Multi-view Subspace Clustering Research Articles

Learning Unified Anchor Graph for Joint Clustering of Hyperspectral and LiDAR Data.

The joint clustering of multimodal remote sensing (RS) data poses a critical and challenging task in Earth observation. Although recent advances in multiview subspace clustering have shown remarkable success, existing methods become computationally prohibitive when dealing with large-scale RS datasets. Moreover, they neglect intrinsic nonlinear and spatial interdependencies among heterogeneous RS data and lack generalization ability for out-of-sample data, thereby restricting their applicability. This article introduces a novel unified framework called anchor-based multiview kernel subspace clustering with spatial regularization (AMKSC). It learns a scalable anchor graph in the kernel space, leveraging contributions from each modality instead of seeking a consensus full graph in the feature space. To ensure spatial consistency, we incorporate a spatial smoothing operation into the formulation. The method is efficiently solved using an alternating optimization strategy, and we provide theoretical evidence of its scalability with linear computational complexity. Furthermore, an out-of-sample extension of AMKSC based on multiview collaborative representation-based classification is introduced, enabling the handling of larger datasets and unseen instances. Extensive experiments on three real heterogeneous RS datasets confirm the superiority of our proposed approach over state-of-the-art methods in terms of clustering performance and time efficiency. The source code is available at https://github.com/AngryCai/AMKSC.

Multi-View Subspace Clustering via Structured Multi-Pathway Network.

Recently, deep multi-view clustering (MVC) has attracted increasing attention in multi-view learning owing to its promising performance. However, most existing deep multi-view methods use single-pathway neural networks to extract features of each view, which cannot explore comprehensive complementary information and multilevel features. To tackle this problem, we propose a deep structured multi-pathway network (SMpNet) for multi-view subspace clustering task in this brief. The proposed SMpNet leverages structured multi-pathway convolutional neural networks to explicitly learn the subspace representations of each view in a layer-wise way. By this means, both low-level and high-level structured features are integrated through a common connection matrix to explore the comprehensive complementary structure among multiple views. Moreover, we impose a low-rank constraint on the connection matrix to decrease the impact of noise and further highlight the consensus information of all the views. Experimental results on five public datasets show the effectiveness of the proposed SMpNet compared with several state-of-the-art deep MVC methods.

Clean and robust multi-level subspace representations learning for deep multi-view subspace clustering

Deep multi-view subspace clustering has achieved increasing attention owing to its encouraging ability to address the nonlinear multi-view data. Despite significant progress, most existing deep multi-view subspace clustering methods still suffer from the following drawbacks. First, they usually focus on utilizing the last-level feature from the last encoder layer of the auto-encoder related to each view, yet often overlook exploiting the earlier-level features from the earlier encoder layers as well as integrating the multi-level features from multiple encoder layers. Second, when learning the subspace representation from the self-expressive layer, they rarely consider the cleanliness and robustness of the learned subspace representation. To overcome these drawbacks, this paper proposes a novel clean and robust multi-level subspace representations learning for deep multi-view subspace clustering (CRMSRL). Specifically, the auto-encoder is adopted to nonlinearly map each view into the multi-level features, and then multiple self-expressive layers are added between the encoder layers and their corresponding decoder layers to provide multiple information flow paths through the auto-encoder and learn the multi-level subspace representations corresponding to the multi-level features. Consequently, the intricate hierarchical information embedded in the multi-level features is passed to the corresponding multi-level subspace representations. Moreover, with the idea of robust principal component analysis (RPCA), the learned multi-level subspace representations can be further purified to achieve the cleaner and more robust ones. In addition, to excavate the structural consistency among different views, the common layer is designed to interact with different view-specific self-expressive layers and achieve the high-quality common subspace representation, which can be applied to the spectral clustering algorithm to obtain the final clustering results. Experimental results show that CRMSRL outperforms twelve state-of-the-art baseline methods on six benchmark datasets. In particular, CRMSRL achieves 4.5% improvements on the MSRCV1 dataset in terms of accuracy, compared with the best baseline method.

