Statistics – Machine Learning
Scientific paper
2008-10-21
Found Comput Math (2009) 9(5): 517-558
Statistics
Machine Learning
40 pages. Minor changes to the previous version (mainly revised Sections 2.2 & 2.3, and added references). Accepted to the Jou
Scientific paper
10.1007/s10208-009-9043-7
The problem of Hybrid Linear Modeling (HLM) is to model and segment data using a mixture of affine subspaces. Different strategies have been proposed to solve this problem, however, rigorous analysis justifying their performance is missing. This paper suggests the Theoretical Spectral Curvature Clustering (TSCC) algorithm for solving the HLM problem, and provides careful analysis to justify it. The TSCC algorithm is practically a combination of Govindu's multi-way spectral clustering framework (CVPR 2005) and Ng et al.'s spectral clustering algorithm (NIPS 2001). The main result of this paper states that if the given data is sampled from a mixture of distributions concentrated around affine subspaces, then with high sampling probability the TSCC algorithm segments well the different underlying clusters. The goodness of clustering depends on the within-cluster errors, the between-clusters interaction, and a tuning parameter applied by TSCC. The proof also provides new insights for the analysis of Ng et al. (NIPS 2001).
Chen Guangliang
Lerman Gilad
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