Abstract
In this work, a new image segmentation algorithm is introduced. The proposed algorithm combines the results of an hybrid clustering ensemble. The ensemble clustering is composed of fuzzy c-means (FCM) algorithm and fuzzy local information c-means (FCM_S1 and FCM_S2) algorithms with different values of the neighbors effect. The consensus technique is performed by the ordered weighted averaging (OWA) method. The weight attributed to each classifier can be modified during the process of classification and is determined by the classifier results of the pixel neighbors classification. Dynamic weights give the method the ability to select the temporal best performance during the classification process. Experiments performed on a synthetic image, and real images show that the proposed algorithm is effective and efficient and provides good noise elimination effect.
Similar content being viewed by others
Abbreviations
- \(X\) :
-
the data set
- \(k\) :
-
number of clusters
- \(C\) :
-
clusters centers vector
- \(d(c_{i}\!,x_{j})\) :
-
distance measure between object \(x_{j}\) and \(c_{i}\) the center of cluster \(i\)
- \(j_{m}\) :
-
objective function
- \({u}_{\mathrm{i,j}}\) :
-
fuzzy membership of the \(i\)th pixel with respect to cluster \(j\)
- \(N_{i}\) :
-
set of neighbors into a window around pixel \(x_{i}\).
- \(N_{R}\) :
-
cardinality of the window
- \(\overline{x}_{r}\) :
-
the average neighboring pixels lying within a window around \(x_{r}\)
- \(a\) :
-
parameter used to control the effect of the neighbors term
- \(N_{d}\) :
-
number of data in \(X\)
- \(N_{c}\) :
-
number of clusterers.
- \(\pi _{i}\) :
-
partition \(i\)
- \(\lambda _{i}\) :
-
Label \(i\)
- \(\pi ^{*}\) :
-
optimal partition
- \(\varPhi ^{\mathrm{NMI}}\) :
-
normalized mutual information
- \(\beta _m\) :
-
average mutual information
- \(\beta _0\) :
-
parameter used to normalize the weights
- \(W\) :
-
weight vector
- \(a_{i}\) :
-
arguments to aggregate
- \(b_{i}\) :
-
the \(i\)th largest element of the collection of aggregated objects
- \(\alpha \) :
-
parameter used to control the effect of the past performance of the classifier
- \(SA\) :
-
the rate of correct pixels classification
- \(A_{i}\) :
-
the set of pixels attributed to the \(i\)th class
- \(B_{i}\) :
-
the set of pixels belonging to the \(i\)th class
- \(OA\) :
-
Overall Accuracy
References
Wells, W.M., LGrimson, W.E., Kikinis, R., Arrdrige, S.R.: Adative segmentation of MRI data. IEEE Trans. Med. Imaging 15, 429–442 (1996)
Fred, A.L., Jain, A.K.: Combining multiple clusterings using evidence accumulation. IEEE PAMI 27(6), 835–850 (2005)
Yager, R.R.: On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Trans. Syst. Man Cybern. 18(1), 183–190 (1988)
Fullér, R., Majlender, P.: On obtaining minimal variability OWA operator weights. Fuzzy Sets Syst. 136(2), 203–215 (2003)
Yager, R.R.: Quantifier guided aggregation using OWA operators. Int. J. Intell. Syst. 11(1), 49–73 (1996)
Yager, R.R.: Decision making with fuzzy probability assessments. IEEE Trans. Fuzzy Syst. 7(4), 462–467 (1999)
Yager, R.R.: On the valuation of alternatives for decision-making under uncertainty. Int. J. Intell. Syst. 17(7), 687–707 (2002)
Ahn, B.S.: On the properties of OWA operator weights functions with constant level of orness. IEEE Trans. Fuzzy Syst. 14(4), 511–515 (2006)