NOODLE: Joint Cross-View Discrepancy Discovery and High-Order Correlation Detection for Multi-View Subspace Clustering

Benefiting from the effective exploration of the valuable topological pair-wise relationship of data points across multiple views, multi-view subspace clustering (MVSC) has received increasing attention in recent years. However, we observe that existing MVSC approaches still suffer from two limitations that need to be further improved to enhance the clustering effectiveness. Firstly, previous MVSC approaches mainly prioritize extracting multi-view consistency, often neglecting the cross-view discrepancy that may arise from noise, outliers, and view-inherent properties. Secondly, existing techniques are constrained by their reliance on pair-wise sample correlation and pair-wise view correlation, failing to capture the high-order correlations that are enclosed within multiple views. To address these issues, we propose a novel MVSC framework via joi N t cr O ss-view discrepancy disc O very an D high-order corre L ation d E tection ( NOODLE ), seeking an informative target subspace representation compatible across multiple features to facilitate the downstream clustering task. Specifically, we first exploit the self-representation mechanism to learn multiple view-specific affinity matrices, which are further decomposed into cohesive factors and incongruous factors to fit the multi-view consistency and discrepancy, respectively. Additionally, an explicit cross-view sparse regularization is applied to incoherent parts, ensuring the consistency and discrepancy to be precisely separated from the initial subspace representations. Meanwhile, the multiple cohesive parts are stacked into a three-dimensional tensor associated with a tensor-Singular Value Decomposition (t-SVD) based weighted tensor nuclear norm constraint, enabling effective detection of the high-order correlations implicit in multi-view data. Our proposed method outperforms state-of-the-art methods for multi-view clustering on six benchmark datasets, demonstrating its effectiveness.

Consensus Multi-view subspace clustering based on Graph Filtering

Multi-view subspace clustering has attracted an increasing amount of attention because it can capture information from multiple views as well as avoid the curse of dimensionality. The existing methods cannot simultaneously achieve both the effective reduction of negative impact of noise and the high-quality consensus representation within a unified framework. To handle this issue, this paper proposes a novel Consensus Multi-view subspace clustering based on Graph Filtering, named CMGF. First, CMGF learns a latent data space by using view-specific k-order filters to reduce noise and redundant information. Then, CMGF obtains the spectral embedding matrix of each view by imposing graph regularization constraint. Ultimately, to generate a consensus representation, we integrate the spectral embedding matrix of each view by using an adaptively weighted scheme. Experimental results on ten real-word datasets show that the proposed method outperforms state-of-the-art baselines significantly. Experiments also demonstrate that the graph filtering employed in CMGF enhances the smoothness of the data and improves the distinctiveness of the cluster structure.

Comprehensive multi-view self-representations for clustering

Subspace learning-based methods have shown excellent performance for multi-view clustering, yet have the following problems: (1) most existing methods obtain the subspace representation from the original space, which might contain noises and cannot guarantee a clean enough subspace representation; (2) existing methods mainly focus on the consistency of the subspace representation, while the unique information of each view is not sufficiently exploited. To solve these two problems, we propose a novel multi-view subspace clustering method called comprehensive multi-view self-representations (CMSR). Specifically, we learn the original coefficient matrix of each view through the self-representation, which can reduce the noise of the original space to some extent. Then, we learn the subspace representation of the original coefficient matrix and decompose it into a consistent coefficient matrix and multiple diverse coefficient matrices, which can exploit the consistent and complementary information of multi-view data. Further, we impose the Schatten p-norm constraint on the consistent coefficient matrix to capture robust consistent information. Finally, the comprehensive results on eight real datasets demonstrate the versatility and effectiveness of the proposed method.

Landmark-based k-factorization multi-view subspace clustering

Multi-view subspace clustering (MSC) has gained significant popularity due to its ability to overcome noise and bias present in single views by fusing information from multiple views. MSC enhances the accuracy and robustness of clustering. However, many existing MSC methods suffer from high computational costs and sub-optimal performance on large-scale datasets, since they often construct a fused graph directly from high-dimensional data and then apply spectral clustering. To address these challenges, we propose a framework called Landmark-based k-Factorization Multi-view Subspace Clustering (LKMSC). Our framework tackles these issues by generating a small number of landmarks p≪n for each view, which form a landmark graph. We represent each entire view as a linear combination of these landmarks, where n is the number of data points. To address inconsistencies that naturally occur in landmark graphs due to multiple views, we utilize Landmark Graphs Alignment. This technique incorporates both feature and structural information to capture the correspondence between landmarks. The aligned graphs are then factorized into consensus k groups, emphasizing structural sparsity. LKMSC efficiently extracts features and reduces dimensionality of the input dataset. It eliminates the need for learning large-scale affinity matrix and feature decomposition. Our approach exhibits linear computational complexity and has demonstrated promising results in numerous experimental evaluations across a range of datasets. The source codes and datasets are available at https://github.com/FY0109/LKMSC.

