In this paper, we introduce a Fast and Scalable Semi-supervised Multi-view Subspace Clustering (FSSMSC) method, a novel solution to the high computational complexity commonly found in existing approaches. FSSMSC features linear computational and space complexity relative to the size of the data. The method generates a consensus anchor graph across all views, representing each data point as a sparse linear combination of chosen landmarks. Unlike traditional methods that manage the anchor graph construction and the label propagation process separately, this paper proposes a unified optimization model that facilitates simultaneous learning of both. An effective alternating update algorithm with convergence guarantees is proposed to solve the unified optimization model. Additionally, the method employs the obtained anchor graph and landmarks' low-dimensional representations to deduce low-dimensional representations for raw data. Following this, a straightforward clustering approach is conducted on these low-dimensional representations to achieve the final clustering results. The effectiveness and efficiency of FSSMSC are validated through extensive experiments on multiple benchmark datasets of varying scales.
Multiview subspace clustering (MVSC) has attracted an increasing amount of attention in recent years. Most existing MVSC methods first collect complementary information from different views and consequently derive a consensus reconstruction coefficient matrix to indicate the subspace structure of a multi-view data set. In this paper, we initially assume the existence of a consensus reconstruction coefficient matrix and then use it to build a consensus graph filter. In each view, the filter is employed for smoothing the data and designing a regularizer for the reconstruction coefficient matrix. Finally, the obtained reconstruction coefficient matrices from different views are used to create constraints for the consensus reconstruction coefficient matrix. Therefore, in the proposed method, the consensus reconstruction coefficient matrix, the consensus graph filter, and the reconstruction coefficient matrices from different views are interdependent. We provide an optimization algorithm to obtain their optimal values. Extensive experiments on diverse multi-view data sets demonstrate that our approach outperforms some state-of-the-art methods.
A growing awareness of multi-view learning as an important component in data science and machine learning is a consequence of the increasing prevalence of multiple views in real-world applications, especially in the context of networks. In this paper we introduce a new scalability framework for multi-view subspace clustering. An efficient optimization strategy is proposed, leveraging kernel feature maps to reduce the computational burden while maintaining good clustering performance. The scalability of the algorithm means that it can be applied to large-scale datasets, including those with millions of data points, using a standard machine, in a few minutes. We conduct extensive experiments on real-world benchmark networks of various sizes in order to evaluate the performance of our algorithm against state-of-the-art multi-view subspace clustering methods and attributed-network multi-view approaches.
Latent multi-view subspace clustering has been demonstrated to have desirable clustering performance. However, the original latent representation method vertically concatenates the data matrices from multiple views into a single matrix along the direction of dimensionality to recover the latent representation matrix, which may result in an incomplete information recovery. To fully recover the latent space representation, we in this paper propose an Enhanced Latent Multi-view Subspace Clustering (ELMSC) method. The ELMSC method involves constructing an augmented data matrix that enhances the representation of multi-view data. Specifically, we stack the data matrices from various views into the block-diagonal locations of the augmented matrix to exploit the complementary information. Meanwhile, the non-block-diagonal entries are composed based on the similarity between different views to capture the consistent information. In addition, we enforce a sparse regularization for the non-diagonal blocks of the augmented self-representation matrix to avoid redundant calculations of consistency information. Finally, a novel iterative algorithm based on the framework of Alternating Direction Method of Multipliers (ADMM) is developed to solve the optimization problem for ELMSC. Extensive experiments on real-world datasets demonstrate that our proposed ELMSC is able to achieve higher clustering performance than some state-of-art multi-view clustering methods.
