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In the big data era, the data are generated from different sources or observed from different views. These data are referred to as multi-view data. Unleashing the power of knowledge in multi-view data is very important in big data mining and analysis. This calls for advanced techniques that consider the diversity of different views, while fusing these data. Multi-view Clustering (MvC) has attracted increasing attention in recent years by aiming to exploit complementary and consensus information across multiple views. This paper summarizes a large number of multi-view clustering algorithms, provides a taxonomy according to the mechanisms and principles involved, and classifies these algorithms into five categories, namely, co-training style algorithms, multi-kernel learning, multi-view graph clustering, multi-view subspace clustering, and multi-task multi-view clustering. Therein, multi-view graph clustering is further categorized as graph-based, network-based, and spectral-based methods. Multi-view subspace clustering is further divided into subspace learning-based, and non-negative matrix factorization-based methods. This paper does not only introduce the mechanisms for each category of methods, but also gives a few examples for how these techniques are used. In addition, it lists some publically available multi-view datasets. Overall, this paper serves as an introductory text and survey for multi-view clustering.

It is expensive to obtain labeled real-world visual data for use in training of supervised algorithms. Therefore, it is valuable to leverage existing databases of labeled data. However, the data in the source databases is often obtained under conditions that differ from those in the new task. Transfer learning provides techniques for transferring learned knowledge from a source domain to a target domain by finding a mapping between them. In this paper, we discuss a method for projecting both source and target data to a generalized subspace where each target sample can be represented by some combination of source samples. By employing a low-rank constraint during this transfer, the structure of source and target domains are preserved. This approach has three benefits. First, good alignment between the domains is ensured through the use of only relevant data in some subspace of the source domain in reconstructing the data in the target domain. Second, the discriminative power of the source domain is naturally passed on to the target domain. Third, noisy information will be filtered out during knowledge transfer. Extensive experiments on synthetic data, and important computer vision problems such as face recognition application and visual domain adaptation for object recognition demonstrate the superiority of the proposed approach over the existing, well-established methods.

The industrial control systems are facing an increasing number of sophisticated cyber attacks that can have very dangerous consequences on humans and their environments. In order to deal with these issues, novel technologies and approaches should be adopted. In this paper, we focus on the security of commands in industrial IoT against forged commands and misrouting of commands. To this end, we propose a security architecture that integrates the Blockchain and the Software-defined network (SDN) technologies. The proposed security architecture is composed of: (a) an intrusion detection system, namely RSL-KNN, which combines the Random Subspace Learning (RSL) and K-Nearest Neighbor (KNN) to defend against the forged commands, which target the industrial control process, and (b) a Blockchain-based Integrity Checking System (BICS), which can prevent the misrouting attack, which tampers with the OpenFlow rules of the SDN-enabled industrial IoT systems. We test the proposed security solution on an Industrial Control System Cyber attack Dataset and on an experimental platform combining software-defined networking and blockchain technologies. The evaluation results demonstrate the effectiveness and efficiency of the proposed security solution.

By leveraging the labeled data samples of the source domain to learn the unlabeled data samples of the target domain, unsupervised domain adaptation (DA) has achieved promising performance. However, it is still a vital problem for unsupervised domain adaptation to deal with cross-domain distribution mismatch. Therefore, we present a new model framework for cross-domain image classification in the paper, which is termed manifold transfer subspace learning based on double relaxed discriminative regression (MTSL-DRDR). First, the global geometry information of the samples from the source and target domain can be preserved by utilizing the low-rank constraint. Second, the two transformation projections are employed to project both domains to a unified subspace, in which each data sample of the target domain can be represented by some samples from the source domain with the sparse and low-rank coefficient matrix. Third, the local structure information of the data points with the same semantics from the different domains is preserved by means of the adaptive weight graph based on the low-rank coefficient matrix. Last, for fully use the discriminative information of data from the source domain, the discriminant information of the source domain based on intra-class and inter-class graphs is encoded to the target domain. Our MTSL-DRDR algorithm is evaluated on challenging benchmark datasets, and a large number of experiment results show the superiority of the proposed method.

