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A New Approach for Automatic Fuzzy Clustering Applied to Magnetic Resonance Image Clustering
American Journal of Remote Sensing
Volume 1, Issue 2, April 2013, Pages: 38-46
Received: Apr. 14, 2013; Published: Apr. 2, 2013
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Authors
E. A. Zanaty, College of Science, Sohag University, Sohag, Egypt.
Ashraf Afifi, Computer Engineering Department, High Technological Institute, 10th of Ramadan City, Egypt.
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Abstract
Many clustering and segmentation algorithms suffer from the limitation that the number of clusters/segments is specified manually by human operators. It is often impractical to expect a human with sufficient domain knowledge to be available to select the number of clusters/segments to return. Thus, the estimation of optimal cluster number during the clustering process is our prime concern. In this paper, we introduce a new validity index method based on multi-degree entropy algorithm for determining the number of clusters automatically. This multi-degree entropy algorithm combines multi-degree immersion and entropy algorithms to partition an image into levels of intensity. The output of the multi-degree immersion processes are regions in which the interior does not contain any sharp grey value transitions, i.e. each level of intensity contains one or more regions of connected points or oversegmentation. These regions are passed to the entropy procedure to perform a suitable merging which produces the final number of clusters based on validity function criteria. Validity functions are used to find a relation between intra-cluster and inter-cluster variability, which is of course a reasonable principle. The latter process uses a region-based similarity representation of the image regions to decide whether regions can be merged. The proposed method is experimented on a discrete image example to prove its efficiency and applicability. The existing validation indices like PC, XB, and CE are evaluated and compared with the proposed index when applied on two simulation and one real life data. A direct benefit of this method is being able to determine the number of clusters for given application medical images.
Keywords
Fuzzy Clustering, Multi-Degree Immersion, Entropy, Validity Index
To cite this article
E. A. Zanaty, Ashraf Afifi, A New Approach for Automatic Fuzzy Clustering Applied to Magnetic Resonance Image Clustering, American Journal of Remote Sensing. Vol. 1, No. 2, 2013, pp. 38-46. doi: 10.11648/j.ajrs.20130102.14
References
[1]
J.C. Bezdek, "Pattern recognition with fuzzy objective function algorithms", Plenum Press, New York, 1981.
[2]
M.N. Ahmed, S.M. Yamany, N. Mohamed, A.A. Farag, T. Moriarty, "A modified fuzzy C-means algorithm for bias field estimation and segmentation of MRI data", IEEE Trans. Med. Imag. 21, 2002, pp. 193-199.
[3]
U. Maulik and S. Bandyopadhyay, "Fuzzy partitioning using a real coded variable length genetic algorithm for pixel clas-sification", IEEE Transactions Geoscience and Remote Sensing, Vol. 41(5), 2003, pp. 1075– 1081.
[4]
S .Wu, AWC. Liew, H. Yan, "Cluster analysis of gene ex-pression data based on self-splitting and merging competitive learning", IEEE Trans. on Information Technology in Bio-medicine, Vol. 8, 2004, pp. 5-15.
[5]
L. Zhu, F. L. Chung, S. Wang, "Generalized fuzzy C-means clustering algorithm with improved fuzzy partitions ", IEEE Transactions on, vol. 39, no. 3., 2009, pp. 578-591.
[6]
D. Q. Zhang, S.-Can Chen, "A novel kernelized fuzzy C-means algorithm with application in medical image segmentation", Artificial Intelligence in Medicine Vol. 32, 2004, pp. 37-50.
[7]
J. Kang, L. Min, Q. Luan, X. Li, J. Liu, " Novel modified fuzzy C-means algorithm with applications", Digital Signal Processing 19, 2009, 309–319.
[8]
D. W. Kim, K. Y. Lee, D. Lee, K. H. Lee, "A kernel-based subtractive clustering method", Pattern Recognition Letters Vol.26 (7), 2005, pp. 879-891.
[9]
E.A. Zanaty, S. Aljahdali, N. Debnath, "A kernelized fuzzy C-means algorithm for automatic Magnetic Resonance Image Segmentation", Journal of Computational Methods in Science and engineering (JCMSE), 2009, pp. 123-136.
[10]
H. Timm, C. Borgelt, C. Doring, R. Kruse, "An extension to possibilistic fuzzy cluster analysis", Fuzzy Sets and Systems", vol. 147, no. 1, 2004, pp. 3–16.
