Abstract In order to explore multi‐view data, existing low‐rank‐based multi‐view subspace clustering methods seek a common low‐rank structure from different views. However, in real‐world scenarios, each view will often hold complex structures resulting from noise or outliers, causing unreliable and imprecise graphs, which the previous methods cannot effectively ameliorate. This study proposes a new method based on low‐rank correlation analysis to overcome these limitations. Firstly, the canonical correlation analysis strategy is introduced to jointly find the low‐rank structures in different views. In order to facilitate a robust solution, a dual regularisation term is further introduced to find such low‐rank structures that maximise the correlation in respective views much better. Thus, a unifying clustering structure is then integrated into the model to characterise the connections between different views adaptively. In this way, noise suppression is achieved more effectively. Furthermore, we avoid the uncertainty of spectral post‐processing of the unifying clustering structure by imposing a rank constraint on its Laplacian matrix to obtain the clustering results explicitly, further enhancing computation efficiency. Experimental results obtained from several clustering and classification experiments performed using 3Sources, Caltech101‐20, 100leaves, WebKB, and Hdigit datasets reveal the proposed method's superiority over compared state‐of‐the‐art methods in Accuracy, Normalised Mutual Information, and F‐score evaluation metrics.

Traditional low-rank methods overlook residuals as corruptions, but we discovered that low-rank residuals actually keep image edges together with corrupt components. Therefore, filtering out such structural information could hamper the discriminative details in images, especially in heavy corruptions. In order to address this limitation, this paper proposes a novel method named ESL-LRR, which preserves image edges by finding image projections from low-rank residuals. Specifically, our approach is built in a manifold learning framework where residuals are regarded as another view of image data. Edge preserved image projections are then pursued using a dynamic affinity graph regularization to capture the more accurate similarity between residuals while suppressing the influence of corrupt ones. With this adaptive approach, the proposed method can also find image intrinsic low-rank representation, and much discriminative edge preserved projections. As a result, a new classification strategy is introduced, aligning both modalities to enhance accuracy. Experiments are conducted on several benchmark image datasets, including MNIST, LFW, and COIL100. The results show that the proposed method has clear advantages over compared state-of-the-art (SOTA) methods, such as Low-Rank Embedding (LRE), Low-Rank Preserving Projection via Graph Regularized Reconstruction (LRPP_GRR), and Feature Selective Projection (FSP) with more than 2% improvement, particularly in corrupted cases.

Manifold learning is a widely used technique for dimensionality reduction as it can reveal the intrinsic geometric structure of data. However, its performance decreases drastically when data samples are contaminated by heavy noise or occlusions, which leads to unsatisfying data processing performance. We propose a novel robust dimensionality reduction method via low-rank Laplacian graph learning for classification and clustering tasks to solve the above problem. First, we construct a low-rank Laplacian graph by combining manifold learning and subspace learning. This graph can capture both global and local structural information of the data. And we introduce rank constraints for the Laplacian graph to make it more discriminative. Second, we put the learning of projection matrix and sample affinity graph into a unified framework. The projection matrix is embedded into a robust low-rank Laplacian graph so that the low-dimensional mapping of data can maintain the structural information in the graph well. Finally, we add a regularization term to the projection matrix to make it have the ability of both feature extraction and feature selection. Therefore, the proposed model can resist the interference of noise or data damage to learn the optimal projection to achieve better performance in dimensionality reduction through such a data dimensionality reduction joint framework. Comprehensive experiments on various benchmark datasets with varying degrees of occlusions or corruptions are carried out to evaluate the performance of the proposed method. Compared with the state-of-the-art dimensionality reduction methods in the literature, the experimental results are inspiring, showing our method’s effectiveness and robustness in classification and clustering, especially in object recognition scenarios with noise or occlusions.

