title: Enhanced low-rank representation via sparse manifold adaption for semi-supervised learning.
abstract: Constructing an informative and discriminative graph plays an important role in various pattern recognition tasks such as clustering and classification. Among the existing graph-based learning models, low-rank representation (LRR) is a very competitive one, which has been extensively employed in spectral clustering and semi-supervised learning (SSL). In SSL, the graph is composed of both labeled and unlabeled samples, where the edge weights are calculated based on the LRR coefficients. However, most of existing LRR related approaches fail to consider the geometrical structure of data, which has been shown beneficial for discriminative tasks. In this paper, we propose an enhanced LRR via sparse manifold adaption, termed manifold low-rank representation (MLRR), to learn low-rank data representation. MLRR can explicitly take the data local manifold structure into consideration, which can be identified by the geometric sparsity idea; specifically, the local tangent space of each data point was sought by solving a sparse representation objective. Therefore, the graph to depict the relationship of data points can be built once the manifold information is obtained. We incorporate a regularizer into LRR to make the learned coefficients preserve the geometric constraints revealed in the data space. As a result, MLRR combines both the global information emphasized by low-rank property and the local information emphasized by the identified manifold structure. Extensive experimental results on semi-supervised classification tasks demonstrate that MLRR is an excellent method in comparison with several state-of-the-art graph construction approaches.
authors: Center for Brain-like Computing and Machine Intelligence, Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, China. Electronic address: stany.peng@gmail.com.
authors: Yong
authors: Y
authors: Peng
authors: Center for Brain-like Computing and Machine Intelligence, Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, China; Key Laboratory of Shanghai Education Commission for Intelligent Interaction and Cognitive Engineering, Shanghai Jiao Tong University, Shanghai 200240, China. Electronic address: bllu@sjtu.edu.cn.
authors: Bao-Liang
authors: BL
authors: Lu
authors: Department of Computer Science and Engineering, Arizona State University, Tempe, AZ 85281, USA.
authors: Suhang
authors: S
authors: Wang
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D002965:Classification / Q000379:methods; D016000:Cluster Analysis; D008962:Models, Theoretical
keywords: Face recognition; Graph construction; Low-rank representation; Semi-supervised learning; Sparse manifold adaption