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'eau 11, 2, 255-282. (In French.) Basu, B., Srinivas, V.V., 2014. Regional flood frequency analysis using kernel-based fuzzy clustering approach. Water Resour. Res., 50, 4, 3295-3316. Basu, B., Srinivas, V.V., 2015. Analytical approach to quantile estimation in regional frequency analysis based on fuzzy framework. J. Hydrol., 524, 30-43. Bellman, R., Kalaba, R., Zadeh, L.A., 1966. Abstraction and pattern classification. J. Math. Anal. Appl., 2, 581-585. Bezdek, J.C., 1974. Cluster validity with fuzzy sets. J. Cybernet., 3, 3, 58-73. Bezdek, J.C., 1981. Pattern

References Bezdek, J. C. Pattern Recognition with Fuzzy Objective Function Algorithms. New York: Plenum Press, 1981. Dembèlè, D., Kastner, P. "Fuzzy c-means method for clustering microarray data," Bioinformatics, Vol. 19, No.8, pp.973-980, May 2003. Futschik, M. E., Kasabov, K. "Fuzzy Clustering of Gene Expression data," Available: http://itb.biologie.huberlin.de/~futschik/publis/futschik_ieee.pdf Tarca, A. L., Romero, R., Draghici, S. "Analysis of microarray experiments of gene expression profiling," American Journal of Obstetrics and Gynecology, Vol.195

F., Font X., On relational possibilistic clustering, Pattern Recognition , 39 , 11, 2006, 2010-2024. [6] Everitt B.S., Landau S., Leese M., Stahl D., Cluster Analysis, 5th Edition , Wiley, Chichester, 2011. [7] Hamasuna Y., Endo Y., Miyamoto S., Fuzzy C -means clustering for data with clusterwise tolerance based on L 2 - and L 1 -regularization, Journal of Advanced Computational Intelligence and Intelligent Informatics , 15 , 1, 2011, 68-75. [8] Höppner F., Klawonn F., Kruse R., Runkler T., Fuzzy Cluster Analysis: Methods for Classification, Data Analysis

. Signal process, vol. 40, pp.901-914, 1992 [6] A. Likas, N. Vlassis, and J. Verbeek, The global k-means clustering algorithm (Technical Report), Computer Science Institute, University of Amsterdam, The Netherlands. ISA-UVA-01-02. 2001. [7] V. P. Guerrero-Bote, et al., Comparison of neural models for document clustering, Int. Journal of Approximate Reasoning, vol. 34, pp.287-305, 2003. [8] G. L. Carl, A fuzzy clustering and fuzzy merging algorithm, Technical Report, CS-UNR-101, 1999. [9] L. A. Zadeh, Fuzzy sets, Information and Control, Vol. 8, pp. 338-353, 1965. [10] R

-161. [11] Zhang, X.G., Li, J., Liu, S.Q. (2006). A method of infrared image segment based on mathematical morphology. Guidance & Fuze , 12, 40-43. [12] Duan, X.D., Wang, C.R., Liu, X.D. (2007). Particle Swarm Optimization Algorithm and Application. Shenyang: Press of Liaoning University, 154-184. [13] Pakhira, M.K., Bandyopadhyay, S., Maulik, U. (2004). Validity index for crisp and fuzzy cluster. Pattern Recognition , 37, 487-501. [14] Liu, X.L. (2006). Research on Fuzzy-Clustering-Based Method of Image Segmentation . Master dissertation of Hefei University of

partitioning we refer to Verleysen and Weeren (2016) and Kaufman and Rousseeuw (1990) . For the present paper we take the analysis a step further by performing a fuzzy cluster analysis on the prior two-cluster result. Whereas the initial hard partitioning attributes all cases to just one of the (here: two) clusters, fuzzy clustering allows for some ambiguity in the data by calculating for each case a membership coefficient, or the degree of belonging of individual authors to each of both clusters ( Kaufman & Rousseeuw, 1990 ). By including this additional information

Networks. A Comprehensive Foundation. Upper Saddle River N. J.: Prentice Hall, Inc., 1999, p 842. F. Höppner, F. Klawonn, R. Kruse, and T. Runkler, Fuzzy Clustering Analysis: Methods for Classification, Data Analysis, and Image Recognition. Chichester: John Willey & Sons Ltd, 1999, p. 289. P. Vuorimaa, Fuzzy self-organizing maps. Fuzzy Sets and Systems, vol. 66, 1994, pp. 223-231. P. Vuorimaa, Use of the fuzzy self-organizing maps in pattern recognition. Proc. 3-rd IEEE Int. Conf. Fuzzy Systems "FUZZ-IEEE'94", Orlando, USA, 1994, pp. 798-801. E. C.-K. Tsao, J. C

An Automatic Hybrid Method for Retinal Blood Vessel Extraction

The extraction of blood vessels from retinal images is an important and challenging task in medical analysis and diagnosis. This paper presents a novel hybrid automatic approach for the extraction of retinal image vessels. The method consists in the application of mathematical morphology and a fuzzy clustering algorithm followed by a purification procedure. In mathematical morphology, the retinal image is smoothed and strengthened so that the blood vessels are enhanced and the background information is suppressed. The fuzzy clustering algorithm is then employed to the previous enhanced image for segmentation. After the fuzzy segmentation, a purification procedure is used to reduce the weak edges and noise, and the final results of the blood vessels are consequently achieved. The performance of the proposed method is compared with some existing segmentation methods and hand-labeled segmentations. The approach has been tested on a series of retinal images, and experimental results show that our technique is promising and effective.

Abstract

Aiming at the problem of recommendation systems, this paper proposes a fuzzy clustering algorithm based on particle swarm optimization. This algorithm can find the best solution, using the capacity of global search in PSO algorithm with a powerful global and defining a proportion factor, which can adjust the position and reduce the search space automatically. Then using mutation particles it replaces the particles flying out the solution space by new particles during the searching process. In order to check the performance of the proposed algorithm, by testing with typical ZDT1, ZDT2, ZDT3 functions, the experimental results show that the improved method not only has a better ability to converge to the global point, but can also efficiently avoid premature convergence.

, vol. 468. Trans Tech Publ, 2012, pp. 704–707. [22] A. A. Al-Mahasneh, S. G. Anavatti, and M. Garratt, Nonlinear Multi-Input Multi-Output System Identification using Neuro-Evolutionary Methods for a Quadcopter, IEEE, pp. 217–222, 2017. [23] M. M. Ferdaus, S. G. Anavatti, M. A. Garratt, and M. Pratama, Fuzzy Clustering based Nonlinear System Identification and Controller Development of Pixhawk based Quadcopter, in Advanced Computational Intelligence (ICACI), 2017 IEEE International Conference on. IEEE, 2017, pp. 223–230. [24] M. M. Ferdaus, S. G. Anavatti, M. A