Multi-view Subspace Clustering Method Research Articles

A new nonconvex multi-view subspace clustering via learning a clean low-rank representation tensor

Abstract Recently, low-rank tensor representation has achieved impressive results for multi-view subspace clustering (MSC). The typical MSC methods utilize the tensor nuclear norm as a convex surrogate of the tensor multi-rank to obtain a low-rank representation, which exhibits limited robustness when dealing with noisy and complex data scenarios. In this paper, we introduce an innovative clean low-rank tensor representation approach that combines the idea of tensor robust principal component analysis with a new nonconvex tensor multi-rank approximation regularization. This integration enhances the robustness of the low-rank representation, resulting in improved performance. Furthermore, to better capture the local geometric features, we employ a high-order manifold regularization term. To effectively address our new model, we develop an iterative algorithm that can be proved to converge to the desired Karush-Kuhn-Tucker critical point. The numerical experiments on widely used datasets serve to demonstrate the efficacy and effectiveness of our new method.

A coarse and fine-grained deep multi view subspace clustering method for unsupervised fault diagnosis of rolling bearings

Abstract To address the issue of insufficient characterization of fault features in inherent vibration data that affects the performance of unsupervised learning-based fault diagnosis, a coarse and fine-grained deep multi view subspace clustering method (CFG-DMVSC) for unsupervised fault diagnosis of rolling bearings is proposed. The proposed method designs a convolutional autoencoder network based on the Gramian angular field transformation for multi-signal analysis domains. A multi-view coarse-grained self-expressive method based on information entropy is designed to handle differences in information across different views. Furthermore, a fine-grained common and independent information separation loss function based on mutual information is proposed to ensure compactness among multiple views. Both the Case Western Reserve University rolling bearing dataset and privately built bearing fault test bench data demonstrate that, compared to existing methods, the proposed method can perform coarse and fine-grained division in multi-view subspaces, achieving better clustering diagnosis performance on the extracted common information among views.

Multiview ensemble clustering of hypergraph p-Laplacian regularization with weighting and denoising

Multiview clustering has gained attention for its ability to incorporate complementary information from multiple sources of data, leading to better clustering results. However, these methods don't sufficiently mine high-dimensional information of non-linear subspace or ignore important high-level information between basic partitions (BPs), which are obtained via single-view clustering that could help to overcome differences between heterogeneous feature spaces and defined in Eq. (4). Additionally, existing multiview ensemble clustering methods neglect the noise arising from the generation phase. In light of this, we first propose a novel multiview subspace clustering method with hypergraph p-Laplacian regularization and denoising. Specifically, to utilize the high-dimensional information, a hypergraph p-Laplacian regularized term is added to the model along with low-rank subspace learning to capture the different hierarchical structures in the data. A denoising algorithm based on KMeans and K-nearest neighbor is used to minimize the noise of similarity matrix. Then utilizing this approach as a backbone, a multiview ensemble clustering of hypergraph p-Laplacian regularization with weighting and denoising method is proposed. A hybrid strategy and a novel global weighting ensemble strategy is further proposed to extract high-level information across all the BPs. By integrating hypergraph p-Laplacian operator, low-rank subspace learning, denoising, and weighting ensemble strategy in a unified framework, this ensemble approach adequately learns latent structures and complementary information. Experimental results on multiple datasets demonstrate the efficacy of this approach.

Adaptive weighted multi-view subspace clustering method for recognizing urban functions from multi-source social sensing data

ABSTRACT Multi-source social sensing data provide new opportunities to identify urban functions from the perspective of human activity. The information embedded in multi-source data typically needs to be fused to obtain a comprehensive view of urban functions. Although multi-view clustering has been successfully used to fuse multi-source social sensing data, the adaptive determination of fusion weights for high-dimensional and noisy multi-source social sensing data remains challenging. Therefore, this study proposes an adaptive weighted multi-view subspace clustering (AWMSC) method. First, we use two neural networks to map multi-source data into a common latent representation and multiple specific latent representations, which serve as the query vector and input vectors of the attention mechanism, respectively. Then, the weight of each type of data is calculated based on the attention mechanism. Finally, the specific latent representations of the multi-source data are weighted and fused into a shared subspace representation, which is used as the input of the spectral clustering algorithm to obtain clustering results. AWMSC is applied to identify urban functional zones in Beijing using bus transactions, taxi trajectories, and points of interest datasets. The results show that AWMSC outperforms the typical single-view, weighted-average, and representative multi-view methods. AWMSC can obtain a comprehensive understanding of urban functional zones which may help government departments make more accurate strategic decisions.

