Branch-and-bound for model selection and its computational complexity

IEEE Transactions on Knowledge and Data Engineering

Volumn 23, Issue 5, 2011, Pages 655-668

  Thakoor, Ninad ^a   Gao, Jean ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b University of Texas at Arlington   (United States)

Author keywords

branch and bound; Clustering; combinatorial optimization; model selection; segmentation

Indexed keywords

BRANCH AND BOUNDS; CLASSICAL APPROACH; CLUSTER PARAMETERS; CLUSTERING; CLUSTERING PROBLEMS; CLUSTERING QUALITY; COHERENT SAMPLING; DATA ANALYSIS; FEATURE SELECTION; IMAGE DATA; IMAGE DATA ANALYSIS; ITERATIVE APPROACH; MODEL SELECTION; NUMBER OF CLUSTERS; OPTIMAL SUBSETS; SEGMENTATION; SPATIAL COHERENCY;

BRANCH AND BOUND METHOD; COMBINATORIAL OPTIMIZATION; COMPUTATIONAL COMPLEXITY; FEATURE EXTRACTION;

CLUSTER ANALYSIS;

EID: 79953200772     PISSN: 10414347     EISSN: None     Source Type: Journal    
DOI: 10.1109/TKDE.2010.156     Document Type: Article

References (41)