High-dimensional and complex spectral structures make the clustering of hyperspectral images (HSI) a challenging task. Subspace clustering is an effective approach for addressing this problem. However, current subspace clustering algorithms are primarily designed for a single view and do not fully exploit the spatial or textural feature information in HSI. In this study, contrastive multi-view subspace clustering of HSI was proposed based on graph convolutional networks. Pixel neighbor textural and spatial-spectral information were sent to construct two graph convolutional subspaces to learn their affinity matrices. To maximize the interaction between different views, a contrastive learning algorithm was introduced to promote the consistency of positive samples and assist the model in extracting robust features. An attention-based fusion module was used to adaptively integrate these affinity matrices, constructing a more discriminative affinity matrix. The model was evaluated using four popular HSI datasets: Indian Pines, Pavia University, Houston, and Xu Zhou. It achieved overall accuracies of 97.61%, 96.69%, 87.21%, and 97.65%, respectively, and significantly outperformed state-of-the-art clustering methods. In conclusion, the proposed model effectively improves the clustering accuracy of HSI.
Recent multi-view subspace clustering achieves impressive results utilizing deep networks, where the self-expressive correlation is typically modeled by a fully connected (FC) layer. However, they still suffer from two limitations. i) The parameter scale of the FC layer is quadratic to sample numbers, resulting in high time and memory costs that significantly degrade their feasibility in large-scale datasets. ii) It is under-explored to extract a unified representation that simultaneously satisfies minimal sufficiency and discriminability. To this end, we propose a novel deep framework, termed Efficient and Effective deep Multi-View Subspace Clustering (E$^2$MVSC). Instead of a parameterized FC layer, we design a Relation-Metric Net that decouples network parameter scale from sample numbers for greater computational efficiency. Most importantly, the proposed method devises a multi-type auto-encoder to explicitly decouple consistent, complementary, and superfluous information from every view, which is supervised by a soft clustering assignment similarity constraint. Following information bottleneck theory and the maximal coding rate reduction principle, a sufficient yet minimal unified representation can be obtained, as well as pursuing intra-cluster aggregation and inter-cluster separability within it. Extensive experiments show that E$^2$MVSC yields comparable results to existing methods and achieves state-of-the-art performance in various types of multi-view datasets.
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.
Tensor-based multi-view subspace clustering (MSC) can capture high-order correlation in the self-representation tensor. Current tensor decompositions for MSC suffer from highly unbalanced unfolding matrices or rotation sensitivity, failing to fully explore inter/intra-view information. Using the advanced tensor network, namely, multi-scale entanglement renormalization ansatz (MERA), we propose a low-rank MERA based MSC (MERA-MSC) algorithm, where MERA factorizes a tensor into contractions of one top core factor and the rest orthogonal/semi-orthogonal factors. Benefiting from multiple interactions among orthogonal/semi-orthogonal (low-rank) factors, the low-rank MERA has a strong representation power to capture the complex inter/intra-view information in the self-representation tensor. The alternating direction method of multipliers is adopted to solve the optimization model. Experimental results on five multi-view datasets demonstrate MERA-MSC has superiority against the compared algorithms on six evaluation metrics. Furthermore, we extend MERA-MSC by incorporating anchor learning to develop a scalable low-rank MERA based multi-view clustering method (sMREA-MVC). The effectiveness and efficiency of sMERA-MVC have been validated on three large-scale multi-view datasets. To our knowledge, this is the first work to introduce MERA to the multi-view clustering topic. The codes of MERA-MSC and sMERA-MVC are publicly available at https://github.com/longzhen520/MERA-MSC.
Deep multi-view subspace clustering (DMVSC) has recently attracted increasing attention due to its promising performance. However, existing DMVSC methods still have two issues: (1) they mainly focus on using autoencoders to nonlinearly embed the data, while the embedding may be suboptimal for clustering because the clustering objective is rarely considered in autoencoders, and (2) existing methods typically have a quadratic or even cubic complexity, which makes it challenging to deal with large-scale data. To address these issues, in this paper we propose a novel deep multi-view subspace clustering method with anchor graph (DMCAG). To be specific, DMCAG firstly learns the embedded features for each view independently, which are used to obtain the subspace representations. To significantly reduce the complexity, we construct an anchor graph with small size for each view. Then, spectral clustering is performed on an integrated anchor graph to obtain pseudo-labels. To overcome the negative impact caused by suboptimal embedded features, we use pseudo-labels to refine the embedding process to make it more suitable for the clustering task. Pseudo-labels and embedded features are updated alternately. Furthermore, we design a strategy to keep the consistency of the labels based on contrastive learning to enhance the clustering performance. Empirical studies on real-world datasets show that our method achieves superior clustering performance over other state-of-the-art methods.