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.

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.

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.

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.

Double-level View-correlation Multi-view Subspace Clustering

In recent years, significant progress has been made in Multi-view Subspace Clustering (MSC). Most existing MSC methods attempt to explore and exploit the view correlations of multi-view data to boost the clustering performance. They achieve the subspace matrices of different views from the original feature space directly. However, the diversity view-correlation and consistency-view correlation of multi-view data are two antagonistic properties, which are improper and challenging to be captured in such a straightforward process. To simultaneously and properly investigate the two antagonistic properties of multi-view data, a novel Double-level View-correlation Multi-view Subspace Clustering method, named DV-MSC, is introduced in this paper. To be specific, DV-MSC adopts a strategy that deals with the diversity view-correlation and consistency view-correlation in different levels: (1) low-level, which excavates the diversity view-correlation in the feature space, and (2) high-level, which explores the consistency view-correlation in subspace representations. The underlying assumption is that different views should be diverse in the feature space while having the same clustering results, in other words, the proposed method explores the Diversity in Low-level Feature Content (DLFC) and the Consistency in High-level Clustering Structure (CHCS). Experimental results show the promising and competitive clustering performance of DV-MSC, compared to several existing state-of-the-arts.

Decomposed deep multi-view subspace clustering with self-labeling supervision

Most deep multi-view subspace clustering (DMVSC) methods usually employ pipeline optimization by learning the self-expression with a deep model first and then applying spectral clustering to group multi-view data. Subsequently, end-to-end DMVSC methods have been proposed by integrating these two steps into a unified optimization framework. However, the pipeline methods may suffer from misaligned clustering accumulation due to the noise or outlying entries, and the end-to-end methods often constitute a relatively complex parameter optimization. In this paper, we propose a novel method named decomposed deep multi-view subspace clustering with self-labeling supervision (D2MVSC) that runs with a decomposed optimization strategy by three-stage training. Specifically, multi-scale features are extracted by autoencoder in the pre-training stage. According to the discriminative contribution of each view, consensus self-expression is learned from these features by adaptive fusion and structure supervision to generate high-quality pseudo-labels in the fine-tuning stage. Finally, the pseudo-labels are used to retrain the model in a self-labeling supervision manner for robust clustering. Exciting, the self-labeling supervision can be used as an add-on module for other DMVSC methods to improve clustering performance. Extensive experiments on six datasets verify the effectiveness and superiority of our method over other state-of-the-art methods.

Deep low-rank tensor embedding for multi-view subspace clustering

Despite the good clustering performance, most of existing multi-view subspace clustering methods fail to consider the non-linear relationships of high-dimensional data, higher-order correlations of different views, and optimal local geometric structure of the latent embedding space simultaneously. To this end, we put forward a novel multi-view subspace clustering model, named deep low-rank tensor embedding (DLTE). In DLTE, we project the high-dimensional data into the low-dimensional embedding space by utilizing deep non-negative matrix factorization (NMF), which can efficiently capture the complex non-linear relationship of data. Moreover, in the deep embedding space, we utilize the weighted low-rank tensor constraint to capture the global structure and higher-order correlations of different views while considering the contributions of different views. Additionally, we introduce an optimal graph Laplacian to learn a more reasonable local geometric structure of data in the deep embedding space. At last, comprehensive experimental results on eleven datasets indicate the superiority and effectiveness of the proposed DLTE method.

Double graphs regularized multi-view subspace clustering

In recent years, there has been an increasing interest in multi-view subspace clustering (MSC). However, existing MSC methods fail to take full advantage of the local geometric structure in each manifold throughout the data flow, which is essential for clustering. To remedy this drawback, in this paper, a novel Double Graphs Regularized Multi-view Subspace Clustering (DGRMSC) method is proposed, which aims to harness both global and local structural information of multi-view data in a unified framework. Specifically, DGRMSC first learns a latent representation to exploit the global complementary information of multiple views. Based on the learned latent representation, we learn a self-representation to explore its global cluster structure. Further, Double Graphs Regularization (DGR) is performed on both latent representation and self-representation to take advantage of their local manifold structures simultaneously. Then, we design an iterative algorithm to solve the optimization problem effectively. Comprehensive experiments on several popular multi-view datasets demonstrate the effectiveness of the proposed method.

