Yan Zhang

Zhao Zhang, Yan Zhang, Sheng Li et al.

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.

Zhao Zhang, Yan Zhang, Guangcan Liu et al.

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.