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Concept Factorization (CF) and its variants may produce inaccuraterepresentation and clustering results due to the sensitivity to noise, hardconstraint on the reconstruction error and pre-obtained approximatesimilarities. To improve the representation ability, a novel unsupervisedRobust Flexible Auto-weighted Local-coordinate Concept Factorization (RFA-LCF)framework is proposed for clustering high-dimensional data. Specifically,RFA-LCF integrates the robust flexible CF by clean data space recovery, robustsparse local-coordinate coding and adaptive weighting into a unified model.RFA-LCF improves the representations by enhancing the robustness of CF to noiseand errors, providing a flexible constraint on the reconstruction error andoptimizing the locality jointly. For robust learning, RFA-LCF clearly learns asparse projection to recover the underlying clean data space, and then theflexible CF is performed in the projected feature space. RFA-LCF also uses aL2,1-norm based flexible residue to encode the mismatch between the recovereddata and its reconstruction, and uses the robust sparse local-coordinate codingto represent data using a few nearby basis concepts. For auto-weighting,RFA-LCF jointly preserves the manifold structures in the basis concept spaceand new coordinate space in an adaptive manner by minimizing the reconstructionerrors on clean data, anchor points and coordinates. By updating thelocal-coordinate preserving data, basis concepts and new coordinatesalternately, the representation abilities can be potentially improved.Extensive results on public databases show that RFA-LCF delivers thestate-of-the-art clustering results compared with other related methods.

Flexible Auto-weighted Local-coordinate Concept Factorization: A Robust Framework for Unsupervised Clustering