A Novel Approach Canberra Measure Minimal Spanning Tree Using Fuzzy C-Means Based on Gaussian Function for Image Data Mining

Senthil; Nithya; Bhuvaneswari

doi:doi:10.11648/j.acis.20180605.11

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A Novel Approach Canberra Measure Minimal Spanning Tree Using Fuzzy C-Means Based on Gaussian Function for Image Data Mining

Senthil, Nithya, Bhuvaneswari

Published in Automation, Control and Intelligent Systems (Volume 6, Issue 5)

Received: 13 February 2019 Accepted: 14 March 2019 Published: 3 April 2019

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Abstract

Clustering analysis has been an emerging research issue in data mining due to its variety of applications. In recently, mathematical algorithm supported automatic segmentation system plays an important role in clustering of images. The fuzzy c-means clustering is a method of cluster analysis which aims to partition n data points into k-clusters. The conventional FCM-based algorithm considers no spatial content information, which means it sensitive to noise. Unsupervised techniques need to be employed, which can be based on minimal spanning tree generated by comparing spatial neighbourhood information, the MST based clustering algorithms have been widely used due to their ability to detect clusters with irregular boundaries. We propose an automatic fuzzy c-means initialization algorithm based on Canberra distance minimal spanning tree for the purpose of segmentation of medical images, where vertices and edges are labelled with multi-dimensional vectors. A Canberra distance measure based, construct the minimal spanning tree clustering algorithm. An efficient method for calculating membership and updating prototypes by minimizing the new objective function of Gaussian based fuzzy c-means. The algorithm uses a new cluster validation criterion based on the geometric property of data partition of the dataset in order to find the proper number of cluster at each level. In this algorithm to apply medical images to reduce the inhomogeneity and allow the labelling of a pixel to be influenced by the labels in its immediate neighbourhood and reduces the time complexity and better clustering results than the existing traditional minimal spanning tree algorithm. The performance of proposed algorithm has been shown with random data set, partition coefficient and validation function are used to evaluate the validity of clustering and then new cluster separation approach to optimal number of clustering. Also this paper compares the results of proposed method with the results of existing basic fuzzy c-means.

Published in	Automation, Control and Intelligent Systems (Volume 6, Issue 5)
DOI	10.11648/j.acis.20180605.11
Page(s)	54-61
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2019. Published by Science Publishing Group

Keywords

Fuzzy C-Means, Gaussian Function, Lagrange Multiplier, Canberra Distance, Minimal Spanning Tree, Cluster Separation, Partition Coefficient, Validation Function

