  Concept Factorization (CF) and its variants may produce inaccurate
representation and clustering results due to the sensitivity to noise, hard
constraint on the reconstruction error and pre-obtained approximate
similarities. To improve the representation ability, a novel unsupervised
Robust 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, robust
sparse local-coordinate coding and adaptive weighting into a unified model.
RFA-LCF improves the representations by enhancing the robustness of CF to noise
and errors, providing a flexible constraint on the reconstruction error and
optimizing the locality jointly. For robust learning, RFA-LCF clearly learns a
sparse projection to recover the underlying clean data space, and then the
flexible CF is performed in the projected feature space. RFA-LCF also uses a
L2,1-norm based flexible residue to encode the mismatch between the recovered
data and its reconstruction, and uses the robust sparse local-coordinate coding
to represent data using a few nearby basis concepts. For auto-weighting,
RFA-LCF jointly preserves the manifold structures in the basis concept space
and new coordinate space in an adaptive manner by minimizing the reconstruction
errors on clean data, anchor points and coordinates. By updating the
local-coordinate preserving data, basis concepts and new coordinates
alternately, the representation abilities can be potentially improved.
Extensive results on public databases show that RFA-LCF delivers the
state-of-the-art clustering results compared with other related methods.