Liu, X.: On the properties of equidifferent OWA operator. Int. J. Approx. Reason. 43(1), 90–107 (2006)
Wang, Y., Parkan, C.: A minimax disparity approach for obtaining OWA operator weights. Inf. Sci. 175(1/2), 20–29 (2005)
Xu, Z.S.: An overview of methods for determining OWA weights. Int. J. Intell. Syst. 20(8), 843–865 (2005)
Filev, D., Yager, R.R.: Analytic properties of maximum entropy OWA operators. Inf. Sci. 85, 11–27 (1995)
Wang, Y.M., Luo, Y., Liu, X.: Two new models for determining OWA operator weights. Comput. Ind. Eng. 52, 203–209 (2007)
Majlender, P.: OWA operators with maximal Renyi entropy. Fuzzy Sets Syst. 155, 340–360 (2005)
Dunn, J.: A fuzzy relative of the ISODATA process and its use in detecting compact well separated clusters. J. Cybern. 3, 32–57 (1974)
Bezdek, J.: Pattern Recognition With Fuzzy Objective Function Algorithms. Plenum, New York (1981)
Groll, L., Jakel, J.: A new convergence proof of fuzzy c-means. IEEE Trans. Fuzzy Syst. 13(5), 717–720 (2005)
Ahmed, M., Yamany, S., Mohamed, N., Farag, A., Moriarty, T.: A modified fuzzy C-means algorithm for bias field estimation and segmentation of MRI data. IEEE Trans. Med. Imaging 21, 193–199 (2002)
Chen, S., Zhang, D.: Robust image segmentation using FCM with spatial constraints based on new kernel-induced distance measure. IEEE Trans. Syst. Man Cybern. 34, 1907–1916 (2004)
Krinidis, S., Chatzis, V.: A robust fuzzy local information c-means clustering algorithm. IEEE Trans. Image Process. 19(5), 1328–1337 (2010)
Riesen, K., Bunke, H.: Cluster ensembles based on vector space embeddings of graphs [J]. Lect. Notes Comput. Sci. 5519(1), 211–221 (2009)
Zhang, L., Zhou, W., Wu, C., Huo, J., Zou, H.: Center matching scheme for K-means cluster ensembles[C]. MIPPR 2009 Pattern Recognit. Comput. Vis. 19(1):77–83 (2009)
Strehl, A., Ghosh, J., Cardie, C.: Cluster ensembles: a knowledge reuse framework for combining multiple partitions[J]. J. Mach. Learn. Res. 3, 583–617 (2002)
Kang, K., Zhang, H.X., Fan, Y.: A novel clusterer ensemble algorithm based on dynamic cooperation [C]. In: Fifth International Conference on Fuzzy Systems and Knowledge Discovery (FSKD’2008), pp. 32–35 (2008)
Haixiong, F., Fuxian, L., Lu, X.: Cluster label aligning algorithm based on programming model. In: 24th Chinese Control and Decision Conference (CCDC), pp 1768–1772 (2012)
Ayed, H.G., Kamel, M.S.: On voting based consensus of cluster ensembles. Pattern Recognit. 43, 1043–1953 (2010)
Ayed, H.G., Kamel, M.S.: Cumulative voting consensus method for partitions with a variable number of clusters. IEEE Trans. Pattern Anal. Mach. Intell. 30, 160–173 (2008)
Kuhn, H.: The Hungarian method for the assignment problem. Nav. Res. Logist. Q. 2, 83–97 (1955)
O’Hagan, M.: Aggregating template or rule antecedents in real-time expert systems with fuzzy set. In: Grove, P. (ed.) Proceedings of 22nd Annual IEEE Asilomar Conference Signals, Systems, and Computers, pp. 681–689. Pacific Grove, CA (1988)
Zhou, Z., Tang, W.: Clusterer ensemble [J]. Knowl. Based Syst. 19(1), 77–83 (2006)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ammour, N., Alajlan, N. A dynamic weights OWA fusion for ensemble clustering. SIViP 9, 727–734 (2015). https://doi.org/10.1007/s11760-013-0499-1
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11760-013-0499-1