References

[1]	Bezdek. J. C, Ehrlich. R and Full. W, FCM: the fuzzy c-means clustering algorithm, Computers & Geosciences, Vol. 10, No. 2-3, pp. 191-203(1984).
[2]	Mac Queen. J, Some methods for classification and analysis of multivariate observations, In Proceedings of the 5th Berkeley symposium on mathematical statistics and probability, University of California press, USA, pp. 14(1967).
[3]	Bezdek J. C., Hall L. O., Clarke L. P, Review of MR image segmentation techniques using pattern recognition, medical physics 20(4), pp. 1033-1048(1993).
[4]	Ferahta N., Moussaoui A., Benmahammed K., Chen V, New fuzzy clustering algorithm applied to RMN image segmentation, international journal of soft computing 1(2), pp. 137-142 (2006).
[5]	Noordam J. C., Van Den Broek W. H. A. M., Buydens L. M. C, Geometrically guided fuzzy C-means clustering for multivariate image segmentation, In. proceedings15-th International conference on pattern recognition, Vol. pp. 462-465(2000).
[6]	Mahipal singh choudhry and Rajiv Kapoor, A novel fuzzy energy based level set method for medical image segmentation, Cogent engineering, vol. 5(2018).
[7]	Perumal K and Latha C, Probability based fuzzy c-means for image segmentation, International Journal of Pure and Applied Mathematics, vol. 18 (17), pp. 779-789(2018).
[8]	Hall L. O., Bensaid A. m., Clarke L. P., Velthuizen R. P., Silbiger M. S., Bezdek J. C, A comparison of Neural network and Fuzzy clustering Techniques in segmenting magnetic Resonance images of the Brain, IEEE Transactions, Neural networks 3(5), pp. 672-682(1992).
[9]	Xue J. H., Pizurica A., Philips W., Kerre E., Walle R. V., Lemahieu I, An integrated method of Adaptive Enhancement for unsupervised segmentation of MRI Brain images, Pattern Recognition Letters 24(15), pp. 2549-2560(2003).
[10]	Krishnan N., Nelson Kennedy Babu C. V., Joseph rajapandian V., Richard Devarajan, A Fuzzy image segmentation using feed forward Neural networks with supervised Learning, In. Proceedings of the International conference on cognition and recognition, pp. 396-402.
[11]	Moussaoui A., Benmahammed K., Ferahta N., Chen V, A new MR Brain image segmentation using an optimal semi supervised Fuzzy C-means and pdf Estimation, Electronic letters on computer vision and image Analysis 5(4), pp. 1-11(2005).
[12]	Aruna Kumar SV and Harish BS, A novel fuzzy clustering based system for medical image segmentation, Int. J. Computational Intelligence Studies, vol. 7(1), pp. 33-66(2018).
[13]	Xiaohong Jia, Yanning Zhang, Superpixel-based fast fuzzy c-means clustering for color image segmentation, IEEE transactions on fuzzy systems, DOI: 10.1109/TFUZZ.2018.28890182018
[14]	Hruschka. E. R, Campello. R. J. G. B, Freitas. A. A and De carvalho. A. C. P. L. F, A survey of evolutionary algorithms for clustering, IEEE-Transactions on systems, man and cybernetics, part C, Applications and review, Vol. 39, No. 2, pp. 133-155(2009).
[15]	Duda. R. O, Hart. P. E and Stork. D. G, Pattern classification, Wiley-Interscience, New York, USA, 2nd edition (2001).
[16]	Girvan M., Newman M. E. J., Community structure in social and biological networks, In Proceeding of the National Academy of Sciences, USA. pp. 8271-8276 (2002).
[17]	Prim R., Shortest connection networks and some generalization, Bell systems technical journal Vol: 36, pp. 1389-1401 (1957).
[18]	Kruskal J, On the shortest spanning subtree and the travelling salesman problem In proceedings of the American Mathematical Society, pp. 48-50 (1956).
[19]	Nesetril J, Milkova E, Nesetrilova H., Otakar Boruvka, On minimal spanning tree problem: Translation of both the 1926 papers, comments, history. DMATH. Discrete Mathematics, pp. 233(2001).
[20]	Edward W. Packel, Functional Analysis, Intext Educational Publishers, New York (1974).
[21]	Feng Luo, Latifur Kahn, Farokh Bastani, T Ling Yen and Jizhong Zhon, A dynamically growing self-organizing tree (DGOST) for hierarchical gene expression profile, Bio Informatics, Vol. 20, No. 16, pp-2605-2617(2004).
[22]	Dunn J. C, A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters, Journal of cybernetics 3(3), pp. 32-57 (1973).
[23]	Bezdek J. C, pattern recognition with fuzzy objective function algorithms, plenum press, New York (1981).

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APA Style

Senthil, Nithya, Bhuvaneswari. (2019). A Novel Approach Canberra Measure Minimal Spanning Tree Using Fuzzy C-Means Based on Gaussian Function for Image Data Mining. Automation, Control and Intelligent Systems, 6(5), 54-61. https://doi.org/10.11648/j.acis.20180605.11

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ACS Style

Senthil; Nithya; Bhuvaneswari. A Novel Approach Canberra Measure Minimal Spanning Tree Using Fuzzy C-Means Based on Gaussian Function for Image Data Mining. Autom. Control Intell. Syst. 2019, 6(5), 54-61. doi: 10.11648/j.acis.20180605.11

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AMA Style

Senthil, Nithya, Bhuvaneswari. A Novel Approach Canberra Measure Minimal Spanning Tree Using Fuzzy C-Means Based on Gaussian Function for Image Data Mining. Autom Control Intell Syst. 2019;6(5):54-61. doi: 10.11648/j.acis.20180605.11

