iccv iccv2013 iccv2013-264 iccv2013-264-reference knowledge-graph by maker-knowledge-mining
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Author: Choon-Meng Lee, Loong-Fah Cheong
Abstract: In contrast to the current motion segmentation paradigm that assumes independence between the motion subspaces, we approach the motion segmentation problem by seeking the parsimonious basis set that can represent the data. Our formulation explicitly looks for the overlap between subspaces in order to achieve a minimal basis representation. This parsimonious basis set is important for the performance of our model selection scheme because the sharing of basis results in savings of model complexity cost. We propose the use of affinity propagation based method to determine the number of motion. The key lies in the incorporation of a global cost model into the factor graph, serving the role of model complexity. The introduction of this global cost model requires additional message update in the factor graph. We derive an efficient update for the new messages associated with this global cost model. An important step in the use of affinity propagation is the subspace hypotheses generation. We use the row-sparse convex proxy solution as an initialization strategy. We further encourage the selection of subspace hypotheses with shared basis by integrat- ing a discount scheme that lowers the factor graph facility cost based on shared basis. We verified the model selection and classification performance of our proposed method on both the original Hopkins 155 dataset and the more balanced Hopkins 380 dataset.
[1] E. J. Candes, M. B. Wakin, and S. P. Boyd. Enhancing sparsity by reweighted l1minimization. Journal of Fourier Analysis and Applications, 14(5-6):877–905, 2008.
[2] T. Chin, D. Suter, and H. Wang. Multi-structure model selection via kernel optimisation. In CVPR, pages 3586–3593, 2010.
[3] T. Chin, H. Wang, and D. Suter. The ordered residual kernel for robust motion subspace clustering. In NIPS, 2009.
[4] F. Chung. Spectral graph theory. Amer Mathematical Society, 1997.
[5] D. Dueck and B. Frey. Non-metric affinity propagation for unsupervised image categorization. In ICCV, pages 1–8, 2007.
[6] E. Elhamifar and R. Vidal. Sparse subspace clustering. In CVPR, pages 2790–2797, 2009.
[7] E. Elhamifar and R. Vidal. Sparse subspace clustering: Algorithm, theory, and applications. PAMI(Under review), 2012.
[8] B. J. Frey and D. Dueck. Clustering by passing messages between data points. Science, 315:972–976, 2007.
[9] I. Givoni. Beyond Affinity Propagation: Message Passing Algorithms for Clustering. Phd thesis, University of Toronto, 2011.
[10] I. Givoni, C. Chung, and B. Frey. Hierarchical affinity propagation. arXiv preprint arXiv:1202.3722, 2012.
[11] I. Givoni and B. Frey. A binary variable model for affinity propagation. Neural computation, 21(6): 1589–1600, 2009.
[12] K. Kanatani and C. Matsunaga. Estimating the number of independent motions for multibody motion segmentation. pages 7–12, 2002.
[13] F. Lauer and C. Schnorr. Spectral clustering of linear subspaces for motion segmentation. In ICCV, pages 678–685, 2009.
[14] N. Lazic, B. Frey, and P. Aarabi. Solving the uncapacitated facility location problem using message passing algorithms. In AISTATS, volume 9, pages 429–436, 2010.
[15] N. Lazic, I. Givoni, B. Frey, and P. Aarabi. Floss: Facility location for subspace segmentation. In ICCV, pages 825–832, 2009.
[16] H. Li. Two-view motion segmentation from linear programming relaxation. In CVPR, pages 1–8, 2007.
[17] G. Liu. Low-rank representation matlab code.
[18]
[19]
[20]
[21]
[22]
[23]
[24]
[25] https://sites.google.com/site/guangcanliu/. G. Liu, Z. Lin, S. Yan, J. Sun, Y. Yu, and Y. Ma. Robust recovery of subspace structures by low-rank representation. PAMI, 34(1 1), 2012. B. Nadler and M. Galun. Fundamental limitations of spectral clustering. In NIPS, volume 19, page 1017, 2007. A. Ng, M. Jordan, and Y. Weiss. On spectral clustering: Analysis and an algorithm. In NIPS, volume 2, pages 849–856, 2002. J. Nocedal and S. Wright. Numerical optimization. Springer, 2006. M. Soltanolkotabi and E. Candes. A geometric analysis of subspace clustering with outliers. To appear in Annals of Statistics, 2011. D. Tarlow, I. Givoni, and R. Zemel. Hopmap: Efficient message passing with high order potentials. AISTATS, 2010. R. Tron and R. Vidal. A benchmark for the comparison of 3-d motion segmentation algorithms. In CVPR, pages 1–8, 2007. U. Von Luxburg. A tutorial on spectral clustering. Statistics and Computing, 17(4):395–416, 2007. 11559922