1. J. Han and M. Kamber, Data Mining: Concepts and Techniques. Morgan Kaufmann Publishers Inc., 2006.
2. D.A. Forsyth and J. Ponce, Computer Vision: A Modern Approach. Prentice Hall, 2002.
3. S. Theodoridis and K. Koutroumbas, Pattern Recognition. Academic Press, 2008.
4. S. Mitra and T. Acharya, Data Mining: Multimedia, Soft Computing, and Bioinformatics. Wiley-Interscience, 2003.
5. S. Zhong and J. Ghosh, "A Unified Framework for Model-Based Clustering," J. Machine Learning Research, vol. 4, pp. 1001-1037, 2003.
6. A.P. Dempster, N.M. Laird, and D.B. Rubin, "Maximum Likelihood from Incomplete Data Via the Em Algorithm," J. Royal Statistical Soc. B, vol. 39, no. 1, pp. 1-38, http://dx.doi.org/10.2307/2984875, 1977.
7. K.P. Burnham and D.A. Anderson, Model Selection and Multi-Model Inference. Springer, 2003.
8. H. Li, "Two-view Motion Segmentation from Linear Programming Relaxation," Proc. IEEE Int'l Conf. Computer Vision and Pattern Recognition, pp. 1-8, June 2007.
9. K. Schindler and D. Suter, "Two-view Multibody Structure-and-Motion with Outliers through Model Selection," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 28, no. 6, pp. 983-995, June 2006.
10. N. Thakoor and J. Gao, "Branch-and-Bound Hypothesis Selection for Two-View Multiple Structure and Motion Segmentation," Proc. IEEE Int'l Conf. Computer Vision and Pattern Recognition, pp. 1-6, June 2008.
11. R.I. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision, second ed. Cambridge Univ. Press, 2004.
12. P.H.S. Torr, "Geometric Motion Segmentation and Model Selection," Philosophical Trans. Royal Soc. London A, vol. 356, no. 1740, pp. 1321-1340, http://dx.doi.org/10.1098/rsta.1998.0224, May 1998. (Pubitemid 128548608)
13. F. Glover and M. Laguna, Modern Heuristic Techniques for Combinatorial Problems. John Wiley & Sons, Inc., pp. 70-150, 1993.
14. F.A. Chudak and D.B. Shmoys, "Improved Approximation Algorithms for the Uncapacitated Facility Location Problem," SIAM J. Computation, vol. 33, no. 1, pp. 1-25, 2004.
15. D.S. Hochbaum, Ed., Approximation Algorithms for NP-hard Problems. PWS Publishing Co., 1997.
16. G. Schwarz, "Estimating the Dimension of a Model," Annals of Statistics, vol. 6, no. 2, pp. 461-464, http://www.jstor.org/stable/2958889, 1978.
17. M. Brusco and S. Stahl, Branch-and-Bound Applications in Combinatorial Data Analysis. Springer, 2005.
18. K. Fukunaga, Introduction to Statistical Pattern Recognition. Academic Press Professional, Inc., 1990.
19. P. Somol, P. Pudil, and J. Kittler, "Fast Branch and Bound Algorithms for Optimal Feature Selection," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 26, no. 7, pp. 900-912, July 2004.
20. L.-K. Shark, A.A. Kurekin, and B.J. Matuszewski, "Development and Evaluation of Fast Branch-and-Bound Algorithm for Feature Matching Based on Line Segments," Pattern Recognition, vol. 40, no. 5, pp. 1432-1450, 2007. (Pubitemid 46123391)
21. M. Roder, J. Cardinal, and R. Hamzaoui, "Branch and Bound Algorithms for Rate-Distortion Optimized Media Streaming," IEEE Trans. Multimedia, vol. 8, no. 1, pp. 170-178, Feb. 2006. (Pubitemid 43146140)
22. J. Jonsson and K. Shin, "A Parametrized Branch-and-Bound Strategy for Scheduling Precedence-Constrained Tasks on a Multiprocessor System," Proc. Int'l Conf. Parallel Processing, pp. 158-165, 1997.
23. S. Fujita, M. Masukawa, and S. Tagashira, "A Fast Branch-and-Bound Algorithm with an Improved Lower Bound for Solving the Multiprocessor Scheduling Problem," Proc. Int'l Conf. Parallel and Distributed Systems, pp. 611-616, 2002.
24. W.L.G. Koontz, P.M. Narendra, and K. Fukunaga, "A Branch and Bound Clustering Algorithm," IEEE Trans. Computation, vol. 24, no. 9, pp. 908-915, 1975.
25. N. Thakoor, V. Devarajan, and J. Gao, "Multi-Stage Branch-and-Bound for Maximum Variance Disparity Clustering," Proc. Int'l Conf. Pattern Recognition, pp. 1-4, Dec. 2008.
26. N. Thakoor, J. Gao, and V. Devarajan, "Multistage Branch-and-Bound Merging for Planar Surface Segmentation in Disparity Space," IEEE Trans. Image Processing, vol. 17, no. 11, pp. 2217-2226, Nov. 2008.
27. L. Devroye and C. Zamora-Cura, "On the Complexity of Branchand Bound Search for Random Trees," Random Structures and Algorithms, vol. 14, no. 4, pp. 309-327, July 1999.
28. D.R. Smith, "On the Computational Complexity of Branch and Bound Search Strategies," PhD dissertation, Duke Univ., 1979.
29. D.R. Smith, "Random Trees and the Analysis of Branch and Bound Procedures," J. ACM, vol. 31, no. 1, pp. 163-188, 1984.
30. H.S. Stone and P. Sipala, "The Average Complexity of Depth-First Search with Backtracking and Cutoff," IBM J. Research and Development, vol. 30, no. 3, pp. 242-258, 1986. (Pubitemid 17652404)
31. W. Zhang, "Branch-and-Bound Search Algorithms and Their Computational Complexity," Univ. of southern California/Information Sciences Inst., Tech. Rep. ISI/RR-96-443, May 1996.
32. W. Zhang and R.E. Korf, "Performance of Linear-Space Search Algorithms," Artificial Intelligence, vol. 79, pp. 241-292, 1995.
33. J.L. Crassidis and J.L. Junkins, Optimal Estimation of Dynamic Systems. Chapman & Hall/CRC, 2004.
34. A.D.R. McQuarrie and C.-L. Tsai, Regression and Time Series Model Selection. World Scientific, 1998.
35. T.H. Cormen, C.E. Leiserson, R.L. Rivest, and C. Stein, Introduction to Algorithms. The MIT Press, 2001.
36. W. Feller, An Introduction to Probability Theory and Its Applications, second ed. vol. 2, John Wiley and Sons, 1966.
37. P. Torr, A Structure and Motion Toolkit in Matlab, http://cms.brookes.ac. uk/staff/PhilipTorr/Beta/torrsam.zip, 2010.
38. P.H.S. Torr and A. Zisserman, "MLESAC: A New Robust Estimator with Application to Estimating Image Geometry," Computer Vision and Image Understanding, vol. 78, no. 1, pp. 138-156, 2000. (Pubitemid 30596414)
39. R. Vidal and S. Sastry, "Optimal Segmentation of Dynamic Scenes from Two Perspective Views," Proc. IEEE Int'l Conf. Computer Vision and Pattern Recognition, vol. 2, pp. 281-286, June 2003.
40. R. Vidal, S. Soatto, Y. Ma, and S. Sastry, "Segmentation of Dynamic Scenes from the Multibody Fundamental Matrix," Proc. European Conf. Computer Vision Workshop Visual Modeling of Dynamic Scenes, 2002.
41. The Hopkins 155 Dataset, http://www.vision.jhu.edu/data/hopkins155/, 2010.