Spectral Curvature Clustering (SCC)

By Guangliang Chen, Gilad Lerman. International Journal of Computer Vision, 2009

390 citations recorded by the source corpus.

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.

Subfields: Computer Vision and Pattern Recognition, Media Technology, Signal Processing

View Paper: https://www.semanticscholar.org/paper/68166aec5176b2f2265d66a8902706265ec7e669

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Citations in the corpus

Robust Recovery of Subspace Structures by Low-Rank Representation (2010, methodology): “Many existing methods, such as Sparse Subspace Clustering (SSC) [13], Spectral Curvature Clustering (SCC) [27], [28], Spectral Local Best-fit Flats (SLBF) [29], [30], the proposed LRR method, and [2], [31], possess such a spectral nature, so-called spectral-type methods.”
A Geometric Analysis of Subspace Clustering with Outliers (2011, background): “For a comprehensive review and comparison of these algorithms, we refer the reader to the tutorial [45] and references therein, [4, 10, 14, 43, 5, 40, 1, 29, 50, 38, 37, 30, 34, 48, 47, 51, 16, 11, 12, 27, 9].”
Deep Subspace Clustering Networks (2017, methodology): “The resulting methods can then be roughly divided into three categories [42]: factorization methods [7, 17, 44, 29, 16], higher-order model based methods [49, 6, 33, 37], and self-expressiveness based methods [9, 24, 26, 46, 15, 12, 22, 52].”
Robust Subspace Clustering (2013, methodology): “An approach of this kind is termed Sparse Curvature Clustering (SCC) [16, 17]; please also see [3, 4].”
Subspace Clustering by Block Diagonal Representation (2018, methodology): “The compared methods include SCC [5], SSC [10], LRR [21], LSR [28], S3C [20], BDR-B (our BDR model by using B) and BDRZ (our BDR model by using Z).”
Scalable Sparse Subspace Clustering by Orthogonal Matching Pursuit (2015, background): “If the OMP algorithm computes q k = 0 for some k ≤ N − 2 , then there is nothing to prove.”
Sparse Subspace Clustering: Algorithm, Theory, and Applications (2013, methodology): “LSA and SCC do not have an explicit way to deal with corrupted data.”
Low rank subspace clustering (LRSC) (2014, methodology): “…al., 2007,Rao et al., 2008, Rao et al., 2010), and spectral clustering-based methods (Boult and Brown, 1991; Yan and Pollefeys, 2006; Zhang et al., 2010; Goh and Vidal, 2007; Elhamifar and Vidal, 2009; Elhamifar and Vidal, 2010; Elhamifar and Vidal, 2013; Liu et al., 2010; Chen and Lerman, 2009).”
High-Dimensional Menger-Type Curvatures - Part I: Geometric Multipoles and Multiscale Inequalities (2008, neutral): “AMS Subject Classification (2000): 49Q15, 42C99, 60D05”
High-Dimensional Menger-Type Curvatures—Part II: d-Separation and a Menagerie of Curvatures (2008, methodology): “1 are used in [2, 3] to solve the problem of hybrid linear modeling.”
Sparse Subspace Clustering: Algorithm, Theory, and Applications (2012, background): “Therefore, there is a need for having clustering algorithms that take into account the multisubspace structure of the data.”
Multi-Scale Fusion Subspace Clustering Using Similarity Constraint (2020, methodology): “The way to build afﬁnity matrix could be roughly split into three categories: factorization based methods [9, 25], model based methods [3, 31], and self-expression based methods [4, 12, 19, 34].”