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@article{10.11648/j.acis.20180605.11,
  author = {Senthil and Nithya and Bhuvaneswari},
  title = {A Novel Approach Canberra Measure Minimal Spanning Tree Using Fuzzy C-Means Based on Gaussian Function for Image Data Mining},
  journal = {Automation, Control and Intelligent Systems},
  volume = {6},
  number = {5},
  pages = {54-61},
  doi = {10.11648/j.acis.20180605.11},
  url = {https://doi.org/10.11648/j.acis.20180605.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acis.20180605.11},
  abstract = {Clustering analysis has been an emerging research issue in data mining due to its variety of applications. In recently, mathematical algorithm supported automatic segmentation system plays an important role in clustering of images. The fuzzy c-means clustering is a method of cluster analysis which aims to partition n data points into k-clusters. The conventional FCM-based algorithm considers no spatial content information, which means it sensitive to noise. Unsupervised techniques need to be employed, which can be based on minimal spanning tree generated by comparing spatial neighbourhood information, the MST based clustering algorithms have been widely used due to their ability to detect clusters with irregular boundaries. We propose an automatic fuzzy c-means initialization algorithm based on Canberra distance minimal spanning tree for the purpose of segmentation of medical images, where vertices and edges are labelled with multi-dimensional vectors. A Canberra distance measure based, construct the minimal spanning tree clustering algorithm. An efficient method for calculating membership and updating prototypes by minimizing the new objective function of Gaussian based fuzzy c-means. The algorithm uses a new cluster validation criterion based on the geometric property of data partition of the dataset in order to find the proper number of cluster at each level. In this algorithm to apply medical images to reduce the inhomogeneity and allow the labelling of a pixel to be influenced by the labels in its immediate neighbourhood and reduces the time complexity and better clustering results than the existing traditional minimal spanning tree algorithm. The performance of proposed algorithm has been shown with random data set, partition coefficient and validation function are used to evaluate the validity of clustering and then new cluster separation approach to optimal number of clustering. Also this paper compares the results of proposed method with the results of existing basic fuzzy c-means.},
 year = {2019}
}

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TY  - JOUR
T1  - A Novel Approach Canberra Measure Minimal Spanning Tree Using Fuzzy C-Means Based on Gaussian Function for Image Data Mining
AU  - Senthil
AU  - Nithya
AU  - Bhuvaneswari
Y1  - 2019/04/03
PY  - 2019
N1  - https://doi.org/10.11648/j.acis.20180605.11
DO  - 10.11648/j.acis.20180605.11
T2  - Automation, Control and Intelligent Systems
JF  - Automation, Control and Intelligent Systems
JO  - Automation, Control and Intelligent Systems
SP  - 54
EP  - 61
PB  - Science Publishing Group
SN  - 2328-5591
UR  - https://doi.org/10.11648/j.acis.20180605.11
AB  - Clustering analysis has been an emerging research issue in data mining due to its variety of applications. In recently, mathematical algorithm supported automatic segmentation system plays an important role in clustering of images. The fuzzy c-means clustering is a method of cluster analysis which aims to partition n data points into k-clusters. The conventional FCM-based algorithm considers no spatial content information, which means it sensitive to noise. Unsupervised techniques need to be employed, which can be based on minimal spanning tree generated by comparing spatial neighbourhood information, the MST based clustering algorithms have been widely used due to their ability to detect clusters with irregular boundaries. We propose an automatic fuzzy c-means initialization algorithm based on Canberra distance minimal spanning tree for the purpose of segmentation of medical images, where vertices and edges are labelled with multi-dimensional vectors. A Canberra distance measure based, construct the minimal spanning tree clustering algorithm. An efficient method for calculating membership and updating prototypes by minimizing the new objective function of Gaussian based fuzzy c-means. The algorithm uses a new cluster validation criterion based on the geometric property of data partition of the dataset in order to find the proper number of cluster at each level. In this algorithm to apply medical images to reduce the inhomogeneity and allow the labelling of a pixel to be influenced by the labels in its immediate neighbourhood and reduces the time complexity and better clustering results than the existing traditional minimal spanning tree algorithm. The performance of proposed algorithm has been shown with random data set, partition coefficient and validation function are used to evaluate the validity of clustering and then new cluster separation approach to optimal number of clustering. Also this paper compares the results of proposed method with the results of existing basic fuzzy c-means.
VL  - 6
IS  - 5
ER  -

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Author Information

Senthil

Department of Economics and Statistics, Government of Tamilnadu, DRDA, Dindigul, India
Nithya

Department of Mathematics, Mother Teresa Women’s University, Kodaikanal, India
Bhuvaneswari

Department of Mathematics, Mother Teresa Women’s University, Kodaikanal, India

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APA Style

Senthil, Nithya, Bhuvaneswari. (2019). A Novel Approach Canberra Measure Minimal Spanning Tree Using Fuzzy C-Means Based on Gaussian Function for Image Data Mining. Automation, Control and Intelligent Systems, 6(5), 54-61. https://doi.org/10.11648/j.acis.20180605.11

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ACS Style

Senthil; Nithya; Bhuvaneswari. A Novel Approach Canberra Measure Minimal Spanning Tree Using Fuzzy C-Means Based on Gaussian Function for Image Data Mining. Autom. Control Intell. Syst. 2019, 6(5), 54-61. doi: 10.11648/j.acis.20180605.11