Error-robust multi-view subspace clustering with nonconvex low-rank tensor approximation and hyper-Laplacian graph embedding

Tensor based subspace clustering, a method aimed at partitioning multi-view data into distinct clusters through the tensor low-rank representation, has gained widespread popularity. Despite the effectiveness of tensor singular value decomposition (t-SVD) based nuclear norm in extracting high-dimensional information from multiple views, certain limitations persist. Firstly, while the commonly used l2,1 norm enhances clustering robustness, it remains susceptible to the impact of high-intensity noises. Secondly, the t-SVD based nuclear norm provides a biased estimation of tensor rank. Thirdly, existing methods either fail to preserve manifold structures from the original space or only extract binary relationships between data points. To address these challenges and enhance clustering performance in both high-intensity noisy and real-world conditions, an error-robust multi-view subspace clustering with nonconvex low-rank tensor approximation and hyper-Laplacian graph embedding (EMSC-NLTHG) method is proposed. Specifically, Cauchy loss function which reduces sensitivity to larger noises and outliers is introduced. Based on the Cauchy loss function, we develop the Cauchy pseudo norm to represent the reconstruction error in clustering to enhance the robustness. Moreover, rather than uniformly weighting all singular values in the t-SVD nuclear norm, a nonconvex tensor nuclear norm is adopted to add weights adaptively and approximate the true tensor rank. Additionally, hypergraph is embedded in the representation matrices to preserve local manifold structures and extract the complex multivariate relationships between data points. Extensive experiments demonstrate that the proposed EMSC-NLTHG method consistently outperforms state-of-the-art techniques by approximately 18% to 40% on datasets corrupted by high-intensity noises and around 1% to 27% on eight real-world datasets across six popular evaluation metrics.

Multi-view Subspace Clustering Based on Weighted Tensor Schatten-P Norm

In the era of advancing technology and continuous societal evolution, an abundance of voluminous data from various domains has become prevalent in the public domain. Managing this wealth of data necessitates a series of preprocessing procedures, encompassing tasks such as data storage, computation, and analysis, with the aim of unveiling intrinsic features and patterns contained within. Among these procedures, clustering stands out as a crucial step, with the primary goal of unveiling the hidden structures within the data and organizing data samples into meaningful clusters based on specific criteria. Early clustering efforts were based on a singleview. Real world data, however, often contains interrelated information, leading to the emergence of multi-view clustering. Multiview subspace clustering (T-SVD) has been widely used in recent years. However, the equal treatment of each singular value in this approach lacks relevance when the data is noisy or contaminated. In order to improve the robustness and clustering performance, this paper presents a T-SVD weighted tensor norm. In order to improve the robustness, a Schatten-P norm was proposed. This paper explores multi-view subspace clustering is based on the Schatten-P norm weighted tensor. Experiments are carried out on 6 benchmark data sets, and the results are compared with 4 existing ones. Experiments show that the proposed approach is better than the most advanced multi-view subspace clustering methods.

Anchor-based scalable multi-view subspace clustering

Multi-view clustering is a major topic in pattern recognition and machine learning. Common multi-view clustering algorithms construct similarity graphs from original samples and use them to perform spectral clustering. The time complexity of the singular value decomposition process in graph construction and spectral clustering is high, leading to high computational and memory costs. In addition, subsequent K-means clustering is sensitive to the initial points, yielding unstable clustering results. To address these issues, this study proposes a novel approach to reduce time overhead and memory space from two perspectives. First, a new anchor selection method is proposed to reduce the dimension of the original data by lowering the cost. Second, the self-representation matrix of multi-views is fused into a consistent graph matrix using the post-fusion technique, and the fused graph is directly processed in postprocessing. Furthermore, the proposed method directly obtains clustering results based on the connectivity of the fusion graph, eliminating the need for K-means postprocessing, which avoids the issue of unstable clustering results. Experimental results on artificial and real multi-view datasets indicate that the proposed algorithm is superior to existing algorithms.

