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Due to the excellent performance in exploring the structure of low-dimensional subspaces, the low-rank representation (LRR) has recently attracted wide attention of the researchers. However, in most current semi-supervised learning problems based on LRR method, the two steps of graph construction and semi-supervised learning are separated. Therefore, the existing label information cannot be well used to guide the construction of the affinity graph. Thus, these methods cannot guarantee the results are the global optimal solutions. In this paper, we propose a graph regularized low-rank representation for semi-supervised learning, termed as GLRSC. Combing the construction of the affinity graph and the semi-supervised learning, and solving the joint optimization, the proposed GLRSC method can get the global optimal solution. The experimental results on some benchmark datasets show that the effectiveness of the proposed GLRSC method.

Subspace clustering analysis has good performance for the clustering problem of high dimensional data. In recent years, subspace clustering analysis algorithms based on representation has also been widely concerned. But when the feature dimension is too high, it not only increases the time complexity of the operation, but also reduces the performance of the algorithm, so it is an important research topic how to use the less feature dimension to carry on the subspace clustering analysis. In this paper, the feature selection method is added to the algorithm framework of low rank representation, and the two are fused into a new single model, and a new subspace clustering algorithm is proposed by using local constraint conditions. The algorithm selects a small number of related feature dimensions to represent low rank data. This not only reduces the complexity of the algorithm, but also helps to accurately reveal the relationship between the data, because the relationship between the data is not influenced by the unrelated feature dimension through the selection of the features. In addition, locality constraints are used in the learning process. Therefore, the learning process of feature and subspace clustering promotes each other and leads to powerful data representation. A large number of experiments on the real datasets have also proved the effectiveness of this method

Low-rank representation (LRR) and its variations have recently attracted a great deal of attention because of its effectiveness in exploring low-dimensional subspace structures embedded in data. LRR-related algorithms have many applications in computer vision, signal processing, semi-supervised learning and pattern recognition. However, most of the existing LRR methods fail to take into account the non-linear geometric structures within data, thus the locality and the similarity information among data may be missing in the learning process, which have been shown to be beneficial for discriminative tasks. To improve LRR in this regard, we propose a manifold locality constrained low-rank representation framework (MLCLRR) for data representation. By taking the local manifold structure of the data into consideration, the proposed MLCLRR method not only can represent the global low-dimensional structures, but also capture the local intrinsic non-linear geometric information in the data. The experimental results on different types of vision problems demonstrate the effectiveness of the proposed method.