Fuzzy granular gravitational clustering algorithm

Given the nature of clustering algorithms of finding automatically, or semi-automatically, an unspecified number of clusters, much work has been done in this area. This paper will introduce a proposed gravitational model for finding clusters, the algorithm is based on the gravitational forces from Newton's law of universal gravitation and the output clusters are then fuzzified. Two examples of datasets are compared, one synthetic and one of the Iris, are benchmarked against the fuzzy subtractive algorithm.

[1]  I. Newton Philosophiæ naturalis principia mathematica , 1973 .

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

[3]  Jyh-Shing Roger Jang,et al.  Fuzzy Modeling Using Generalized Neural Networks and Kalman Filter Algorithm , 1991, AAAI.

[4]  Jyh-Shing Roger Jang,et al.  ANFIS: adaptive-network-based fuzzy inference system , 1993, IEEE Trans. Syst. Man Cybern..

[5]  Dimitar Filev,et al.  Generation of Fuzzy Rules by Mountain Clustering , 1994, J. Intell. Fuzzy Syst..

[6]  Witold Pedrycz,et al.  Conditional Fuzzy C-Means , 1996, Pattern Recognit. Lett..

[7]  Hans-Peter Kriegel,et al.  A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise , 1996, KDD.

[8]  Sukhamay Kundu,et al.  Gravitational clustering: a new approach based on the spatial distribution of the points , 1999, Pattern Recognit..

[9]  Witold Pedrycz,et al.  Granular Computing - The Emerging Paradigm , 2007 .

[10]  Olfa Nasraoui,et al.  A New Gravitational Clustering Algorithm , 2003, SDM.

[11]  Olfa Nasraoui,et al.  RAIN: data clustering using randomized interactions between data points , 2004, 2004 International Conference on Machine Learning and Applications, 2004. Proceedings..

[12]  Lianwen Jin,et al.  A New Simplified Gravitational Clustering Method for Multi-prototype Learning Based on Minimum Classification Error Training , 2006, IWICPAS.

[13]  Andrzej Bargiela,et al.  Toward a Theory of Granular Computing for Human-Centered Information Processing , 2008, IEEE Transactions on Fuzzy Systems.

[14]  Xin Rui,et al.  An Improved Clustering Algorithm , 2008, 2008 International Symposium on Computational Intelligence and Design.

[15]  Wesley E. Snyder,et al.  Pattern Recognition by Cluster Accumulation , 2010, 2010 IEEE Intelligent Vehicles Symposium.

[16]  Giles Oatley,et al.  Data mining and crime analysis , 2011, WIREs Data Mining Knowl. Discov..

[17]  Witold Pedrycz,et al.  Design of interval type-2 fuzzy models through optimal granularity allocation , 2011, Appl. Soft Comput..

[18]  Mandava Rajeswari,et al.  Multi-objective nature-inspired clustering and classification techniques for image segmentation , 2011, Appl. Soft Comput..

[19]  Oscar Castillo,et al.  An optimization method for designing type-2 fuzzy inference systems based on the footprint of uncertainty using genetic algorithms , 2012, Expert Syst. Appl..

[20]  Milos Manic,et al.  General Type-2 Fuzzy C-Means Algorithm for Uncertain Fuzzy Clustering , 2012, IEEE Transactions on Fuzzy Systems.