Multi-view subspace clustering methods have employed learned self-representation tensors from different tensor decompositions to exploit low rank information. However, the data structures embedded with self-representation tensors may vary in different multi-view datasets. Therefore, a pre-defined tensor decomposition may not fully exploit low rank information for a certain dataset, resulting in sub-optimal multi-view clustering performance. To alleviate the aforementioned limitations, we propose the adaptively topological tensor network (ATTN) by determining the edge ranks from the structural information of the self-representation tensor, and it can give a better tensor representation with the data-driven strategy. Specifically, in multi-view tensor clustering, we analyze the higher-order correlations among different modes of a self-representation tensor, and prune the links of the weakly correlated ones from a fully connected tensor network. Therefore, the newly obtained tensor networks can efficiently explore the essential clustering information with self-representation with different tensor structures for various datasets. A greedy adaptive rank-increasing strategy is further applied to improve the capture capacity of low rank structure. We apply ATTN on multi-view subspace clustering and utilize the alternating direction method of multipliers to solve it. Experimental results show that multi-view subspace clustering based on ATTN outperforms the counterparts on six multi-view datasets.
Tensor-oriented multi-view subspace clustering has achieved significant strides in assessing high-order correlations and improving clustering analysis of multi-view data. Nevertheless, most of existing investigations are typically hampered by the two flaws. First, self-representation based tensor subspace learning usually induces high time and space complexity, and is limited in perceiving nonlinear local structure in the embedding space. Second, the tensor singular value decomposition (t-SVD) model redistributes each singular value equally without considering the diverse importance among them. To well cope with the issues, we propose a hyper-Laplacian regularized concept factorization (HLRCF) in low-rank tensor space for multi-view clustering. Specifically, we adopt the concept factorization to explore the latent cluster-wise representation of each view. Further, the hypergraph Laplacian regularization endows the model with the capability of extracting the nonlinear local structures in the latent space. Considering that different tensor singular values associate structural information with unequal importance, we develop a self-weighted tensor Schatten p-norm to constrain the tensor comprised of all cluster-wise representations. Notably, the tensor with smaller size greatly decreases the time and space complexity in the low-rank optimization. Finally, experimental results on eight benchmark datasets exhibit that HLRCF outperforms other multi-view methods, showingcasing its superior performance.
Recent years have witnessed a growing academic interest in multi-view subspace clustering. In this paper, we propose a novel Double Graphs Regularized Multi-view Subspace Clustering (DGRMSC) method, which aims to harness both global and local structural information of multi-view data in a unified framework. Specifically, DGRMSC firstly 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. Extensive experimental results on real-world datasets demonstrate the effectiveness of the proposed method.
Subspace clustering is to find underlying low-dimensional subspaces and cluster the data points correctly. In this paper, we propose a novel multi-view subspace clustering method. Most existing methods suffer from two critical issues. First, they usually adopt a two-stage framework and isolate the processes of affinity learning, multi-view information fusion and clustering. Second, they assume the data lies in a linear subspace which may fail in practice as most real-world datasets may have non-linearity structures. To address the above issues, in this paper we propose a novel Enriched Robust Multi-View Kernel Subspace Clustering framework where the consensus affinity matrix is learned from both multi-view data and spectral clustering. Due to the objective and constraints which is difficult to optimize, we propose an iterative optimization method which is easy to implement and can yield closed solution in each step. Extensive experiments have validated the superiority of our method over state-of-the-art clustering methods.