Multi-label classification remains a challenging task for high-dimensional data samples and their labels both increase the complexity of training models. In this paper, we propose a Robust Label and Feature Space Co-Learning method, referred to as RLFSCL, for multi-label classification. Different from traditional multi-label classification methods which focus on feature space learning through regression directly between data samples and labels, our proposed method can further learn robust low rank label space from this traditional regression method. Therefore, our RLFSCL can learn better low rank feature and label representations simultaneously in original noisy and high dimensional spaces. Experimental comparison on five benchmark datasets, including Rcv1s5, Cal500, and Corel16k4 shows that the proposed RLFSCL algorithm outperforms state-of-the-art multi-label classification methods. The code of RLFSCL is made available onhttps://github.com/JingChuanTang/RLFSCL.

Cross domain adaptation aims to improve the performance of the target domain model by making full use of information rich source domain samples. However, as information becomes richer, the noise also increases. In order to improve the reliability of cross domain adaptation, we propose a novel method based on deep robust low rank correlation. Borrowed from the traditional idea of Canonical Correlation Analysis (CCA), we developed a robust correlation model to maximize the correlation between source and target domains. Also, the low-rank characteristics of cross domain data can effectively reduce the negative influence of noisy data. Furthermore, in order that the cross-domain data can share a unifying clustering structure, we introduced a common Laplacian affinity structure. Then the learned features can be smoothed and aligned to the unifying structure. In this way, we obtain a deep robust low rank correlation model with the help of the unifying clustering structure, which can effectively reduce the influence of noise and improve the performance of cross domain adaptation. Experimental results on three datasets including Office-31, ImageCLEF-DA and Office-Home show that our model significantly outperforms state-of-the-art cross domain adaptation methods.

Abstract In the last years, subspace‐based multi‐view face recognition has attracted increasing attention and many related methods have been proposed. However, the most existing methods ignore the specific local structure of different views. This drawback can cause these methods' discriminating ability to degrade when many noisy samples exist in data. To tackle this problem, a multi‐view low‐rank representation method is proposed, which exploits both intrinsic relationships and specific local structures of different views simultaneously. It is achieved by hierarchical Bayesian methods that constrain the low‐rank representation of each view so that it matches a linear combination of an intrinsic representation matrix and a specific representation matrix to obtain common and specific characteristics of different views. The intrinsic representation matrix holds the consensus information between views, and the specific representation matrices indicate the diversity among views. Furthermore, the model injects a clustering structure into the low‐rank representation. This approach allows for adaptive adjustment of the clustering structure while pursuing the optimization of the low‐rank representation. Hence, the model can well capture both the relationship between data and the clustering structure explicitly. Extensive experiments on several datasets demonstrated the effectiveness of the proposed method compared to similar state‐of‐the‐art methods in classification and clustering.

Multi-view subspace clustering (MVSC) finds a shared structure in latent low-dimensional subspaces of multi-view data to enhance clustering performance. Nonetheless, we observe that most existing MVSC methods neglect the diversity in multi-view data by considering only the common knowledge to find a shared structure either directly or by merging different similarity matrices learned for each view. In the presence of noise, this predefined shared structure becomes a biased representation of the different views. Thus, in this article, we propose a MVSC method based on coupled low-rank representation to address the above limitation. Our method first obtains a low-rank representation for each view, constrained to be a linear combination of the view-specific representation and the shared representation by simultaneously encouraging the sparsity of view-specific one. Then, it uses the k -block diagonal regularizer to learn a manifold recovery matrix for each view through respective low-rank matrices to recover more manifold structures from them. In this way, the proposed method can find an ideal similarity matrix by approximating clustering projection matrices obtained from the recovery structures. Hence, this similarity matrix denotes our clustering structure with exactly k connected components by applying a rank constraint on the similarity matrix’s relaxed Laplacian matrix to avoid spectral post-processing of the low-dimensional embedding matrix. The core of our idea is such that we introduce dynamic approximation into the low-rank representation to allow the clustering structure and the shared representation to guide each other to learn cleaner low-rank matrices that would lead to a better clustering structure. Therefore, our approach is notably different from existing methods in which the local manifold structure of data is captured in advance. Extensive experiments on six benchmark datasets show that our method outperforms 10 similar state-of-the-art compared methods in six evaluation metrics.