Multi-View Subspace Clustering by Joint Measuring of Consistency and Diversity

In multi-view subspace clustering, it is significant to find a common latent space in which the multi-view datasets are located. A number of multi-view subspace clustering methods have been proposed to explore the common latent subspace and achieved promising performance. However, previous multi-view subspace clustering algorithms seldom consider the multi-view consistency and multi-view diversity, let alone take them into consideration simultaneously. In this paper, we propose a novel multi-view subspace clustering by joint measuring the consistency and diversity, which is able to exploit these two complementary criteria seamlessly into a holistic design of clustering algorithms. The proposed model first searches a pure graph for each view by detecting the intrinsic consistent and diverse parts. A consensus graph is then obtained by fusing the multiple pure graphs. Moreover, the consensus graph is structurized to contain exactly <inline-formula><tex-math notation="LaTeX">$c$</tex-math></inline-formula> connected components where <inline-formula><tex-math notation="LaTeX">$c$</tex-math></inline-formula> is the number of clusters. In this way, the final clustering result can be obtained directly since each connected component precisely corresponds to an individual cluster. Extensive experimental studies on various datasets manifest that our model achieves comparable performance than the other state-of-the-art methods.

Multi-view subspace clustering via adaptive graph learning and late fusion alignment

Multi-view subspace clustering has attracted great attention due to its ability to explore data structure by utilizing complementary information from different views. Most of existing methods learn a sample representation coefficient matrix or an affinity graph for each single view, then the final clustering result is obtained from the spectral embedding of a consensus graph using certain traditional clustering techniques, such as k-means. However, clustering performance will be degenerated if the early fusion of partitions cannot fully exploit relationships between all samples. Different from existing methods, we propose a multi-view subspace clustering method via adaptive graph learning and late fusion alignment (AGLLFA). For each view, AGLLFA learns an affinity graph adaptively to capture the similarity relationship among samples. Moreover, a spectral embedding learning term is designed to exploit the latent feature space of different views. Furthermore, we design a late fusion alignment mechanism to generate an optimal clustering partition by fusing view-specific partitions obtained from multiple views. An alternate updating algorithm with validated convergence is developed to solve the resultant optimization problem. Extensive experiments on several benchmark datasets are conducted to illustrate the effectiveness of the proposed method when compared with other state-of-the-art methods. The demo code of this work is publicly available at https://github.com/tangchuan2000/AGLLFA.

Invertible linear transforms based adaptive multi-view subspace clustering

Constructing tensor with low-rank prior is the crucial issue of tensor based multi-view subspace clustering methods, but there are still some shortcomings. First, they cannot adaptively allocate the contribution of different views, resulting in the learned tensor being suboptimal. Second, they pursue low-rank tensor for different data through Discrete Fourier Transform based tensor nuclear norm, which lacks generality. To overcome these problems, we propose an invertible linear transforms based adaptive multi-view subspace clustering method, named ILTMSC. Firstly, we mine the potential low-order representation of each view through self-representation subspace learning. Then, we capture high-order representation by integrating low-order representations with adaptive weights into a tensor and then rotated. This strategy can integrate tensor adaptively and handle the noise effectively. Finally, we approximate the low-rank tensor with a recently proposed invertible linear transforms based tensor nuclear norm. Such a new tensor nuclear norm makes our model more general because it can use different invertible linear transforms for different tensor data. Moreover, an adaptive weighted tensor singular value thresholding operator is proposed for capturing the new tensor nuclear norm. Our model could be solved by convex optimization efficiently. Extensive experiments on multi-view datasets validate the effectiveness and robustness of our method.

