Generalized principal component analysis (GPCA)

IEEE Transactions on Pattern Analysis and Machine Intelligence

Volumn 27, Issue 12, 2005, Pages 1945-1959

  Vidal, René ^a   Ma, Yi ^b   Sastry, Shankar ^c  

^a Johns Hopkins University   (United States)

^b United States of America   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Dimensionality reduction; Dynamic scenes and motion segmentation; Principal component analysis (PCA); Subspace segmentation; Temporal video segmentation; Veronese map

Indexed keywords

ALGORITHMS; COMPUTER VISION; POLYNOMIALS; PRINCIPAL COMPONENT ANALYSIS; THEOREM PROVING; VECTORS;

DIMENSIONALITY REDUCTION; SUBSPACE SEGMENTATION; TEMPORAL VIDEO SEGMENTATION;

IMAGE SEGMENTATION;

ALGORITHM; ARTICLE; ARTIFICIAL INTELLIGENCE; AUTOMATED PATTERN RECOGNITION; CLUSTER ANALYSIS; COMPUTER ASSISTED DIAGNOSIS; COMPUTER SIMULATION; IMAGE ENHANCEMENT; INFORMATION RETRIEVAL; METHODOLOGY; PRINCIPAL COMPONENT ANALYSIS; STATISTICAL MODEL; THREE DIMENSIONAL IMAGING;

ALGORITHMS; ARTIFICIAL INTELLIGENCE; CLUSTER ANALYSIS; COMPUTER SIMULATION; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; IMAGING, THREE-DIMENSIONAL; INFORMATION STORAGE AND RETRIEVAL; MODELS, STATISTICAL; PATTERN RECOGNITION, AUTOMATED; PRINCIPAL COMPONENT ANALYSIS;

EID: 30144438432     PISSN: 01628828     EISSN: None     Source Type: Journal    
DOI: 10.1109/TPAMI.2005.244     Document Type: Article

References (28)

1. D.S. Broomhead and M. Kirby, "A New Approach to Dimensionality Reduction Theory and Algorithms," SIAM J. Applied Math., vol. 60, no. 6, pp. 2114-2142, 2000.
2. M. Collins, S. Dasgupta, and R. Schapire, "A Generalization of Principal Component Analysis to the Exponential Family," Advances on Neural Information Processing Systems, vol. 14, 2001.
3. J. Costeira and T. Kanade, "A Multibody Factorization Method for Independently Moving Objects," Int'l J. Computer Vision, vol. 29, no. 3, pp. 159-179, 1998.
4. C. Eckart and G. Young, "The Approximation of One Matrix by Another of Lower Rank," Psychometrika, vol. 1, pp. 211-218, 1936.
5. M.A. Fischler and R.C. Bolles, "RANSAC Random Sample Consensus: A Paradigm for Model Fitting with Applications to Image Analysis and Automated Cartography," Comm. ACM, vol. 26, pp. 381-395, 1981.
6. I.M. Gelfand, M.M. Kapranov, and A.V. Zelevinsky, Discriminants, Resultants, and Multidimensional Determinants. Birkhäuser, 1994.
7. J. Harris, Algebraic Geometry: A First Course. Springer-Verlag, 1992.
8. R. Hartshorne, Algebraic Geometry. Springer, 1977.
9. M. Hirsch, Differential Topology. Springer, 1976.
10. J. Ho, M.-H. Yang, J. Lim, K.-C. Lee, and D. Kriegman, "Clustering Apperances of Objects under Varying Illumination Conditions," Proc. IEEE Conf. Computer Vision and Pattern Recognition, vol. 1, pp. 11-18, 2003.
11. K. Huang, Y. Ma, and R. Vidal, "Minimum Effective Dimension for Mixtures of Subspaces: A Robust GPCA Algorithm and Its Applications," Proc. IEEE Conf. Computer Vision and Pattern Recognition, vol. 2, pp. 631-638, 2004.
12. I. Jolliffe, Principal Component Analysis. New York: Springer-Verlag, 1986.
13. K. Kanatani, "Motion Segmentation by Subspace Separation and Model Selection," Proc. IEEE Int'l Conf. Computer Vision, vol. 2, pp. 586-591, 2001.
14. K. Kanatani and Y. Sugaya, "Multi-Stage Optimization for Multi-Body Motion Segmentation," Proc. Australia-Japan Advanced Workshop Computer Vision, pp. 335-349, 2003.
15. A. Leonardis, H. Bischof, and J. Maver, "Multiple Eigenspaces," Pattern Recognition, vol. 35, no. 11, pp. 2613-2627, 2002.
16. B. Scholkopf, A. Smola, and K.-R. Muller, "Nonlinear Component Analysis as a Kernel Eigenvalue Problem," Neural Computation, vol. 10, pp. 1299-1319, 1998.
17. M. Shizawa and K. Mase, "A Unified Computational Theory for Motion Transparency and Motion Boundaries Based on Eigen-energy Analysis," Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 289-295, 1991.
18. H. Stark and J.W. Woods, Probability and Random Processes with Applications to Signal Processing, third ed. Prentice Hall, 2001.
19. M. Tipping and C. Bishop, "Mixtures of Probabilistic Principal Component Analyzers," Neural Computation, vol. 11, no. 2, pp. 443-482, 1999.
20. M. Tipping and C. Bishop, "Probabilistic Principal Component Analysis," J. Royal Statistical Soc., vol. 61, no. 3, pp. 611-622, 1999.
21. P. Torr, R. Szeliski, and P. Anandan "An Integrated Bayesian Approach to Layer Extraction from Image Sequences," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 23, no. 3, pp. 297-303, Mar. 2001.
22. R. Vidal and R. Hartley, "Motion Segmentation with Missing Data by Power Factorization and Generalized PCA," Proc. IEEE Conf. Computer Vision and Pattern Recognition, vol. 11, pp. 310-316, 2004.
23. R. Vidal, Y. Ma, and J. Piazzi, "A New GPCA Algorithm for Clustering Subspaces by Fitting, Differentiating, and Dividing Polynomials," Proc. IEEE Conf. Computer Vision and Pattern Recognition, vol. I, pp. 510-517, 2004.
24. R. Vidal, Y. Ma, and S. Sastry, "Generalized Principal Component Analysis (GPCA)," Proc. IEEE Conf. Computer Vision and Pattern Recognition, vol. I, pp. 621-628, 2003.
25. R. Vidal, Y. Ma, S. Soatto, and S. Sastry, "Two-View Multibody Structure from Motion," Int'l J. Computer Vision, to be published in 2006.
26. R. Vidal and Y. Ma, "A Unified Algebraic Approach to 2-D and 3-D Motion Segmentation," Proc. European Conf. Computer Vision, pp. 1-15, 2004.
27. Y. Wu, Z. Zhang, T.S. Huang, and J.Y. Lin, "Multibody Grouping via Orthogonal Subspace Decomposition," Proc. IEEE Conf. Computer Vision and Pattern Recognition, vol. 2, pp. 252-257, 2001.
28. L. Zelnik-Manor and M. Irani, "Degeneracies, Dependencies and Their Implications in Multi-Body and Multi-Sequence Factorization," Proc. IEEE Conf. Computer Vision and Pattern Recognition, vol. 2, pp. 287-293, 2003.