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AMA Style

Senthil, Nithya, Bhuvaneswari. A Novel Approach Canberra Measure Minimal Spanning Tree Using Fuzzy C-Means Based on Gaussian Function for Image Data Mining. Autom Control Intell Syst. 2019;6(5):54-61. doi: 10.11648/j.acis.20180605.11

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@article{10.11648/j.acis.20180605.11,
  author = {Senthil and Nithya and Bhuvaneswari},
  title = {A Novel Approach Canberra Measure Minimal Spanning Tree Using Fuzzy C-Means Based on Gaussian Function for Image Data Mining},
  journal = {Automation, Control and Intelligent Systems},
  volume = {6},
  number = {5},
  pages = {54-61},
  doi = {10.11648/j.acis.20180605.11},
  url = {https://doi.org/10.11648/j.acis.20180605.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acis.20180605.11},
  abstract = {Clustering analysis has been an emerging research issue in data mining due to its variety of applications. In recently, mathematical algorithm supported automatic segmentation system plays an important role in clustering of images. The fuzzy c-means clustering is a method of cluster analysis which aims to partition n data points into k-clusters. The conventional FCM-based algorithm considers no spatial content information, which means it sensitive to noise. Unsupervised techniques need to be employed, which can be based on minimal spanning tree generated by comparing spatial neighbourhood information, the MST based clustering algorithms have been widely used due to their ability to detect clusters with irregular boundaries. We propose an automatic fuzzy c-means initialization algorithm based on Canberra distance minimal spanning tree for the purpose of segmentation of medical images, where vertices and edges are labelled with multi-dimensional vectors. A Canberra distance measure based, construct the minimal spanning tree clustering algorithm. An efficient method for calculating membership and updating prototypes by minimizing the new objective function of Gaussian based fuzzy c-means. The algorithm uses a new cluster validation criterion based on the geometric property of data partition of the dataset in order to find the proper number of cluster at each level. In this algorithm to apply medical images to reduce the inhomogeneity and allow the labelling of a pixel to be influenced by the labels in its immediate neighbourhood and reduces the time complexity and better clustering results than the existing traditional minimal spanning tree algorithm. The performance of proposed algorithm has been shown with random data set, partition coefficient and validation function are used to evaluate the validity of clustering and then new cluster separation approach to optimal number of clustering. Also this paper compares the results of proposed method with the results of existing basic fuzzy c-means.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - A Novel Approach Canberra Measure Minimal Spanning Tree Using Fuzzy C-Means Based on Gaussian Function for Image Data Mining
AU  - Senthil
AU  - Nithya
AU  - Bhuvaneswari
Y1  - 2019/04/03
PY  - 2019
N1  - https://doi.org/10.11648/j.acis.20180605.11
DO  - 10.11648/j.acis.20180605.11
T2  - Automation, Control and Intelligent Systems
JF  - Automation, Control and Intelligent Systems
JO  - Automation, Control and Intelligent Systems
SP  - 54
EP  - 61
PB  - Science Publishing Group
SN  - 2328-5591
UR  - https://doi.org/10.11648/j.acis.20180605.11
AB  - Clustering analysis has been an emerging research issue in data mining due to its variety of applications. In recently, mathematical algorithm supported automatic segmentation system plays an important role in clustering of images. The fuzzy c-means clustering is a method of cluster analysis which aims to partition n data points into k-clusters. The conventional FCM-based algorithm considers no spatial content information, which means it sensitive to noise. Unsupervised techniques need to be employed, which can be based on minimal spanning tree generated by comparing spatial neighbourhood information, the MST based clustering algorithms have been widely used due to their ability to detect clusters with irregular boundaries. We propose an automatic fuzzy c-means initialization algorithm based on Canberra distance minimal spanning tree for the purpose of segmentation of medical images, where vertices and edges are labelled with multi-dimensional vectors. A Canberra distance measure based, construct the minimal spanning tree clustering algorithm. An efficient method for calculating membership and updating prototypes by minimizing the new objective function of Gaussian based fuzzy c-means. The algorithm uses a new cluster validation criterion based on the geometric property of data partition of the dataset in order to find the proper number of cluster at each level. In this algorithm to apply medical images to reduce the inhomogeneity and allow the labelling of a pixel to be influenced by the labels in its immediate neighbourhood and reduces the time complexity and better clustering results than the existing traditional minimal spanning tree algorithm. The performance of proposed algorithm has been shown with random data set, partition coefficient and validation function are used to evaluate the validity of clustering and then new cluster separation approach to optimal number of clustering. Also this paper compares the results of proposed method with the results of existing basic fuzzy c-means.
VL  - 6
IS  - 5
ER  -

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