Enhanced tensor low-rank representation learning for multi-view clustering

Multi-view subspace clustering (MSC), assuming the multi-view data are generated from a latent subspace, has attracted considerable attention in multi-view clustering. To recover the underlying subspace structure, a successful approach adopted recently is subspace clustering based on tensor nuclear norm (TNN). But there are some limitations to this approach that the existing TNN-based methods usually fail to exploit the intrinsic cluster structure and high-order correlations well, which leads to limited clustering performance. To address this problem, the main purpose of this paper is to propose a novel tensor low-rank representation (TLRR) learning method to perform multi-view clustering. First, we construct a 3rd-order tensor by organizing the features from all views, and then use the t-product in the tensor space to obtain the self-representation tensor of the tensorial data. Second, we use the ℓ1,2 norm to constrain the self-representation tensor to make it capture the class-specificity distribution, that is important for depicting the intrinsic cluster structure. And simultaneously, we rotate the self-representation tensor, and use the tensor singular value decomposition-based weighted TNN as a tighter tensor rank approximation to constrain the rotated tensor. For the challenged mathematical optimization problem, we present an effective optimization algorithm with a theoretical convergence guarantee and relatively low computation complexity. The constructed convergent sequence to the Karush–Kuhn–Tucker (KKT) critical point solution is mathematically validated in detail. We perform extensive experiments on four datasets and demonstrate that TLRR outperforms state-of-the-art multi-view subspace clustering methods.

Multi-scale deep multi-view subspace clustering with self-weighting fusion and structure preserving

Deep subspace clustering methods for multi-view have achieved impressive clustering performance over other clustering methods. However, the existing methods either cannot integrate the global and local information of multi-view or fail to explore the discriminative contributions among views. In this paper, we propose a novel multi-scale deep multi-view subspace clustering (MDMVSC) method, which unifies the multi-scale learning (ML) module, self-weighting fusion (SF) module and structure preserving (SP) constraint. Specifically, to take advantage of the complementarity and diversity of different views, ML module first learns specific self-representation matrix for each view from the multi-scale low-dimensional latent features with the global and local information. Then, using the SF module, these matrices are fused to obtain the consensus representation of multi-view via attention mechanism guided weights according to their discriminative contributions. Moreover, SP constraint encourages the multi-scale latent features to preserve the consistent structural information of the original multi-view for enhancing representation ability. Extensive experimental results on five datasets demonstrate the superiority of MDMVSC in comparison with several state-of-the-art methods.

Sequential multi-view subspace clustering

Self-representation based subspace learning has shown its effectiveness in many applications, but most existing methods do not consider the difference between different views. As a result, the learned self-representation matrix cannot well characterize the clustering structure. Moreover, some methods involve an undesired weighted vector of the tensor nuclear norm, which reduces the flexibility of the algorithm in practical applications. To handle these problems, we present a tensorized multi-view subspace clustering. Specifically, our method employs matrix factorization and decomposes the self-representation matrix to orthogonal projection matrix and affinity matrix. We also add ℓ1,2-norm regularization on affinity representation to characterize the cluster structure. Moreover, the proposed method uses weighted tensor Schatten p-norm to explore higher-order structure and complementary information embedded in multi-view data, which can allocate the ideal weight for each view automatically without additional weight and penalty parameters. We apply the adaptive loss function to the model to maintain the robustness to outliers and efficiently learn the data distribution. Extensive experimental results on different datasets reveal that our method is superior to other state-of-the-art multi-view subspace clustering methods.

A Method with Adaptive Graphs to Constrain Multi-View Subspace Clustering of Geospatial Big Data from Multiple Sources

Clustering of multi-source geospatial big data provides opportunities to comprehensively describe urban structures. Most existing studies focus only on the clustering of a single type of geospatial big data, which leads to biased results. Although multi-view subspace clustering methods are advantageous for fusing multi-source geospatial big data, exploiting a robust shared subspace in high-dimensional, non-uniform, and noisy geospatial big data remains a challenge. Therefore, we developed a method with adaptive graphs to constrain multi-view subspace clustering of multi-source geospatial big data (agc2msc). First, for each type of data, high-dimensional and noisy original features were projected into a low-dimensional latent representation using autoencoder networks. Then, adaptive graph constraints were used to fuse the latent representations of multi-source data into a shared subspace representation, which preserved the neighboring relationships of data points. Finally, the shared subspace representation was used to obtain the clustering results by employing a spectral clustering algorithm. Experiments on four benchmark datasets showed that agc2msc outperformed nine state-of-the-art methods. agc2msc was applied to infer urban land use types in Beijing using the taxi GPS trajectory, bus smart card transaction, and points of interest datasets. The clustering results may provide useful calibration and reference for urban planning.