Scaling analysis of affinity propagation

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 81, Issue 6, 2010, Pages

  Furtlehner, Cyril ^a   Sebag, Michèle ^b   Zhang, Xiangliang ^c  

^a INRIA SACLAY   (France)

^b CNRS   (France)

^c INRIA   (France)

Author keywords

[No Author keywords available]

Indexed keywords

CONDENSED MATTER PHYSICS; PHYSICS;

AFFINITY PROPAGATION; D-DIMENSIONAL SPACES; DIVIDE AND CONQUER; HIERARCHICAL STRATEGIES; NUMBER OF CLUSTERS; PENALTY COEFFICIENT; SCALING PROPERTIES; SELF SIMILARITY PROPERTIES;

CLUSTERING ALGORITHMS;

EID: 77953470265     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.81.066102     Document Type: Article

References (23)

1. A. P. Dempster, N. M. Laird, and D. B. Rubin, J. R. Stat. Soc. Ser. B (Methodol.) 39, 1 (1977).
2. In these algorithms, k is the number of centers to be obtained by alternatively assigning data points to candidate centers (expectation step) and then taking the mean of each newly defined cluster as new candidate centers (optimization step).
3. S. Wiseman, M. Blatt, and E. Domany, Phys. Rev. E 57, 3767 (1998). 10.1103/PhysRevE.57.3767
4. J. Pearl, Probabilistic Reasoning in Intelligent Systems: Network of Plausible Inference (Morgan Kaufmann, San Francisco, CA, 1988).
5. J. S. Yedidia, W. T. Freeman, and Y. Weiss, Adv. Neural Inf. Process. Syst. 13, 689 (2001).
6. F. R. Kschischang, B. J. Frey, and H. A. Loeliger, IEEE Trans. Inf. Theory 47, 498 (2001). 10.1109/18.910572
7. B. Frey and D. Dueck, Science 315, 972 (2007). 10.1126/science.1136800
8. M. Leone, Sumedha, and M. Wright, Bioinformatics 23, 2708 (2007). 10.1093/bioinformatics/btm414
9. M. Leone, Sumedha, and M. Weight, Eur. Phys. J. B 66, 125 (2008). 10.1140/epjb/e2008-00381-8
10. C. Fraley and A. Raftery, Comput. J. 41, 578 (1998). 10.1093/comjnl/41.8. 578
11. S. Still and W. Bialek, Neural Comput. 16, 2483 (2004). 10.1162/0899766042321751
12. S. Dudoit and J. Fridlyand, Genome Biol. 2, 0036.1 (2002).
13. K. Wang, J. Zhang, D. Li, X. Zhang, and T. Guo, Acta Automatica Sin. 33, 1242 (2007).
14. X. Zhang, C. Furtlehner, and M. Sebag, Data Streaming with Affinity Propagation (ECML/PKDD, Antwerp, 2008), pp. 628-643.
15. X. Zhang, C. Furtlehner, J. Perez, C. Germain-Renaud, and M. Sebag, Toward Autonomic Grids: Analyzing the Job Flow with Affinity Streaming (KDD, Paris, 2009), pp. 628-643.
16. Y. Kabashima, J. Phys. Soc. Jpn. 72, 1645 (2003). 10.1143/JPSJ.72.1645
17. Except if the similarity matrix is sparse, in which case the complexity reduces to N k log (N) with k the average connectivity of the similarity matrix.
18. S. Guha, A. Meyerson, N. Mishra, R. Motwani, and L. O'Callaghan, IEEE Transaction on Knowledge and Data Engineering 15, 515-528 (2003). 10.1109/TKDE.2003.1198387
19. L. de Haan and A. Ferreira, Extreme Value Theory (Springer, New York, 2006).
20. / d ω in 5.4.
21. Lihi Zelnik-manor and Pietro Perona, in Advances in Neural Information Processing Systems 17 (MIT Press, Cambridge, MA, 2004), pp. 1601-1608.
22. M. Meila, The Uniqueness of a Good Optimum for k -Means (ACM, Pittsburgh, PA, 2006), pp. 625-632.
23. Fluctuations are neglected in this argument. In practice the exemplars which emerge from the coalescence of two clusters might originate from both clusters, when considering different subsets, if the number of data is not sufficiently large.