How the result of graph clustering methods depends on the construction of the graph

ESAIM - Probability and Statistics

Volumn 17, Issue , 2013, Pages 370-418

  Maier, Markus ^a   von Luxburg, Ulrike ^a,b   Hein, Matthias ^c  

^a MAX PLANCK INSTITUTE FOR INTELLIGENT SYSTEMS   (Germany)

^b UNIVERSITY OF HAMBURG   (Germany)

^c SAARLAND UNIVERSITY   (Germany)

Author keywords

Clustering; Graph cuts; Random geometric graph

Indexed keywords

EID: 84996143328     PISSN: 12928100     EISSN: 12623318     Source Type: Journal    
DOI: 10.1051/ps/2012001     Document Type: Article

References (14)

1. D. Angluin and L. Valiant, Fast probabilistic algorithms for Hamiltonian circuits. J. Comput. Syst. Sci. 18 (1979) 155-193.
2. G. Biau, B. Cadre and B. Pelletier, A graph-based estimator of the number of clusters. ESAIM: PS 11 (2007) 272-280.
3. M. Brito, E. Chavez, A. Quiroz and J. Yukich, Connectivity of the mutual fc-nearest-neighbor graph in clustering and outlier detection. Stat. Probab. Lett. 35 (1997) 33-42.
4. S. Bubeck and U. von Luxburg, Nearest neighbor clustering: a baseline method for consistent clustering with arbitrary objective functions. J. Mach. Learn. Res. 10 (2009) 657-698.
5. J.W. Harris and H. Stocker, Handbook of Mathematics and Computational Science. Springer (1998).
6. W. Hoeffding, Probability inequalities for sums of bounded random variables. J. Am. Stat. Assoc. 58 (1963) 13-30.
7. D.O. Loftsgaarden and C.P. Quesenberry, A nonparametric estimate of a multivariate density function. Ann. Math. Stat. 36 (1965) 1049-1051.
8. M. Maier, M. Hein and U. von Luxburg, Optimal construction of k-nearest neighbor graphs for identifying noisy clusters. Theoret. Comput. Sci. 410 (2009) 1749-1764.
9. M. Maier, U. von Luxburg and M. Hein, Influence of graph construction on graph-based clustering measures, in Advances in Neural Information Processing Systems, vol. 21, edited by D. Koller, D. Schuurmans, Y. Bengio and L. Bottou. MIT Press (2009) 1025-1032.
10. G. Miller, S. Teng, W. Thurston and S. Vavasis, Separators for sphere-packings and nearest neighbor graphs. J. ACM 44 (1997) 1-29.
11. H. Narayanan, M. Belkin and P. Niyogi, On the relation between low density separation, spectral clustering and graph cuts, in Advances in Neural Information Processing Systems, vol. 19, edited by B. Schölkopf, J. Platt and T. Hoffman. MIT Press (2007) 1025-1032.
12. A. Srivastav and P. Stangier, Algorithmic Chernoff-Hoeffding inequalities in integer programming. Random Struct. Algorithms 8 (1996) 27-58.
13. U. von Luxburg, A tutorial on spectral clustering. Stat. Comput. 17 (2007) 395-416.
14. U. von Luxburg, M. Belkin and O. Bousquet, Consistency of spectral clustering. Ann. Stat. 36 (2008) 555-586.