With the enormous amount of multi-source data produced by various sensors and feature extraction approaches, multi-view clustering (MVC) has attracted developing research attention and is widely exploited in data analysis. Most of the existing multi-view clustering methods hold on the assumption that all of the views are complete. However, in many real scenarios, multi-view data are often incomplete for many reasons, e.g., hardware failure or incomplete data collection. In this paper, we propose an adaptive weighted graph fusion incomplete multi-view subspace clustering (AWGF-IMSC) method to solve the incomplete multi-view clustering problem. Firstly, to eliminate the noise existing in the original space, we transform complete original data into latent representations which contribute to better graph construction for each view. Then, we incorporate feature extraction and incomplete graph fusion into a unified framework, whereas two processes can negotiate with each other, serving for graph learning tasks. A sparse regularization is imposed on the complete graph to make it more robust to the view-inconsistency. Besides, the importance of different views is automatically learned, further guiding the construction of the complete graph. An effective iterative algorithm is proposed to solve the resulting optimization problem with convergence. Compared with the existing state-of-the-art methods, the experiment results on several real-world datasets demonstrate the effectiveness and advancement of our proposed method.

The one‐class classification (OCC) problem has always been a popular topic because it is difficult or expensive to obtain abnormal data in many practical applications. Most of OCC methods focused on monomodal data, such as support vector data description (SVDD) and its variants, while we often face multimodal data in reality. The data come from the same task in multimodal learning, and thus, the inherent structures among all modalities should be hold, which is called the consistency principle. However, each modality contains unique information that can be used to repair the incompleteness of other modalities. It is called the complementarity principle. To follow the above two principles, we designed a multimodal graph–regularized term and a sparse projection matrix–regularized term. The former aims to preserve the within‐modal structural and between‐modal relationships, while the latter aims to richly use the complementarity information hidden in multimodal data. Further, we follow the multimodal subspace (MS) SVDD architecture and use two regularized terms to regularize SVDD. Consequently, a novel OCC method for multimodal data is proposed, called the consistency and complementarity jointly regularized subspace SVDD (CCS‐SVDD). Extensive experimental results demonstrate that our approach is more effective and competitive than other algorithms. The source codes are available at https://github.com/wongchuang/CCS_SVDD .

In multi-label learning (MLL), label-specific feature (LSF) learning assumes that labels are determined by their inherent characteristics. However, in multi-view multi-label learning (MVMLL), the heterogeneity problem persists within the feature space. The views with varying dimensions can result in different dimensions of extracted LSF. Existing algorithms extract the LSF for each view separately, suffering the inadequate communication of the LSF and poor classification accuracy. The subspace learning method can address the dimension-inconsistency problem in multi-views by extracting extract the shared subspace for each view by substituting the original view feature space. However, the individual subspaces contain relatively homogeneous information. Based on this analysis, the GLocal Shared Subspace Learning (GLSSL) algorithm was proposed for multi-view multi-label learning to access more informative subspaces. First, the label groups were obtained through spectral clustering, entirely considering the correlation between the label groups and features to identify the specific relevant view features corresponding to each label group. Subsequently, the global shared subspace (global subspace) and local shared subspace (local subspace) were extracted from the original feature space and feature sets, respectively. Finally, the local subspace was complemented with the global subspace for LSF learning. The proposed algorithm was validated through comparative experiments with several state-of-the-art algorithms on multiple benchmark multi-view multi-label datasets.

