Persistence-based clustering in Riemannian manifolds

Proceedings of the Annual Symposium on Computational Geometry

Volumn , Issue , 2011, Pages 97-106

  Chazal, Frédéric ^a   Oudot, Steve ^a   Skraba, Primoz ^a   Guibas, Leonidas J ^b  

^a INRIA SACLAY   (France)

^b Stanford University   (United States)

Author keywords

Clustering; Mode Seeking; Morse Theory; Topological Persistence; Unsupervised Learning

Indexed keywords

COMPUTATIONAL GEOMETRY; GRAPHIC METHODS; MERGING; TOPOLOGY; UNSUPERVISED LEARNING;

CLUSTERING; EXPERIMENTAL ASPECTS; MODE SEEKING; MORSE THE-ORY; RIEMANNIAN MANIFOLD; SAMPLING CONDITIONS; THEORETICAL GUARANTEES; TOPOLOGICAL PERSISTENCES;

CLUSTERING ALGORITHMS;

EID: 79960162399     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1998196.1998212     Document Type: Conference Paper

References (29)

1. G. Carlsson. Topology and data. Bulletin of the American Mathematical Society, 46(2):255-308, 2009.
2. G. Carlsson, T. Ishkhanov, V. Silva, and A. Zomorodian. On the local behavior of spaces of natural images. Int. J. Computer Vision, 76(1):1-12, 2008. (Pubitemid 350234084)
3. G. Carlsson, A. Zomorodian, A. Collins, and L. Guibas. Persistence barcodes for shapes. In Proc. Symp. Geom. Process., pages 127-138, 2004.
4. F. Chazal, D. Cohen-Steiner, L. J. Guibas, M. Glisse, and S. Y. Oudot. Proximity of persistence modules and their diagrams. In Proc. 25th ACM Sympos. Comput. Geom., pages 237-246, 2009.
5. F. Chazal, D. Cohen-Steiner, and Q. Merigot. Geometric inference for measures based on distance functions. Technical report, INRIA, May 2009.
6. F. Chazal, L. J. Guibas, S. Y. Oudot, and P. Skraba. Analysis of scalarfields over point cloud data. In Proc. 20th ACM-SIAM Sympos. Discrete Algorithms, pages 1021-1030, 2009.
7. F. Chazal, L. J. Guibas, S. Y. Oudot, and P. Skraba. Persistence-based clustering in Riemannian manifolds. Research Report 6968, INRIA, June 2009.
8. W.-Y. Chen, Y. Song, H. Bai, C.-J. Lin, and E. Y. Chang. PSC: Parallel Spectral Clustering, 2008.. http://www.cs.ucsb.edu/~wychen/sc.
9. J. D. Chodera, N. Singhal, V. S. Pande, K. A. Dill, and W. C. Swope. Automatic discovery of metastable states for the construction of markov models of macromolecular conformational dynamics. The Journal of Chemical Physics, 126(15):155101, 2007.
10. J. D. Chodera, W. C. Swope, J. W. Pitera, and K. A. Dill. Long-time protein folding dynamics from short-time molecular dynamics simulations. Multiscale Modeling & Simulation, 5(4):1214-1226, 2006. (Pubitemid 350285620)
11. J. D. Chodera, W. C. Swope, J. W. Pitera, C. Seok, and K. A. Dill. Use of the weighted histogram analysis method for the analysis of simulated and parallel tempering simulations. Journal of Chemical Theory and Computation, 3(1):26-41, 2007.
12. D. Cohen-Steiner, H. Edelsbrunner, and J. Harer. Stability of persistence diagrams. Discrete Comput. Geom., 37(1):103-120, 2007.
13. D. Comaniciu and P. Meer. Mean shift: A robust approach toward feature space analysis. IEEE Trans. on Pattern Analysis and Machine Intelligence, 24(5):603-619, May 2002. (Pubitemid 34550429)
14. H. Edelsbrunner, D. Letscher, and A. Zomorodian. Topological persistence and simplification. Discrete Comput. Geom., 28:511-533, 2002. (Pubitemid 36161396)
15. M. Ester, H.-P. Kriegel, J. Sander, and X. Xu. A density-based algorithm for discovering clusters in large spatial databases with noise. In Proc. 2nd Internat. Conf. on Knowledge Discovery and Data Mining (KDD-96), pages 226-231. AAAI Press, 1996.
16. R. Ghrist. Barcodes: the persistent topology of data. Amer. Math. Soc. Current Events Bulletin, 45(1):61-75, January 2007.
17. J. Hartigan. Clustering Algorithms. Wiley, 1975.
18. T. Hastie, R. Tibshirani, and J. H. Friedman. The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer Series in Statistics. Springer, 2009. Second edition.
19. W. Huisinga and B. Schmidt. Advances in algorithms for macromolecular simulation, chapter metastability and dominant eigenvalues of transfer operators. Lecture Notes in Computational Science and Engineering. Springer, 2005.
20. W. L. Koontz, P. M. Narendra, and K. Fukunaga. A graph-theoretic approach to nonparametric cluster analysis. IEEE Trans. on Computers, 24:936-944, September 1976.
21. S. P. Lloyd. Least squares quantization in pcm. IEEE Trans. on Information Theory, 28(2):129-136, 1982.
22. S. Paris and F. Durand. A topological approach to hierarchical segmentation using Mean Shift. In Proc. IEEE conf. on Computer Vision and Pattern Recognition, 2007.
23. J. Sander, M. Ester, H.-P. Kriegel, and X. Xu. Density-based clustering in spatial databases: The algorithm GDBSCAN and its applications. Data Mining and Knowledge Discovery, 2(2):169-194, 1998.
24. Y. A. Sheikh, E. Khan, and T. Kanade. Mode-seeking by medoidshifts. In Proc. 11th IEEE Internat. Conf. on Computer Vision (ICCV 2007), October 2007.
25. D. L. Theobald. Rapid calculation of rmsds using a quaternion-based characteristic polynomial. Acta Crystallographica Section A: Foundations of Crystallography, 61(4):478-480, 2005. (Pubitemid 43034346)
26. G. T. Toussaint. The relative neighbourhood graph of a infinite planar set. Pattern Recognition, 12:261-268, 1980.
27. A. Vedaldi and S. Soatto. Quick shift and kernel methods for mode seeking. In Proc. European Conf. on Computer Vision (ECCV), 2008.
28. U. von Luxburg. A tutorial on spec tral clustering. Statistics and Computing, 17(4):395-416, 2007.
29. A. Zomorodian and G. Carlsson. Computing persistent homology. Discrete Comput. Geom., 33(2):249-274, 2005. (Pubitemid 40176437)