Incremental Spectral Clustering

In the present contribution, a novel algorithm for off-line spectral clustering algorithm is introduced and an online extension is derived in order to deal with sequential data. The proposed algorithm aims at dealing with nonconvex clusters having different forms. It relies on the notion of communicability that allows to handle the contiguity of data distribution. In the second part of the paper, an incremental extension of the fuzzy c-varieties is proposed to serve as a building block of the incremental spectral clustering algorithm (ISC). Initial simulations are presented towards the end of the contribution to show the performance of the ISC algorithm.

[1]  Donald Gustafson,et al.  Fuzzy clustering with a fuzzy covariance matrix , 1978, 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes.

[2]  James C. Bezdek,et al.  Pattern Recognition with Fuzzy Objective Function Algorithms , 1981, Advanced Applications in Pattern Recognition.

[3]  Yihong Gong,et al.  Incremental spectral clustering by efficiently updating the eigen-system , 2010, Pattern Recognit..

[4]  Isak Gath,et al.  Fuzzy clustering of elliptic ring-shaped clusters , 1995, Pattern Recognit. Lett..

[5]  Igor Fischer,et al.  New Methods for Spectral Clustering. , 2004 .

[6]  Hichem Frigui,et al.  The fuzzy c spherical shells algorithm: A new approach , 1992, IEEE Trans. Neural Networks.

[7]  Abdelhamid Bouchachia,et al.  Incremental learning with multi-level adaptation , 2011, Neurocomputing.

[8]  Michael I. Jordan,et al.  Multiple Non-Redundant Spectral Clustering Views , 2010, ICML.

[9]  Abdelhamid Bouchachia,et al.  A hybrid ensemble approach for the Steiner tree problem in large graphs: A geographical application , 2011, Appl. Soft Comput..

[10]  Rajesh N. Davé,et al.  Adaptive fuzzy c-shells clustering and detection of ellipses , 1992, IEEE Trans. Neural Networks.

[11]  Abdelhamid Bouchachia,et al.  Fuzzy classification in dynamic environments , 2011, Soft Comput..

[12]  Hichem Frigui,et al.  Fuzzy and possibilistic shell clustering algorithms and their application to boundary detection and surface approximation. II , 1995, IEEE Trans. Fuzzy Syst..

[13]  Abdelhamid Bouchachia,et al.  An evolving classification cascade with self-learning , 2010, Evol. Syst..

[14]  João Pedro Hespanha,et al.  Hierarchical max-flow routing , 2005, GLOBECOM '05. IEEE Global Telecommunications Conference, 2005..

[15]  W. Marsden.  I and J , 2012 .

[16]  Abdelhamid Bouchachia,et al.  Ant colony optimization for Steiner tree problems , 2008, CSTST.

[17]  Jianbo Shi,et al.  Learning Segmentation by Random Walks , 2000, NIPS.

[18]  Jacek M. Leski,et al.  Fuzzy c-varieties/elliptotypes clustering in reproducing kernel Hilbert space , 2004, Fuzzy Sets Syst..

[19]  Tom Duckett,et al.  Incremental Spectral Clustering and Its Application To Topological Mapping , 2007, Proceedings 2007 IEEE International Conference on Robotics and Automation.

[20]  Achim J. Lilienthal,et al.  Incremental spectral clustering and seasons: Appearance-based localization in outdoor environments , 2008, 2008 IEEE International Conference on Robotics and Automation.

[21]  J. Łȩski.  Fuzzy c-varieties/elliptotypes clustering in reproducing kernel Hilbert space , 2004 .

[22]  Thomas A. Runkler,et al.  Identification of nonlinear systems using regular fuzzy c-elliptotype clustering , 1996, Proceedings of IEEE 5th International Fuzzy Systems.

[23]  Witold Pedrycz,et al.  Enhancement of fuzzy clustering by mechanisms of partial supervision , 2006, Fuzzy Sets Syst..

[24]  Jitendra Malik,et al.  Normalized cuts and image segmentation , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[25]  David A. Clausi,et al.  Enabling scalable spectral clustering for image segmentation , 2010, Pattern Recognit..

[26]  Andrew B. Kahng,et al.  New spectral methods for ratio cut partitioning and clustering , 1991, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[27]  Hichem Frigui,et al.  A comparison of fuzzy shell-clustering methods for the detection of ellipses , 1996, IEEE Trans. Fuzzy Syst..

[28]  Dit-Yan Yeung,et al.  Robust path-based spectral clustering , 2008, Pattern Recognit..

[29]  Hichem Frigui,et al.  Fuzzy and possibilistic shell clustering algorithms and their application to boundary detection and surface approximation. II , 1995, IEEE Trans. Fuzzy Syst..

[30]  J. A. Rodríguez-Velázquez,et al.  Subgraph centrality in complex networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  Michael I. Jordan,et al.  On Spectral Clustering: Analysis and an algorithm , 2001, NIPS.

[32]  Rajesh N. Davé,et al.  Validating fuzzy partitions obtained through c-shells clustering , 1996, Pattern Recognit. Lett..

[33]  Michael I. Jordan,et al.  Spectral Clustering for Speech Separation , 2009 .

[34]  Kotagiri Ramamohanarao,et al.  Approximate pairwise clustering for large data sets via sampling plus extension , 2011, Pattern Recognit..

[35]  James C. Bezdek,et al.  Numerical convergence and interpretation of the fuzzy c-shells clustering algorithm , 1992, IEEE Trans. Neural Networks.

[36]  Frank Hoeppner,et al.  Fuzzy shell clustering algorithms in image processing: fuzzy C-rectangular and 2-rectangular shells , 1997, IEEE Trans. Fuzzy Syst..

[37]  Ling Huang,et al.  Fast approximate spectral clustering , 2009, KDD.