Robust subspace clustering
This work addresses the challenge of robust subspace clustering for noisy datasets, which is incremental as it builds on existing sparse subspace clustering methods.
The paper tackles the problem of subspace clustering for noisy data by introducing an algorithm inspired by sparse subspace clustering, with theoretical guarantees on accurate subspace recovery under minimal requirements on orientation and sample numbers, and demonstrates effectiveness through synthetic and real data experiments.
Subspace clustering refers to the task of finding a multi-subspace representation that best fits a collection of points taken from a high-dimensional space. This paper introduces an algorithm inspired by sparse subspace clustering (SSC) [In IEEE Conference on Computer Vision and Pattern Recognition, CVPR (2009) 2790-2797] to cluster noisy data, and develops some novel theory demonstrating its correctness. In particular, the theory uses ideas from geometric functional analysis to show that the algorithm can accurately recover the underlying subspaces under minimal requirements on their orientation, and on the number of samples per subspace. Synthetic as well as real data experiments complement our theoretical study, illustrating our approach and demonstrating its effectiveness.