Multi-view subspace clustering based on adaptive search

Multi-view clustering has been widely applied to image classification, information retrieval, medical pathology analysis, and other fields. So far, many multi-view subspace clustering algorithms based on self-representation learning have been developed. However, most of them use the original data as a dictionary to construct affinity graphs, and their clustering performance depends largely on the quality of the original data features. If the raw data is corrupted by noise, directly using these noisy data as a self-representing dictionary may pose a series of research challenges. Secondly, in the process of self-representation learning, the internal relationship between data points is actually continuously updated and changed, and fixed data points not only affect the selection of view feature diversity, but also may lead to clustering results that are unusually sensitive to the input data. Finally, the coefficient matrix obtained by self-representation learning may contain noise or data structures that are not relevant to multi-view clustering. To remedy these shortcomings, this work proposes a new multi-view clustering algorithm, namely, multi-view subspace clustering based on adaptive search. Specifically, first, we find its similar data matrix for each view’s original data and perform dictionary learning by using the similar data matrix as a dictionary. This not only facilitates identifying the continuously varied internal relationships between data points, but also alleviates the errors that occur when the raw data is directly selected as a dictionary. Second, we introduce robust principal component analysis (RPCA) and rank constraints into the construction of affinity matrices to obtain cleaner and more robust affinity matrices that explore the same clustering properties among different views. In addition, we develop an augmented Lagrange multiplier (ALM) based method to solve the objective function of the model. Finally, we conducted substantial experiments on six real multi-view datasets to demonstrate that the MSC-AS algorithm is more robust and effective than some other advanced clustering algorithms.

Prior Indicator Guided Anchor Learning for Multi-View Subspace Clustering

Prior Indicator Guided Anchor Learning for Multi-View Subspace Clustering

Multimodality Fusion Method Based on Multiview Subspace Clustering for Pulmonary Embolism Diagnosis.

Pulmonary embolism (PE) is an important clinical disorder that will result in lung tissue damage or low blood oxygen levels, which need early diagnosis and timely treatment. While computed tomographic pulmonary angiography (CTPA) is the gold standard to diagnose PE, previous studies have verified the effectiveness of combing CTPA and EMR data in computer-aided PE detection or diagnosis. In this paper, we proposed a multimodality fusion method based on multi-view subspace clustering guided feature selection (MSCUFS). The extracted high-dimensional image and EMR features are firstly selected and fused by the MSCUFS, and then are feed into different machine learning models with different fusion strategy to construct the PE classifier. The experiment results showed that the joint fusion strategy with MSCUFS achieved best AUROC of 0.947, surpassing other early fusion and late fusion models. The comparison between single modality and multimodality also illustrated the effectiveness of the proposed method.

Anchor-based multi-view subspace clustering with hierarchical feature descent

Multi-view clustering has attracted growing attention owing to its capabilities of aggregating information from various sources and its promising horizons in public affairs. Up till now, many advanced approaches have been proposed in recent literature. However, there are several ongoing difficulties to be tackled. One common dilemma occurs while attempting to align the features of different views. Moreover, due to the fact that many existing multi-view clustering algorithms stem from spectral clustering, this results to cubic time complexity w.r.t. the number of dataset. However, we propose Anchor-based Multi-view Subspace Clustering with Hierarchical Feature Descent(MVSC-HFD) to tackle the discrepancy among views through hierarchical feature descent and project to a common subspace( STAGE 1), which reveals dependency of different views. We further reduce the computational complexity to linear time cost through a unified sampling strategy in the common subspace( STAGE 2), followed by anchor-based subspace clustering to learn the bipartite graph collectively( STAGE 3). Extensive experimental results on public benchmark datasets demonstrate that our proposed model consistently outperforms the state-of-the-art techniques. Our code is publicly available at https://github.com/QiyuanOu/MVSC-HFD/tree/main.

