The week's pick
Random Articles
Reseach Article
Overlapping Patterns Recognition with Linear and Non-Linear Separations using Positive Definite Kernels
| International Journal of Computer Applications |
| Foundation of Computer Science (FCS), NY, USA |
| Volume 56 - Number 9 |
| Year of Publication: 2012 |
| Authors: Chiheb-eddine Ben N’cir, Nadia Essoussi |
10.5120/8916-2981
|
Chiheb-eddine Ben N’cir, Nadia Essoussi . Overlapping Patterns Recognition with Linear and Non-Linear Separations using Positive Definite Kernels. International Journal of Computer Applications. 56, 9 ( October 2012), 1-8. DOI=10.5120/8916-2981
Abstract
The detection of overlapping patterns in unlabeled data sets referred as overlapping clustering is an important issue in data mining. In real life applications, overlapping clustering algorithm should be able to detect clusters with linear and non-linear separations between clusters. We propose in this paper an overlapping clustering method based k-means algorithm using positive definite kernel. The proposed method is well adapted for clustering multi label data with linear and non linear separations between clusters. Experiments, performed on overlapping data sets, show the ability of the proposed method to detect clusters with complex and non linear boundaries. Empirical results obtained with the proposed method outperforms existing overlapping methods.
References
- Arindam Banerjee, Chase Krumpelman, Sugato Basu, Raymond J. Mooney, and Joydeep Ghosh. Model based overlapping clustering. In International Conference on Knowledge Discovery and Data Mining, Chicago, USA, 2005. SciTePress.
- Asa Ben-Hur, David Horn, Hava T. Siegelmann, and Vladimir Vapnik. Support vector clustering. Journal Of Machine Learning Re-search, 2:125–137, 2001.
- Chiheb BenN'Cir, Nadia Essoussi, and Patrice Bertrand. Kernel overlapping k-means for clustering in feature space. In International Conference on Knowledge discovery and Information Retrieval KDIR, pages 250–256, Valencia, SPA, 2010. SciTePress Digital Library.
- P. Bertrand and M. F. Janowitz. The k-weak hierarchical representations: an extension of the indexed closed weak hierarchies. Discrete Applied Mathematics, 127(2):199–220, 2003.
- James C. Bezdek, Robert Ehrlich, and William Full. Fcm: The fuzzy c-means clustering algorithm. Computers amp; Geosciences, 10(23):191 – 203, 1984.
- Francesco Camastra and Alessandro Verri. A novel kernel method for clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence, 27:801–804, 2005.
- Guillaume Cleuziou. An extended version of the k-means method for overlapping clustering. In International Conference on Pattern Recognition ICPR, pages 1–4, Florida, USA, 2008. IEEE.
- Corinna Cortes and Vladimir Vapnik. Support vector networks. Machine Learning, 20:273–297, 1995.
- E. Diday. Orders and overlapping clusters by pyramids. Technical Report 730, INRIA, France, 1984.
- Walter Didimo, Francesco Giordano, and Giuseppe Liotta. Overlapping cluster planarity. In Proceedings of the six International Asia-Pacific Symposium on Visualization, pages 73–80, 2007.
- Michael R. Fellows, Jiong Guo, Christian Komusiewicz, Rolf Niedermeier, and Johannes Uhlmann. Graph-based data clustering with overlaps. Discrete Optimization, 8(1):2–17, 2011.
- Maurizio Filippone, Francesco Camastra, Francesco Masulli, and Stefano Rovetta. A survey of kernel and spectral methods for clustering. Pattern Recognition, 41(1):176 – 190, 2008.
- Mark Girolami. Mercer kernel-based clustering in feature space. IEEE Transactions on Neural Networks, 13(13):780–784, 2002.
- A. K. Qinand and P. N. Suganthan. Kernel neural gas algorithms with application to cluster analysis. International Conference on Pattern Recognition, 4:617–620, 2004.
- Bernhard Sch¨olkopf, Alexander Smola, and Klaus-Robert M¨uller. Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation, 10(5):1299–1319, 1998.
- Grigorios Tsoumakas, Ioannis Katakis, and Ioannis Vlahavas. Mining Multi-label Data. In Data Mining and Knowledge Discovery Handbook, chapter 34, pages 667–685. Boston, MA, 2010.
- Daoqiang Zhang and Songcan Chen. Kernel-based fuzzy and possibilistic c-means clustering. In International Conference on Artificial Neural Networks (ICANN03), pages 122–125, Istanbul, Turkey, 2003.
- Daoqiang Zhang and Songcan Chen. A novel kernelized fuzzy cmeans algorithm with application in medical image segmentation. Artificial Intelligence in Medicine, 32(1):37–50, 2004.
Index Terms
Keywords