Novel Subspace Clustering Algorithms And Applications

High-dimensional datasets exist in many application areas, especially in the era of “big data”, while this brings a big challenge for the traditional clustering algorithms. As a useful method for processing the high-dimensional data, the subspoace clustering methods attract many researchers' attentation. Recently, the subspace clustering methods based on sparse representation(SR) and low-rank representation(LRR) have become the new research hot topic. This paper focus on the SR and LRR related subspace clustering methods, by the depth research and analysis, this paper proposes several improvements of the related methods, and improves the performance of the subspace lustering methods. The main works of this papere are as follows:1. Low-rank representation(LRR) of data has been successfully applied in exploring the subspace structures of data. However, the LRR-related algorithms are divided into a two-stage approach. Firstly, an affinity graph is constructed by using low-rank minimization techniques. Secondly, spectral clustering is used on this affinity graph to get the final segmentation. This implies that the affinity graph construction and spectral segmentation are depended on each other while the traditional LRR-related methods cannot guarantee to achieve the best result. In this paper, we propose a robust structure low-rank representation approach, termed as RSLRR. By solving the joint optimization framework for learning both the affinity graph and the segmentation, the proposed RSLRR algorithm can get both the segmentation and the structure low-rank representation. Extensive experiments of subspace segmentation on several benchmark datasets demonstrate the effectiveness of our approach.2. 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.3. This paper presents a robust low-rank representation(LRR) method that incorporates structure constraints and dimensionality reduction for subspace clustering. The existing LRR and its extensions use noise data as the dictionary, while this will influence the final clustering effect. The proposed method takes advantage of the discriminative dictionary to seek the lowest-rank representation by virtue of matrix recovery and completion techniques. One of the main advantages of our method is that its computationally efficient as the representation coefficients are found in the low-dimensional latent space. Extensive experimental results on benchmark image datasets demonstrate the efficiency and effectiveness of the proposed algorithm for subspace clustering.4. In this paper, we propose a novel method for semi-supervised learning by combining graph embedding and sparse regression, termed as GESR-LR, in which the embedding learning and the sparse regression are combined performed. Most of the graph based semi-supervised learning methods take into account of the local neighborhood information while ignore the global structure of the sample data. The proposed GESR-LR method learns a low-rank weight matrix by projecting the data onto a low-dimensional subspace. The GESR-LR makes full use of the supervision information in the construction of the affinity matrix, and the affinity construction is combined with graph embedding into one step to guarantee the global optimal solution. In the dimensionality reduction procedure, the proposed GESR-LR can preserve the global structure of the data, and the learned low-rank weight matrix can effectively reduce the influence of the noise. An effective algorithm to solve the corresponding optimization problem is designed. Extensive experimental results demonstrate that GESR-LR can obtain a higher classification accuracy than other state-of-the-art methods.5. In order to get better clustering precision, the traditional clustering algorithms usually need the support of large amount of historical data. The impact it brings about is: the previous clustering algorithms seem not effective if there exists some information losses in the current situation data collection and the division relationship between datasets is not significant. In this study, a novel clustering technique called transfer entropy weighting soft subspace clustering algorithm(T_EWSC) is proposed by employing the historical information. The properties of this algorithm are investigated and performance is evaluated experimentally using real datasets, including UCI benchmarking datasets, high dimensional gene expression datasets. The experimental results demonstrate that the proposed algorithm is able to use historical information to make up for the inadequacy of the current information and perform well.