NCM: Neutrosophic c-means clustering algorithm

In this paper, a new clustering algorithm, neutrosophic c-means (NCM), is introduced for uncertain data clustering, which is inspired from fuzzy c-means and the neutrosophic set framework. To derive such a structure, a novel suitable objective function is defined and minimized, and the clustering pr...

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Published in:Pattern recognition Vol. 48; no. 8; pp. 2710 - 2724
Main Authors: Guo, Yanhui, Sengur, Abdulkadir
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.08.2015
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ISSN:0031-3203, 1873-5142
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Abstract In this paper, a new clustering algorithm, neutrosophic c-means (NCM), is introduced for uncertain data clustering, which is inspired from fuzzy c-means and the neutrosophic set framework. To derive such a structure, a novel suitable objective function is defined and minimized, and the clustering problem is formulated as a constrained minimization problem, whose solution depends on the objective function. In the objective function, two new types of rejection have been introduced: the ambiguity rejection which concerns the patterns lying near the cluster boundaries, and the distance rejection dealing with patterns that are far away from all the clusters. These measures are able to manage uncertainty due to imprecise and/or incomplete definition of the clusters. We conducted several experiments with synthetic and real data sets. The results are encouraging and compared favorably with results from other methods as FCM, PCM and FPCM algorithms on the same data sets. Finally, the proposed method was applied into image segmentation algorithm. The experimental results show that the proposed algorithm can be considered as a promising tool for data clustering and image processing. •Neutrosophic set was employed to deal with indeterminate data in clustering analysis.•A new objective function is defined to handle the indeterminacy of data.•Both the degrees belonging to determinate and indeterminate clusters are calculated.
AbstractList In this paper, a new clustering algorithm, neutrosophic c-means (NCM), is introduced for uncertain data clustering, which is inspired from fuzzy c-means and the neutrosophic set framework. To derive such a structure, a novel suitable objective function is defined and minimized, and the clustering problem is formulated as a constrained minimization problem, whose solution depends on the objective function. In the objective function, two new types of rejection have been introduced: the ambiguity rejection which concerns the patterns lying near the cluster boundaries, and the distance rejection dealing with patterns that are far away from all the clusters. These measures are able to manage uncertainty due to imprecise and/or incomplete definition of the clusters. We conducted several experiments with synthetic and real data sets. The results are encouraging and compared favorably with results from other methods as FCM, PCM and FPCM algorithms on the same data sets. Finally, the proposed method was applied into image segmentation algorithm. The experimental results show that the proposed algorithm can be considered as a promising tool for data clustering and image processing. •Neutrosophic set was employed to deal with indeterminate data in clustering analysis.•A new objective function is defined to handle the indeterminacy of data.•Both the degrees belonging to determinate and indeterminate clusters are calculated.
Author Guo, Yanhui
Sengur, Abdulkadir
Author_xml – sequence: 1
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  orcidid: 0000-0003-1814-9682
  surname: Guo
  fullname: Guo, Yanhui
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  organization: School of Science, St. Thomas University, Miami Gardens, FL 33054, USA
– sequence: 2
  givenname: Abdulkadir
  surname: Sengur
  fullname: Sengur, Abdulkadir
  organization: Department of Electrical and Electronics Engineering, Firat University, 23119 Elazig, Turkey
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Keywords Image segmentation
Neutrosophic set
Neutrosophic clustering
Fuzzy c-means clustering
Data clustering
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Snippet In this paper, a new clustering algorithm, neutrosophic c-means (NCM), is introduced for uncertain data clustering, which is inspired from fuzzy c-means and...
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SubjectTerms Data clustering
Fuzzy c-means clustering
Image segmentation
Neutrosophic clustering
Neutrosophic set
Title NCM: Neutrosophic c-means clustering algorithm
URI https://dx.doi.org/10.1016/j.patcog.2015.02.018
Volume 48
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