Spectral Curvature Clustering (SCC)
- 2.7k Downloads
This paper presents novel techniques for improving the performance of a multi-way spectral clustering framework (Govindu in Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’05), vol. 1, pp. 1150–1157, 2005; Chen and Lerman, 2007, preprint in the supplementary webpage) for segmenting affine subspaces. Specifically, it suggests an iterative sampling procedure to improve the uniform sampling strategy, an automatic scheme of inferring the tuning parameter from the data, a precise initialization procedure for K-means, as well as a simple strategy for isolating outliers. The resulting algorithm, Spectral Curvature Clustering (SCC), requires only linear storage and takes linear running time in the size of the data. It is supported by theory which both justifies its successful performance and guides our practical choices. We compare it with other existing methods on a few artificial instances of affine subspaces. Application of the algorithm to several real-world problems is also discussed.
KeywordsHybrid linear modeling Multi-way spectral clustering Polar curvature Iterative sampling Motion segmentation Face clustering
- Agarwal, S., Branson, K., & Belongie, S. (2006). Higher order learning with graphs. In Proceedings of the 23rd international conference on machine learning (Vol. 148, pp. 17–24). Google Scholar
- Agarwal, S., Lim, J., Zelnik-Manor, L., Perona, P., Kriegman, D., & Belongie, S. (2005). Beyond pairwise clustering. In Proceedings of the 2005 IEEE computer society conference on computer vision and pattern recognition (CVPR’05) (Vol. 2, pp. 838–845). Google Scholar
- Bader, B., & Kolda, T. (2004). Matlab tensor classes for fast algorithm prototyping (Technical Report SAND2004-5187). Sandia National Laboratories. Google Scholar
- Brand, M. (2003). Fast online SVD revisions for lightweight recommender systems. In Proc. SIAM international conference on data mining. Google Scholar
- Chen, G., & Lerman, G. (2007, submitted). Curvature-driven diffusion and hybrid flat-surfaces modeling. Foundations of Computational Mathematics. Latest version available at the supplementary webpage. Google Scholar
- Epstein, R., Hallinan, P., & Yuille, A. (1995). 5±2 eigenimages suffice: An empirical investigation of low-dimensional lighting models. In IEEE workshop on physics-based modeling in computer vision (pp. 108–116). Google Scholar
- Govindu, V. (2005). A tensor decomposition for geometric grouping and segmentation. In Proceedings of the 2005 IEEE computer society conference on computer vision and pattern recognition (CVPR’05) (Vol. 1, pp. 1150–1157). Google Scholar
- Gruber, P., & Theis, F. (2006). Grassmann clustering. In Proc. EUSIPCO 2006. Florence, Italy. Google Scholar
- Haro, G., Randall, G., & Sapiro, G. (2006). Stratification learning: Detecting mixed density and dimensionality in high dimensional point clouds. Neural Information Processing Systems. Google Scholar
- Ho, J., Yang, M., Lim, J., Lee, K., & Kriegman, D. (2003). Clustering appearances of objects under varying illumination conditions. In Proceedings of international conference on computer vision and pattern recognition (Vol. 1, pp. 11–18). Google Scholar
- Kanatani, K. (2001). Motion segmentation by subspace separation and model selection. In Proc. of 8th ICCV (Vol. 3, pp. 586–591). Vancouver, Canada. Google Scholar
- Kanatani, K. (2002). Evaluation and selection of models for motion segmentation. In 7th ECCV (Vol. 3, pp. 335–349). Google Scholar
- Lerman, G., & Whitehouse, J. T. (2008b). High-dimensional Menger-type curvatures—part I: Geometric multipoles and multiscale inequalities. http://front.math.ucdavis.edu/0805.1425.
- Lerman, G., & Whitehouse, J. T. (2008c). High-dimensional Menger-type curvatures—part II: d-Separation and a menagerie of curvatures. http://front.math.ucdavis.edu/0809.0137.
- Lerman, G., & Whitehouse, J. T. (2008d, in preparation). Least squares approximations for probability measures via multi-way curvatures. Will appear at the supplementary webpage once ready. Google Scholar
- Ng, A., Jordan, M., & Weiss, Y. (2002). On spectral clustering: Analysis and an algorithm. In Advances in neural information processing systems (Vol. 14). Google Scholar
- Shashua, A., Zass, R., & Hazan, T. (2006). Multi-way clustering using super-symmetric non-negative tensor factorization. In ECCV06 (Vol. IV, pp. 595–608). Google Scholar
- Souvenir, R., & Pless, R. (2005). Manifold clustering. In The 10th international conference on computer vision (ICCV 2005). Google Scholar
- Sugaya, Y., & Kanatani, K. (2004). Multi-stage unsupervised learning for multi-body motion segmentation. IEICE Transactions on Information and Systems, E87–D(7), 1935–1942. Google Scholar
- Tseng, P. (1999). Nearest q -flat to m points (Technical report). Google Scholar