Spectral Curvature Clustering (SCC)

Spectral Curvature Clustering (SCC) is a multi-way spectral clustering algorithm for solving the problem of hybrid linear modeling, that is, to model and segment data using an arrangement of affine subspaces. For the justification of the algorithm and its underlying theory, please refer to the FoCM paper below; for the practical techniques and numerical results, please see the IJCV paper below.

Publications

• Motion Segmentation for Hopkins 155 Database Via SCC [PDF], G. Chen and G. Lerman, The 4th ICCV Workshop on Dynamical Vision, September 2009, Kyoto, Japan.
• Foundations of a Multi-way Spectral Clustering Framework for Hybrid Linear Modeling [PDF], G. Chen and G. Lerman, Found. Comput. Math. (2009) 9: 517–558, DOI 10.1007/s10208-009-9043-7.
• Spectral Curvature Clustering (SCC) [PDF], G. Chen and G. Lerman, Int. J. Comput. Vis. (2009) 81:317-330, DOI 10.1007/s11263-008-0178-9.

Talks

• Multi-manifold data modeling via spectral curvature clustering, Gilad Lerman, IMA Hot Topics Workshop: Multi-Manifold Data Modeling and Applications, University of Minnesota, October 27-30, 2008
• Spectral Curvature Clustering for Hybrid Linear Modeling, Guangliang Chen, Applied Math Seminar, Duke University, 09/28/2009

Matlab Codes

• SCC (implemented by the authors, with some help from Stefan Atev to improve speed)
• Other algorithms compared with in the IJCV paper:
• K-flats (by Guangliang Chen)
• Mixtures of Probabilistic PCA (by Stefan Atev)
• GPCA-voting (can be downloaded at the GPCA website)

C++ implementation

• SCC (implemented by Amit Hooda; have NOT been tested by the authors)

Supplemental Data

• Artificial data: generated by using 'generate_samples.m' which is contained in the GPCA-voting folder
• Real data
• Motion Segmentation (Data, copied from the Hopkins 155 dataset)
• Face Clustering (Yale Face Database B)
• Temporal Partitioning of Video Sequences (Video, provided by Rene Vidal)
• Benchmark: Hopkins 155 Database

Extensions to Multi-Manifold Data Modeling

• Kernel Spectral Curvature Clustering (KSCC)
• Higher Order Spectral Clustering (HOSC)

Contact Info

• Gilad Lerman, lerman (at) umn.edu
• Guangliang Chen, guangliang.chen (at) sjsu.edu

Acknowledgement

• The research described here was supported by NSF grant #0612608.

Last updated on 12/12/2021. Maintained by Guangliang Chen.