The learnware paradigm was recently proposed by Zhou ( 2016 ) with the wish of developing the learnware market to help users build models more efficiently by reusing existing well-performed models rather than starting from scratch. Specifically, a learnware in the learnware market is a well-performed pre-trained model with a specification describing its specialty and utility, and the market identifies helpful learnware(s) for the user’s task based on the specification. Recent studies have attempted to realize a homogeneous prototype learnware market initially through Reduced Kernel Mean Embedding (RKME) specification, which requires all models in the market to share the same feature space. However, this limits the application scope of the learnware paradigm because various pre-trained models are often obtained from different feature spaces in real-world scenarios. In this paper, we make the first attempt to enable the learnware to handle heterogeneous feature spaces. We propose a more powerful specification to manage heterogeneous learnwares by integrating subspace learning in the specification design, along with a practical approach for identifying and reusing helpful learnwares for the user’s task. Empirical studies on both synthetic data and real-world tasks validate the efficacy of our approach.

Domain Adaptation (DA) commonly finds a shared subspace, in which the discrepancy between the source and target domains is reduced and the target samples could be correctly classified. Existing studies mainly learn domain-invariant features via one shared subspaces or by two decoupled subspaces. However, since the learning of the source and target domains may interact with each other, they may neglect that (a) the domain-specific features are unique to each domain and they are not compatible in a shared subspace; and (b) insufficient transferable features between the two domains may lead to unsatisfactory performance. To address these problems, this study introduces a three-step optimization learning framework called Guidance, Imitation, and Generalization Subspace Learning (GIG). GIG first decouples the synchronous learning of the source and target domains into three subspaces, including guidance subspace for the source domain, imitation subspace for the shared domain, and generalization subspace for the target domain, so that both the domain-invariant and domain-specific knowledge can be learned as much as possible. It then learns domain-specific features by employing spectral clustering to the Guidance and Generalization subspaces, respectively, and captures the domain-invariant knowledge by aligning the marginal distribution on the Imitation subspace. In this way, the negative impacts caused by the interactions between the source and target domains are alleviated. At last, Distilled Label Regression (DLR) is proposed to incorporate the posterior probabilities of classifiers and labels as a new semantic embedding and regress the data into the semantic embedding, so that the discriminability of the Guidance subspace is improved. Two relaxed variables are introduced to optimization, such that the range of the candidate transferable information is extended and the acquisition of extreme values is ensured. By sequentially learning these three subspaces, GIG extracts more knowledge-transferable features and achieves significant performance improvements. Experiments conducted on eight benchmark datasets demonstrate the superiority of GIG.

Hyperspectral unmixing (HU) is fundamental for conducting quantitative analyses in remote sensing, yet existing methods face a persistent tradeoff between model performance and physical interpretability. Although deep learning models achieve superior performance, even “gray-box” models that incorporate physical constraints still suffer from an intrinsically opaque decision-making process, which hinders their trustworthiness in critical applications. To address this challenge, this paper introduces a theory-guided unmixing framework aimed at enhancing mechanistic interpretability called the sparse and subspace-attentive transformer unmixing network (SSTU-Net). Unlike heuristic architectures, SSTU-Net is rigorously derived from the first principles of sparse rate reduction (SRR) theory. Its core modules—the multi-head subspace self-attention (MSSA) and the iterative shrinkage-thresholding algorithm (ISTA)—directly implement the essential mathematical steps of information compression and sparsification within the SRR theory, respectively. Extensive experiments on both synthetic and real hyperspectral datasets demonstrate that SSTU-Net achieves competitive performance compared to representative state-of-the-art methods—including advanced autoencoder-based networks (e.g., CyCU-Net and DAAN) and recent transformer-based unmixing architectures (e.g., DeepTrans and MAT-Net)—while strictly adhering to theoretically predicted evolutionary trajectories. More importantly, a series of specifically designed structural interpretability validation experiments mechanistically confirm the theoretically predicted behaviors, such as layer-wise information compression, feature sparsification, and subspace orthogonalization. These results reveal the internal working mechanisms of SSTU-Net, validating the feasibility and significant potential of our principled theory-guided framework for developing high-performance and trustworthy intelligent models in remote sensing.