[11]
J. S. Zhang, Y. W. Leung, "Improved possibilistic c-means clustering algorithms", IEEE Transactions On Fuzzy Systems, Vol. 12( 2), 2004, pp. 209–17.
[12]
Z. XuanJi, Q. SenSun, D. ShenXia, "A modified possibilistic fuzzy c-means clustering algorithm for biasfield estimation and segmentation of brain MR image", Computerized Medical Imaging and Graphics, Computerized Medical Imaging and Graphics , Vol. 35, No. 5 , 2011, pp. 383-397.
[13]
G. Yuhua, O. H. Lawrence, "Kernel based fuzzy ant clustering with partition validity", IEEE International Conference on Fuzzy Systems Sheraton Vancouver Wall Centre Hotel, Vancouver, BC, Canada July , 2006, pp.16-21.
[14]
Z. Volkovich, Z. Barzily, L. Morozensky, "A statistical model of cluster stability", Pattern Recognition, Vol.41, 2008, pp. 2174 – 2188.
[15]
M. K. Pakhira, S. Bandyopadhyay, U. Maulic, "Validity index for crisp and fuzzy clusters", Pattern Recognition, Vol.37, 2004, pp.487–501.
[16]
K. Malay, Pakhiraa, B. Sanghamitr, U. Maulik, "A study of some fuzzy cluster validity indices, genetic clustering and application to pixel classification", Fuzzy Sets and Systems, vol.155, 2005, pp.91–214.
[17]
L.J. Deborah, R.Baskaran, A.Kannan,"Survey on internal validity measure for cluster validation", International Journal of Computer Science and Engineering Survey (IJCSES) Vol.1, No.2, 2010.
[18]
N. A. Erilli, U.Yolcu, E.˘riog˘lu , Ç. H. Aladag, YükselÖner, "Determining the most proper number of cluster in fuzzy clustering by using artificial neural networks", Expert Systems with Applications 38, 2011, pp. 2248–2252.
[19]
M.T.El-Melegy, E.A.Zanaty, W.M.Abd-Elhafiez, A. Farag, "On cluster validity indexes in fuzzy and hard clustering al-gorithms for image segmentation", IEEE international con-ference on computer vision, vol. 6, VI 5-8, 2007.
[20]
Y. Xu, G. Richard, and A. Brereton, "A comparative study of cluster validation indices applied to genotyping data", Chemometrics and Intelligent Laboratory Systems, vol. 78, 2005, pp. 30–40.
[21]
K.L. Wu, and M.S. Yang, "A cluster validity index for fuzzy clustering", Pattern Recognition Letters, vol. 26, 2005, pp.1275–1291.
[22]
D. Jong K.,Young-woon P.,and D. -Jo P.,"A noval validity index for determination of the optimal number of clusters". IEICE Trans. Inf.&Syst. ,Vol. E84-D,No.2, 2001, pp. 281-285.
[23]
Bezdek, "Numerical taxonomy with fuzzy sets". Journal of Mathematical Biology, Vol.1, 1974, pp. 57–71.
[24]
Xie, L., Beni, G. ,"A validity measure for fuzzy clustering". IEEE Transactions Pattern Analysis and Machine Intelligence, Vol.13(4), 1991, pp. 841–846.
[25]
F. Maria, S. Gabriella B.,."Oversegmentation reduction in watershed-based gray-level image segmentation."Int. J. Signal and Imaging Engineering. Vol.1, 2008, pp. 4-10.
[26]
K.,K.,Mikolajczak,P.." Information theory based medical image processing". OPTO-Electronics Review. Vol.11, 2003, pp.253-259.
[27]
C.E.Shaannon, "A mathematical theory of communication". The Bell system Technical Journal. Vol. 27, 1948, pp. 379-423,623-656.
[28]
S. B., Cho, S. H. Yoo, "Fuzzy Bayesian validation for fuzzy clustering of yeastcell-cycle data". Pattern Recognition, 2005.
[29]
M. R., Rezaee, B. P. F. Lelieveldt, J. H. C. Reiber, " A new cluster validity index for the FCM". Pattern Recognition Letters, Vol.19, 1998, pp. 237–246.
[30]
N. S. Rhee, Oh, K. W., "A validity measure for fuzzy clustering and its use in selecting optimal number of clusters". IEEE International Conference on Fuzzy Systems, Vol. 2, 1996, pp.1020–1025.
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