Tensorial multi-view subspace clustering with side constraints for elevator security warning

Tensorial multi-view subspace clustering with side constraints for elevator security warning

Multiview Subspace Clustering via Low-Rank Symmetric Affinity Graph.

Multiview subspace clustering (MVSC) has been used to explore the internal structure of multiview datasets by revealing unique information from different views. Most existing methods ignore the consistent information and angular information of different views. In this article, we propose a novel MVSC via low-rank symmetric affinity graph (LSGMC) to tackle these problems. Specifically, considering the consistent information, we pursue a consistent low-rank structure across views by decomposing the coefficient matrix into three factors. Then, the symmetry constraint is utilized to guarantee weight consistency for each pair of data samples. In addition, considering the angular information, we utilize the fusion mechanism to capture the inherent structure of data. Furthermore, to alleviate the effect brought by the noise and the high redundant data, the Schatten p-norm is employed to obtain a low-rank coefficient matrix. Finally, an adaptive information reduction strategy is designed to generate a high-quality similarity matrix for spectral clustering. Experimental results on 11 datasets demonstrate the superiority of LSGMC in clustering performance compared with ten state-of-the-art multiview clustering methods.

Double Discrete Cosine Transform-Oriented Multi-View Subspace Clustering.

Low-rank tensor representation with the tensor nuclear norm has been rising in popularity in multi-view subspace clustering (MVSC), in which the tensor nuclear norm is commonly implemented using discrete Fourier transform (DFT). Unfortunately, existing DFT-oriented MVSC methods may provide unsatisfactory results since (1) DFT exploits complex arithmetic in the Fourier domain, usually resulting in high tubal tensor rank, and (2) local structural information is rarely considered. To solve these problems, in this paper, we propose a novel double discrete cosine transform (DCT)-oriented multi-view subspace clustering (D2CTMSC) method, in which the first DCT aims to derive the tensor nuclear norm without complex arithmetic while the second DCT aims to explore the local structure of the self-representation tensor, such that the essential low-rankness and sparsity embedding in multi-view features can be thoroughly exploited. Moreover, we design an effective alternating iteration strategy to solve the proposed model. Experimental results on four types of multi-view datasets (News stories, Face images, Scene images, and Generic objects) demonstrate the superiority of the D2CTMSC method compared with DFT-based methods and other state-of-the-art clustering methods.

Fine-Grained Essential Tensor Learning for Robust Multi-View Spectral Clustering.

Multi-view subspace clustering (MVSC) has drawn significant attention in recent study. In this paper, we propose a novel approach to MVSC. First, the new method is capable of preserving high-order neighbor information of the data, which provides essential and complicated underlying relationships of the data that is not straightforwardly preserved by the first-order neighbors. Second, we design log-based nonconvex approximations to both tensor rank and tensor sparsity, which are effective and more accurate than the convex approximations. For the associated shrinkage problems, we provide elegant theoretical results for the closed-form solutions, for which the convergence is guaranteed by theoretical analysis. Moreover, the new approximations have some interesting properties of shrinkage effects, which are guaranteed by elegant theoretical results. Extensive experimental results confirm the effectiveness of the proposed method.

Partial Tubal Nuclear Norm-Regularized Multiview Subspace Learning.

In this article, a unified multiview subspace learning model, called partial tubal nuclear norm-regularized multiview subspace learning (PTN 2 MSL), was proposed for unsupervised multiview subspace clustering (MVSC), semisupervised MVSC, and multiview dimension reduction. Unlike most of the existing methods which treat the above three related tasks independently, PTN 2 MSL integrates the projection learning and the low-rank tensor representation to promote each other and mine their underlying correlations. Moreover, instead of minimizing the tensor nuclear norm which treats all singular values equally and neglects their differences, PTN 2 MSL develops the partial tubal nuclear norm (PTNN) as a better alternative solution by minimizing the partial sum of tubal singular values. The PTN 2 MSL method was applied to the above three multiview subspace learning tasks. It demonstrated that these tasks organically benefited from each other and PTN 2 MSL has achieved better performance in comparison to state-of-the-art methods.

Contrastive Consistency and Attentive Complementarity for Deep Multi-View Subspace Clustering

Contrastive Consistency and Attentive Complementarity for Deep Multi-View Subspace Clustering