997 .

[34]  Paolo Giordani,et al.  A toolbox for fuzzy clustering using the R programming language , 2015, Fuzzy Sets Syst..

[35]  Ali S. Hadi,et al.  Finding Groups in Data: An Introduction to Chster Analysis , 1991 .