A nonparametric statistical approach to clustering via mode identification

Journal of Machine Learning Research

Volumn 8, Issue , 2007, Pages 1687-1723

  Li, Jia ^a   Ray, Surajit ^b   Lindsay, Bruce G ^a  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

^b Boston University   (United States)

Author keywords

Mixture modeling; Modal clustering; Modal EM; Mode based clustering; Nonparametric density; Ridgeline EM

Indexed keywords

HIERARCHICAL SYSTEMS; MATHEMATICAL MODELS; PROBABILITY DENSITY FUNCTION; PROBLEM SOLVING; STATISTICAL METHODS;

MIXTURE MODELING; MODAL CLUSTERING; MODE IDENTIFICATION; NONPARAMETRIC DENSITY ESTIMATORS;

CLUSTERING ALGORITHMS;

EID: 34547875342     PISSN: 15324435     EISSN: 15337928     Source Type: Journal    
DOI: None     Document Type: Article

References (37)

1. A. Banerjee, I. S. Dhillon, J. Ghosh, and S. Sra. Clustering on the unit hypersphere using von Mises-Fisher distributions. Journal of Machine Learning Research, 6:1345-1382, 2005.
2. J. D. Banfield and A. E. Raftery. Model-based Gaussian and non-Gaussian clustering. Biometrics, 49:803-821, 1993.
3. C. Blake, E. Keogh, and C. J. Merz. UCI repository of machine learning databases. http://www.ics.uci.edu/mlearn/MLRepository.html, Dept. of Information and Computer Science, UCI, 1998.
4. G. Celeux and G. Govaert. Comparison of the mixture and the classification maximum likelihood in cluster analysis. Journal of Statistical Computation & Simulation, 47:127-146, 1993.
5. S. V. Chakravarthy and J. Ghosh. Scale-based clustering using the radial basis function network. IEEE Trans. Neural Networks, 7(5):1250-1261, 1996.
6. M.-Y. Cheng, P. Hall, and J. A. Hartigan. Estimating gradient trees. A Festschrift for Herman Rubin, IMS Lecture Notes Monogr. Ser., 45:237-49, Inst. Math. Statist., Beachwood, OH, 2004.
7. H. Chipman and R. Tibshirani. Hybrid hierarchical clustering with applications to microarray data. Biostatistics, 7(2):286-301, 2006.
8. T. M. Cover and J. A. Thomas. Elements of Information Theory. John Wiley & Sons, Inc., 1991.
9. A. P. Dempster, N. M. Laird, and D. B. Rubin. Maximum likelihood from incomplete data via the EM algorithm. Journal Royal Statistics Society, 39(1):1-21, 1977.
10. B. S. Everitt, S. Landau, and M. Leese. Cluster Analysis. Oxford University Press US, 2001.
11. C. Fraley and A. E. Raftery. Model-based clustering, discriminant analysis, and density estimation. Journal of the American Statistical Association, 97:611-631, 2002.
12. C. Fraley and A. E. Raftery. MCLUST Version 3 for R: Normal mixture modeling and model-based clustering. Technical Report, no. 504, Department of Statistics, University of Washington, 2006.
13. T. F. Gonzalez. Clustering to minimize the maximum intercluster distance. Theoret. Comp. Sci., 38(22):293-306, 1985.
14. J. C. Gower and G. J. S. Ross. Minimum spanning trees and single linkage cluster analysis. Applied Statistics, 18(1):54-64, 1969.
15. T. Hastie, R. Tibshirani, and J. Friedman. The Elements of Statistical Learning. Springer-Verlag, 2001.
16. A. K. Jain and R. C. Dubes. Algorithms for Clustering Data. Prentice-Hall, Inc., NJ, USA, 1988.
17. A. K. Jain , M. N. Murty, and P. J. Flynn. Data clustering: A review. ACM Computing Surveys, 31(3):264-323, 1999.
18. D. Joshi, J. Li, and J. Z. Wang. A computationally efficient approach to the estimation of two- and three-dimensional hidden Markov models. IEEE Transactions on Image Processing, 15(7):1871-1886, 2006.
19. J. R. Kettenring. The practice of cluster analysis. Journal of Classification, 23(1):3-30, 2006.
20. K. Lang. NewsWeeder: Learning to filter netnews. In Proceeding of the International Conference on Machine Learning, pages 331-339, 1995.
21. Y. Leung, J.-S. Zhang, and Z.-B. Xu. Clustering by scale-space filtering. IEEE Trans. Pattern Analysis and Machine Intelligence, 22(12):1396-1410, 2000.
22. J. Li. Two-scale image retrieval with significant meta-information feedback. In Proc. ACM Multimedia, pages 499-502, Singapore, November 2005.
23. J. Li. Clustering based on a multi-layer mixture model. Journal of Computational and Graphical Statistics, 14(3):547-568, 2005.
24. J. Li and R. M. Gray. Image Segmentation and Compression Using Hidden Markov Models. Springer, 2000.
25. J. Li and J. Z. Wang. Real-time computerized annotation of pictures. In Proc. ACM Multimedia Conference, pages 911-920, ACM, Santa Barbara, CA, October 2006.
26. J. Li and H. Zha. Two-way Poisson mixture models for simultaneous document classification and word clustering. Computational Statistics and Data Analysis, 50(1):163-180, 2006.
27. G. J. McLachlan and D. Peel. Finite Mixture Models. New York: Wiley, 2000.
28. M. C. Minnotte and D. W. Scott. The mode tree: A tool for visualization of nonparametric density features. Journal of Computational and Graphical Statistics, 2(1):51-68, 1993.
29. M. C. Minnotte, D. J. Marchette, and E. J. Wegman. The bumpy road to the mode forest. Journal of Computational and Graphical Statistics, 7(2):239-51, 1998.
30. N. R. Pal and S. K. Pal. A review on image segmentation techniques. Pattern Recognition, 26:1277-94, 1993.
31. A. Pothen, H. D. Simon, and K. Liou. Partitioning sparse matrices with eigenvectors of graphs. SIAM Journal on Matrix Analysis and Applications, 11(3):430-452, 1990.
32. S. Ray and B. G. Lindsay. The topography of multivariate normal mixtures. Annals of Statistics, 33(5):2042-2065, 2005.
33. S. J. Roberts. Parametric and nonparametric unsupervised clustering analysis. Pattern Recognition, 30(2):261-272, 1997.
34. J. Shi and J. Malik. Normalized cuts and image segmentation. IEEE Trans. Pattern Analysis and Machine Intelligence, 22(8):888-905, 2000.
35. J. Z. Wang, J. Li, and G. Wiederhold. SIMPLIcity: Semantics-sensitive integrated matching for picture libraries. IEEE Transactions on Pattern Analysis and Machine Intelligence, 23(9):947-963, 2001.
36. R. Wilson and M. Spann. A new approach to clustering. Pattern Recognition, 23(12):1413-25, 1990.
37. C. F. J. Wu. On the convergence properties of the EM algorithm. The Annals of Statistics, 11(1):95-103, 1983.