An Efficient Nonnegative Matrix Factorization & Game Theoretic Framework Based Data Clustering

International Journal of Computer Trends and Technology (IJCTT)          
© 2017 by IJCTT Journal
Volume-49 Number-1
Year of Publication : 2017
Authors : Dr. V. Umadevi, R.Sumithra
DOI :  10.14445/22312803/IJCTT-V49P109


Dr. V. Umadevi, R.Sumithra "An Efficient Nonnegative Matrix Factorization & Game Theoretic Framework Based Data Clustering". International Journal of Computer Trends and Technology (IJCTT) V49(1):51-57, July 2017. ISSN:2231-2803. Published by Seventh Sense Research Group.

Abstract -
This Mostly, factorization of matrices is not unique, Non-negative Matrix Factorization (NMF) changes from the Principal Component Analysis, Singular Value Decomposition, Nystrom Method, and it imposes the controls that the factors must be non-negative. The proposed method utilizes a most powerful tool derivative from evolutionary game theory, which permits re-organizing the clustering attained with NMF method, making it consistent with the structure of the data set. The new propose a method to filter the clustering results obtained with the nonnegative matrix factorization (NMF) technique, imposing consistency constraints on the final labeling of the data set. The research community focused its effort on the initialization and on the optimization part of this method, without paying concentration to the final cluster assignments. The propose a game theoretic framework in which each object to be clustered is symbolized as a player, which has to choose its cluster membership. The detailed obtained with NMF method is used to initialize the approach space of the players and a weighted graph is worn to model the interactions among all the players. These connections allow the players to choose a cluster which is coherent with the clusters chosen by similar players, a property which is not guaranteed by NMF, since it produces a soft clustering of the data. The proposed results on common benchmarks show that our model is able to progress the performances of many NMF formulations.

[1] A. Banerjee, S. Merugu, I. S. Dhillon, and J. Ghosh, ?Clustering with bregman divergences. Journal of Machine Learning Research, vol. 6, pp. 1705–1749, 2005.
[2] M. Belkin and P. Niyogi. ?Laplacian eigenmaps and spectral techniques for embedding and clustering. ? In NIPS, 2001.
[3] P. Carmona-Saez, R. D. Pascual-Marqui and A. Pascual-Montano, ?Biclustering of gene expression data by non-smooth nonnegative matrix factorization. BMC Bioinformatics, vol. 7(78), pp. 1–18, 2006.
[4] H. Cho, I. Dhillon, Y. Guan, and S. Sra, ?Minimum sum squared residue based co-clustering of gene expression data. SIAM SDM, pp. 114–125, 2004.
[5] I. S. Dhillon. ?Co-clustering documents and words using bipartite spectral graph partitioning.? ACM SIGKDD, pages 269–274, 2001.
[6] N.Mahendran, Collaborative Location Based Sleep Scheduling with Load Balancing in Sensor-Cloud ?International Journal of Computer Science and Information Security (IJCSIS), ISSN: 1947-5500, volume 14, Special Issue, October 2016, PP: 20-27.
[7] N.Mahendran, ?Sleep Scheduling Schemes Based on Location of Mobile User in Sensor-Cloud, International Journal of Computer, Electrical, Automation, Control and Information Engineering Volume 10, No: 3, 2016 PP: 615-620.
[8] C. HQ, Ding, T. Li and M. Jordan. I. ?Convex and semi nonnegative matrix factorizations.? TPAMI, 32(1), pp. 45–55, 2010.
[9] Q. Gu and J. Zhou, ?Co-clustering on manifolds.? ACM SIGKDD, 2009.
[10] J. Kim and H. Park., ?Sparse nonnegative matrix factorization for clustering. Technical report, Georgia Institute of Technology, 2008.
[11] T. Li and C. Ding., ?The relationships among various nonnegative matrix factorization methods for clustering. IEEE ICDM, pp. 362— 371, 2006.
[12] F. Shahnaz, M. Berry, P. Pauca, and R. Plemmons, ?Document clustering using non-negative matrix factorization. Information Processing and Management, vol. 42, pp. 373–386, 2006.
[13] A. Strehl and J. Ghosh, ?Cluster ensembles - a knowledge reuse framework for combining multiple partitions.? Machine Learning Research, pp. 583–617, 2002.
[14] H. Wang, F. Nie, H. Huang and F. Makedon, ?Fast nonnegative matrix tri-factorization for large-scale data co-clustering.? IJCAI, 2011.
[15] R. Zass and A. Shashua, ?A unifying approach to hard and probabilistic clustering. IEEE ICCV, pp. 294–301, 2005.
[16] Z. Zhang and Z. Zha. ?Principal manifolds and nonlinear dimensionality reduction via tangent space alignment.? SIAM Scientific Computing, Vol 26, pp. 313–338, 2004.
[17] Z. Y. Zhirong Yang and J. Laaksonen, ?Projective nonnegative matrix factorization with applications to facial image processing. Pattern Recognition and Artificial Intelligence, vol. 21(8), pp. 1353– 1362, 2007.
[18] D. Cai and X. He and J. Han, ?SRDA: An efficient algorithm for large-scale discriminant analysis. TKDE, vol. 20, pp. 1–12, 2008.
[19] L. Lov´asz and M.D. Plummer, ?Matching Theory. AMS Chelsea Publishing Series, American Mathematical Soc., 2009.
[20] R Gomathi, N Mahendran, ?An efficient data packet scheduling schemes in wireless sensor networks, in Proceeding 2015 IEEE international Conference on Electronics and Communication Systems (ICECS’15), ISBN: 978-1-4799-7225-8, PP:542-547, 2015
[21] S Vanithamani, N Mahendran, ?Performance analysis of queue based scheduling schemes in wireless sensor networks?, in proceeding 2014 IEEE international Conference on Electronics and Communication Systems (ICECS’14), ISBN: 978-1-4799-2320-5, PP: 1-6, 2014.
[22] P Kalaiselvi, N Mahendran, ?An efficient resource sharing and multicast scheduling for video over wireless networks ?,in proceeding 2013 IEEE international Conference on Emerging Trends in Computing, Communication and Nanotechnology (ICECCN’13), ISBN: 978-1-4673-5036-5, PP:378-383, 2013.

Enter Data Cluster; Nonnegative Matrix Factorization; Weighted Graph ; Game Theoretic.