A generalized single linkage method for estimating the cluster tree of a density

Journal of Computational and Graphical Statistics

Volumn 19, Issue 2, 2010, Pages 397-418

  Stuetzle, Werner ^a   Nugent, Rebecca ^b  

^a UNIVERSITY OF WASHINGTON   (United States)

^b CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

Cluster analysis; Excess mass; Level set; Nearest neighbor density estimation; Runt test; Single linkage clustering

Indexed keywords

EID: 77956662186     PISSN: 10618600     EISSN: None     Source Type: Journal    
DOI: 10.1198/jcgs.2009.07049     Document Type: Article

References (33)

1. Ankerst, M., Breuning, M. M., Kriegel, H. P., and Sander, J. (1999), "Optics: Ordering Points to Identify the Clustering Structure," in Proceedings of the ACM SIGMOD International Conference on Management of Data (SIGMOD'99), Philadelphia, PA: ACM Press, pp. 49-60. [400]
2. Carmichael, J. W., George, G. A., and Julius, R. S. (1968), "Finding Natural Clusters," Systematic Zoology, 17, 144-150. [397]
3. Cuevas, A., Febrero, M., and Fraiman, R. (2000), "Estimating the Number of Clusters," Canadian Journal of Statistics, 28 (2), 367-382. [400,402]
4. - (2001), "Cluster Analysis: A Further Approach Based on Density Estimation," Computational Statistics and Data Analysis, 36 (4), 441-459. [400,402]
5. Ester, M., Kriegel, H. P., Sander, J., and Xu, X. (1996), "A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases With Noise," in Proceedings of the 2nd International Conference on Knowledge Discovery and Data Mining (KDD-96), AAAI Press, pp. 226-231. [400]
6. Fraley, C, and Raftery, A. (1998), "How Many Clusters? Which Clustering Method?-Answers via Model-Based Cluster Analysis," The Computer Journal, 41, 578-588. [398,408]
7. - (1999), "Mclust: Software for Model-Based Cluster Analysis," Journal of Classification, 16, 297-306. [398,408]
8. - (2006), "Mclust Version 3 for R: Normal Mixture Modeling and Model-Based Clustering," Technical Report 504, University of Washington, Dept. of Statistics. [398,408]
9. - (2008), "mclust: Model-Based Clustering/Normal Mixture Modeling," R package version 3.1-5. [408]
10. Friedman, J. H. (1987), "Exploratory Projection Pursuit," Journal of the American Statistical Association, 82, 249-266. [416]
11. Friedman, J. H., Stuetzle, W, and Schroeder, A. (1984), "Projection Pursuit Density Estimation," Journal of the American Statistical Association, 79, 599-608. [416]
12. Hartigan, J. A. (1975), Clustering Algorithms, New York: Wiley. [398,399]
13. - (1981), "Consistency of Single Linkage for High-Density Clusters," Journal of the American Statistical Association, 76, 388-394. [398]
14. - (1987), "Estimation of a Convex Density Contour in Two Dimensions," Journal of the American Statis tical Association, 82 (397), 267-270. [406]
15. Hartigan, J. A., and Mohanty, S. (1992), "The Runt Test for Multimodality," Journal of Classification, 9, 63-70. [407]
16. Hubert, L., and Arabie, P. (1985), "Comparing Partitions," Journal of Classification, 2, 193-217. [410]
17. Klemelae, J. (2004), "Visualization of Multivariate Density Estimates With Level Set Trees," Journal of Computational and Graphical Statistics, 13 (3), 599-620. [401]
18. - (2005), "Algorithms for Manipulation of Level Sets of Nonparametric Density Estimates," Computa tional Statistics, 20 (2), 349-368. [401]
19. McLachlan, G. J., and Peel, D. (2000), Finite Mixture Models, New York: Wiley. [398,408]
20. Mueller, D. W., and Sawitzki, G. (1991), "Excess Mass Estimates and Tests of Multimodality," Journal of the American Statistical Association, 86, 738-746. [406]
21. Murua, A., Stanberry, L., and Stuetzle, W. (2008), "On Potts Model Clustering, Kernel k-Means and Density Estimation," Journal of Computational and Graphical Statistics, 17 (4), 629-658. [415]
22. Nugent, R. (2006), "Algorithms for Estimating the Cluster Tree of a Density," Ph.D. thesis, University of Washington. [401,403,416]
23. Polonik, W. (1995), "Measuring Mass Concentrations and Estimating Density Contour Clusters-An Excess Mass Approach," The Annals of Statistics, 23 (3), 855-881. [406]
24. R Development Core Team (2008), R: A Language and Environment for Statistical Computing, Vienna, Austria: R Foundation for Statistical Computing. [408]
25. Shao, J., and Tu, D. (1995), The Jackknife and Bootstrap, New York: Springer. [411]
26. Silverman, B. W (1986), Density Estimation for Statistics and Data Analysis, London-New York: Chapman & Hall. [400,408]
27. Stuetzle, W (2003), "Estimating the Cluster Tree of a Density by Analyzing the Minimal Spanning Tree of a Sample," Journal of Classification, 20 (5), 25-47. [398,401,408,415]
28. Tukey, P. A., and Tukey, J. W. (1981), "Data Driven View Selection, Agglomeration, and Sharpening," in Interpreting Multivariate Data, ed. V Barnett, Chichester-New York: Wiley, pp. 215-243. [400]
29. Walther, G. (1997), "Granulometric Smoothing," The Annals of Statistics, 25 (6), 2273-2299. [400]
30. Wishart, D. (1969), "Mode Analysis: A Generalization of Nearest Neighbor Which Reduces Chaining Effects,"in Numerical Taxonomy, ed. A. J. Cole, London-New York: Academic Press, pp. 282-311. [398-400]
31. Wong, M. A. (1979), "Hybrid Clustering," Ph.D. thesis, Yale University. [401]
32. Wong, M. A., and Lane, T. (1983), "A kth Nearest Neighbor Clustering Procedure," Journal of the Royal Statistical Society, Ser. B, 45, 362-368. [401]
33. Yeoh, E. J., Ross, M. E., Shurtle, S. A., Williams, W K., Patel, D., Mahfouz, R., Behm, F. G., Raimondi, S. C, Relling, M. V, Patel, A., Cheng, C, Campana, D., Wilkins, D., Zhou, X., Li, J., Liu, H., Pui, C. H., Evans, W E., Naeve, C, Wong, L., and Downing, J. R. (2002), "Classification, Subtype Discovery, and Prediction of Outcome in Pediatric Acute Lymphoblastic Leukemia by Gene Expression Profiling," Cancer Cell, 1, 133-143. [414]