  Constrained Concept Factorization (CCF) yields the enhanced representation
ability over CF by incorporating label information as additional constraints,
but it cannot classify and group unlabeled data appropriately. Minimizing the
difference between the original data and its reconstruction directly can enable
CCF to model a small noisy perturbation, but is not robust to gross sparse
errors. Besides, CCF cannot preserve the manifold structures in new
representation space explicitly, especially in an adaptive manner. In this
paper, we propose a joint label prediction based Robust Semi-Supervised
Adaptive Concept Factorization (RS2ACF) framework. To obtain robust
representation, RS2ACF relaxes the factorization to make it simultaneously
stable to small entrywise noise and robust to sparse errors. To enrich prior
knowledge to enhance the discrimination, RS2ACF clearly uses class information
of labeled data and more importantly propagates it to unlabeled data by jointly
learning an explicit label indicator for unlabeled data. By the label
indicator, RS2ACF can ensure the unlabeled data of the same predicted label to
be mapped into the same class in feature space. Besides, RS2ACF incorporates
the joint neighborhood reconstruction error over the new representations and
predicted labels of both labeled and unlabeled data, so the manifold structures
can be preserved explicitly and adaptively in the representation space and
label space at the same time. Owing to the adaptive manner, the tricky process
of determining the neighborhood size or kernel width can be avoided. Extensive
results on public databases verify that our RS2ACF can deliver state-of-the-art
data representation, compared with other related methods.
