A new multi-objective cluster ensemble based on modularity maximization

Mohammad Khodaparasti, Mohadeseh Ganji, Saeed Amirgholipour, Aboosaleh Mohammad Sharifi


Conventional clustering algorithms utilize only one single criterion that may not    conform to diverse shapes of the underlying clusters. But in this paper, we hire two important criteria and propose a new multi-objective cluster ensemble model to empower finding clusters of different types. The first criteria is the well-known sum of squared error. The second criterion is modularity which is originally a measure of evaluating communities in social networks. We maximize modularity as a consensus function of cluster ensemble. In order to further improvement, we also modify Non Dominant Sorting Genetic Algorithm (NSGAII) and propose a specialized crossover operator for it. Experimental results over seven UCI real data sets show that the proposed method significantly outperforms other clustering methods.


Multi-objective clustering, Cluster ensemble, Non-dominant Sorting Genetic Algo-rithm, Modularity

Full Text:



H. Alizadeh, B. Minaei-Bidgoli, H. Parvin, Optimizing Fuzzy Cluster Ensemble in String Representation, International Journal of Pattern Recognition and Artificial Intelligence (IJPRAI), Vol 27, No. 2, 2013.

M. Law, A. Topchy, A.K. Jain, Multi objective data clustering, in: Proceedings of CVPR 2004, Vol. 2, 2004.

J. Handl, J. Knowles, An evolutionary approach to multi objective clustering, IEEE Transactions on Evolutionary Computation 11 (1) 56–76, 2007.

Y. Zheng, L. Jia, and H. Cao,Multi-Objective Gene Expression Programming for Clustering, Information Technology and Control, Vol. 41, No.3, 2012.

A. Strehl and J. Ghosh, Cluster ensembles, a knowledge reuse framework for combining multiple partitions. Journal of Machine Learning Research, 3:583–617, 2002.

Topchy, A., Jain, A., & Punch, W. A mixture model for clustering ensembles, SIAM internationalconference on data mining, pp. 379– 390, 2004.

A.Fred, andA. K. Jain, Learning pairwise similarity for data clustering, The18thinternational conference on pattern recognition, pp. 925– 928, (ICPR’06), 2006.

M. E. J. Newman,Communities, modules and large-scale structure in net-works, Nature Physics 8, 25-31, 2012.

M. E. J. Newman and M. Girvan, Finding and evaluating community structure in networks, Phys. Rev. E 69, 026113, 2004.

H. Alizadeh, Cluster Ensemble Selection Based on Mathematical and Social Optimization, PhD thesis, Iran University of Science and Technology, 2013.

K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, A Fast and Elitist Multi-objective Genetic Algorithm:NSGA-II, IEEE Transactions onEvolutionary Computa-tion, Vol. 6, No. 2, 2002.

A. Fred, and A. K. Jain."Combining multiple clusterings using evidence accu-mulation."IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 27, No.6, pp. 835-850, 2005‏.


  • There are currently no refbacks.