Multi-view clustering method based on anchor graph has been widely concerned due to its high efficiency and effectiveness. In order to avoid post-processing, most of the existing anchor graph-based methods learn bipartite graphs with connected components. However, such methods have high requirements on parameters, and in some cases it may not be possible to obtain bipartite graphs with clear connected components. To end this, we propose a label learning method based on tensor projection (LLMTP). Specifically, we project anchor graph into the label space through an orthogonal projection matrix to obtain cluster labels directly. Considering that the spatial structure information of multi-view data may be ignored to a certain extent when projected in different views separately, we extend the matrix projection transformation to tensor projection, so that the spatial structure information between views can be fully utilized. In addition, we introduce the tensor Schatten p-norm regularization to make the clustering label matrices of different views as consistent as possible. Extensive experiments have proved the effectiveness of the proposed method.

Despite the promising results, tensor robust principal component analysis (TRPCA), which aims to recover underlying low-rank structure of clean tensor data corrupted with noise/outliers by shrinking all singular values equally, cannot well preserve the salient content of image. The major reason is that, in real applications, there is a salient difference information between all singular values of a tensor image, and the larger singular values are generally associated with some salient parts in the image. Thus, the singular values should be treated differently. Inspired by this observation, we investigate whether there is a better alternative solution when using tensor rank minimization. In this paper, we develop an enhanced TRPCA (ETRPCA) which explicitly considers the salient difference information between singular values of tensor data by the weighted tensor Schatten p-norm minimization, and then propose an efficient algorithm, which has a good convergence, to solve ETRPCA. Extensive experimental results reveal that the proposed method ETRPCA is superior to several state-of-the-art variant RPCA methods in terms of performance.

Low-rank representation based on tensor-Singular Value Decomposition (t-SVD) has achieved impressive results for multi-view subspace clustering, but it does not well deal with noise and illumination changes embedded in multi-view data. The major reason is that all the singular values have the same contribution in tensor-nuclear norm based on t-SVD, which does not make sense in the existence of noise and illumination change. To improve the robustness and clustering performance, we study the weighted tensor-nuclear norm based on t-SVD and develop an efficient algorithm to optimize the weighted tensor-nuclear norm minimization (WTNNM) problem. We further apply the WTNNM algorithm to multi-view subspace clustering by exploiting the high order correlations embedded in different views. Extensive experimental results reveal that our WTNNM method is superior to several state-of-the-art multi-view subspace clustering methods in terms of performance.

Graph neural networks (GNNs) have made considerable achievements in processing graph-structured data. However, existing methods can not allocate learnable weights to different nodes in the neighborhood and lack of robustness on account of neglecting both node attributes and graph reconstruction. Moreover, most of multi-view GNNs mainly focus on the case of multiple graphs, while designing GNNs for solving graph-structured data of multi-view attributes is still under-explored. In this paper, we propose a novel Multi-View Attribute Graph Convolution Networks (MAGCN) model for the clustering task. MAGCN is designed with two-pathway encoders that map graph embedding features and learn the view-consistency information. Specifically, the first pathway develops multi-view attribute graph attention networks to reduce the noise/redundancy and learn the graph embedding features for each multi-view graph data. The second pathway develops consistent embedding encoders to capture the geometric relationship and probability distribution consistency among different views, which adaptively finds a consistent clustering embedding space for multi-view attributes. Experiments on three benchmark graph datasets show the superiority of our method compared with several state-of-the-art algorithms.

Low‐rank representation (LRR) and its variants have been proved to be powerful tools for handling subspace clustering problems. Most of these methods involve a sub‐problem of computing the singular value decomposition of an matrix, which leads to a computation complexity of . Obviously, when n is large, it will be time consuming. To address this problem, the authors introduce a fast solution, which reformulates the large‐scale problem to an equal form with smaller size. Thus, the proposed method remarkably reduces the computation complexity by solving a small‐scale problem. Theoretical analysis proves the efficiency of the proposed model. Furthermore, we extend LRR to a general model by using Schatten p ‐norm instead of nuclear norm and present a fast algorithm to solve large‐scale problem. Experiments on MNIST and Caltech101 databse illustrate the equivalence of the proposed algorithm and the original LRR solver. Experimental results show that the proposed algorithm is remarkably faster than traditional LRR algorithm, especially in the case of large sample number.

Subspace learning-based multiview clustering has achieved impressive experimental results. However, the similarity matrix, which is learned by most existing methods, cannot well characterize both the intrinsic geometric structure of data and the neighbor relationship between data. To consider the fact that original data space does not well characterize the intrinsic geometric structure, we learn the latent representation of data, which is shared by different views, from the latent subspace rather than the original data space by linear transformation. Thus, the learned latent representation has a low-rank structure without solving the nuclear-norm. This reduces the computational complexity. Then, the similarity matrix is adaptively learned from the learned latent representation by manifold learning which well characterizes the local intrinsic geometric structure and neighbor relationship between data. Finally, we integrate clustering, manifold learning, and latent representation into a unified framework and develop a novel subspace learning-based multiview clustering method. Extensive experiments on benchmark datasets demonstrate the superiority of our method.

Zero-shot learning (ZSL) aims to build models to recognize novel visual categories that have no associated labelled training samples. The basic framework is to transfer knowledge from seen classes to unseen classes by learning the visual-semantic embedding. However, most of approaches do not preserve the underlying sub-manifold of samples in the embedding space. In addition, whether the mapping can precisely reconstruct the original visual feature is not investigated in-depth. In order to solve these problems, we formulate a novel framework named Graph and Autoencoder Based Feature Extraction (GAFE) to seek a low-rank mapping to preserve the sub-manifold of samples. Taking the encoder-decoder paradigm, the encoder part learns a mapping from the visual feature to the semantic space, while decoder part reconstructs the original features with the learned mapping. In addition, a graph is constructed to guarantee the learned mapping can preserve the local intrinsic structure of the data. To this end, an L21 norm sparsity constraint is imposed on the mapping to identify features relevant to the target domain. Extensive experiments on five attribute datasets demonstrate the effectiveness of the proposed model.

Locality preserving projection (LPP) is one of the most representative linear manifold learning methods and well exploits intrinsic structure of data. However, the performance of LPP remarkably degenerate in the presence of outliers. To alleviate this problem, the authors propose a robust LPP, namely LPP‐L21. LPP‐L21 employs L2‐norm as the distance metric in spatial dimension of data and L1‐norm as the distance metric over different data points. Moreover, the authors employ L1‐norm to construct similarity graph, this helps to improve robustness of algorithm. Accordingly, the authors present an efficient iterative algorithm to solve LPP‐L21. The authors’ proposed method not only well suppresses outliers but also retains LPP's some nice properties. Experimental results on several image data sets show its advantages.

Recently, discriminant locality preserving projection based on L1-norm (DLPP-L1) was developed for robust subspace learning and image classification. It obtains projection vectors by greedy strategy, i.e., all projection vectors are optimized individually through maximizing the objective function. Thus, the obtained solution does not necessarily best optimize the corresponding trace ratio optimization algorithm, which is the essential objective function for general dimensionality reduction. It results in insufficient recognition accuracy. To tackle this problem, we propose a nongreedy algorithm to solve the trace ratio formula of DLPP-L1, and analyze its convergence. Experimental results on three databases illustrate the effectiveness of our proposed algorithm.