CUR Decompositions, Similarity Matrices, and Subspace Clustering

Date

2019-01-21

Author

Aldroubi, Akram
Hamm, Keaton
Koku, Ahmet Buğra
Sekmen, Ali

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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A general framework for solving the subspace clustering problem using the CUR decomposition is presented. The CUR decomposition provides a natural way to construct similarity matrices for data that come from a union of unknown subspaces U=⋃Mi=1Si. The similarity matrices thus constructed give the exact clustering in the noise-free case. Additionally, this decomposition gives rise to many distinct similarity matrices from a given set of data, which allow enough flexibility to perform accurate clustering of noisy data. We also show that two known methods for subspace clustering can be derived from the CUR decomposition. An algorithm based on the theoretical construction of similarity matrices is presented, and experiments on synthetic and real data are presented to test the method. Additionally, an adaptation of our CUR based similarity matrices is utilized to provide a heuristic algorithm for subspace clustering; this algorithm yields the best overall performance to date for clustering the Hopkins155 motion segmentation dataset.

Subject Keywords

Computer vision and pattern recognition, Machine learning, Numerical analysis

URI

https://hdl.handle.net/11511/41456

Journal

Frontiers in Applied Mathematics and Statistics

DOI

https://doi.org/10.3389/fams.2018.00065

Collections

Department of Mechanical Engineering, Article

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Citation Formats

A. Aldroubi, K. Hamm, A. B. Koku, and A. Sekmen, “CUR Decompositions, Similarity Matrices, and Subspace Clustering,” Frontiers in Applied Mathematics and Statistics, pp. 0–0, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/41456.