Model selection and stability in k-means clustering

21st Annual Conference on Learning Theory, COLT 2008

Volumn , Issue , 2008, Pages 367-378

  Shamir, Ohad ^a   Tishby, Naftali ^a  

^a HEBREW UNIVERSITY OF JERUSALEM   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

APPROPRIATE MODELS; CLUSTERING STABILITY; DATA CLUSTERING; K-MEANS CLUSTERING; MODEL SELECTION; MODEL SELECTION TECHNIQUES; REGULARITY CONDITION; SAMPLE SIZES;

CLUSTERING ALGORITHMS;

EID: 78649406645     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (18)

1. Shai Ben-David, Ulrike von Luxburg, and Dávid Pál. A sober look at clustering stability. In Proceedings of the Nineteenth Annual Conference on Computational Learning Theory, pages 5-19, 2006.
2. Asa Ben-Hur, André Elisseeff, and Isabelle Guyon. A stability based method for discovering structure in clustered data. In Pacific Symposium on Biocomputing, pages 6-17, 2002.
3. V.I. Bogachev. Gaussian Measures. American Mathematical Society, 1998.
4. S. Dudoit and J. Fridlyand. A prediction-based resampling method for estimating the number of clusters in a dataset. Genome Biology, 3(7), 2002.
5. Roger A. Horn and Charles R. Johnson. Matrix Analysis. Cambridge University Press, 1985.
6. A. Krieger and P. Green. A cautionary note on using internal cross validation to select the number of clusters. Psychometrika, 64(3): 341-353, 1999.
7. Tilman Lange, Volker Roth, Mikio L. Braun, and Joachim M. Buhmann. Stability-based validation of clustering solutions. Neural Computation, 16(6): 1299-1323, June 2004.
8. Rafałlatała and Krzysztof Oleszkiewicz. Gaussian measures of dilatations of convex symmetric sets. Annals of Probability, 27(4): 1922-1938, 1999.
9. Erel Levine and Eytan Domany. Resampling method for unsupervised estimation of cluster validity. Neural Computation, 13(11): 2573-2593, 2001.
10. T. Linder. Principles of nonparametric learning, chapter 4: Learning-theoretic methods in vector quantization. Number 434 in CISM Courses and Lecture Notes (L. Gyorfi ed.). Springer-Verlag, New York, 2002.
11. Vitali D. Milman and Gideon Schechtman. Asymptotic Theory of Finite Dimensional Normed Spaces. Springer, 1986.
12. David Pollard. Personal communication.
13. David Pollard. A central limit theorem for k-means clustering. The Annals of Probability, 10(4): 919-926, November 1982.
14. Peter Radchenko. Asymptotics Under Nonstandard Conditions. PhD thesis, Yale University, 2004.
15. Ohad Shamir and Naftali Tishby. Cluster stability for finite samples. In Advances in Neural Information Processing Systems 21, 2007.
16. E. V. Slud. Distribution inequalities for the binomial law. The Annals of Probability, 5(3): 402-412, June 1977.
17. Y.L. Tong. The Multivariate Normal Distribution. Springer, 1990.
18. Aad W. Van Der Vaart and Jon A. Wellner. Weak Convergence and Empirical Processes: With Applications to Statistics. Springer, 1996.