In this paper, we explore the problem of deep multi-view subspace clustering framework from an information-theoretic point of view. We extend the traditional information bottleneck principle to learn common information among different views in a self-supervised manner, and accordingly establish a new framework called Self-supervised Information Bottleneck based Multi-view Subspace Clustering (SIB-MSC). Inheriting the advantages from information bottleneck, SIB-MSC can learn a latent space for each view to capture common information among the latent representations of different views by removing superfluous information from the view itself while retaining sufficient information for the latent representations of other views. Actually, the latent representation of each view provides a kind of self-supervised signal for training the latent representations of other views. Moreover, SIB-MSC attempts to learn the other latent space for each view to capture the view-specific information by introducing mutual information based regularization terms, so as to further improve the performance of multi-view subspace clustering. To the best of our knowledge, this is the first work to explore information bottleneck for multi-view subspace clustering. Extensive experiments on real-world multi-view data demonstrate that our method achieves superior performance over the related state-of-the-art methods.
Multi-view subspace clustering aims to discover the hidden subspace structures from multiple views for robust clustering, and has been attracting considerable attention in recent years. Despite significant progress, most of the previous multi-view subspace clustering algorithms are still faced with two limitations. First, they usually focus on the consistency (or commonness) of multiple views, yet often lack the ability to capture the cross-view inconsistencies in subspace representations. Second, many of them overlook the local structures of multiple views and cannot jointly leverage multiple local structures to enhance the subspace representation learning. To address these two limitations, in this paper, we propose a jointly smoothed multi-view subspace clustering (JSMC) approach. Specifically, we simultaneously incorporate the cross-view commonness and inconsistencies into the subspace representation learning. The view-consensus grouping effect is presented to jointly exploit the local structures of multiple views to regularize the view-commonness representation, which is further associated with the low-rank constraint via the nuclear norm to strengthen its cluster structure. Thus the cross-view commonness and inconsistencies, the view-consensus grouping effect, and the low-rank representation are seamlessly incorporated into a unified objective function, upon which an alternating optimization algorithm is performed to achieve a robust subspace representation for clustering. Experimental results on a variety of real-world multi-view datasets confirm the superiority of our approach. Code available: https://github.com/huangdonghere/JSMC.
Multi-view subspace clustering (MSC) is a popular unsupervised method by integrating heterogeneous information to reveal the intrinsic clustering structure hidden across views. Usually, MSC methods use graphs (or affinity matrices) fusion to learn a common structure, and further apply graph-based approaches to clustering. Despite progress, most of the methods do not establish the connection between graph learning and clustering. Meanwhile, conventional graph fusion strategies assign coarse-grained weights to combine multi-graph, ignoring the importance of local structure. In this paper, we propose a fine-grained graph learning framework for multi-view subspace clustering (FGL-MSC) to address these issues. To utilize the multi-view information sufficiently, we design a specific graph learning method by introducing graph regularization and a local structure fusion pattern. The main challenge is how to optimize the fine-grained fusion weights while generating the learned graph that fits the clustering task, thus making the clustering representation meaningful and competitive. Accordingly, an iterative algorithm is proposed to solve the above joint optimization problem, which obtains the learned graph, the clustering representation, and the fusion weights simultaneously. Extensive experiments on eight real-world datasets show that the proposed framework has comparable performance to the state-of-the-art methods. The source code of the proposed method is available at https://github.com/siriuslay/FGL-MSC.
Multi-view subspace clustering always performs well in high-dimensional data analysis, but is sensitive to the quality of data representation. To this end, a two stage fusion strategy is proposed to embed representation learning into the process of multi-view subspace clustering. This paper first propose a novel matrix factorization method that can separate the coupling consistent and complementary information from observations of multiple views. Based on the obtained latent representations, we further propose two subspace clustering strategies: feature-level fusion and subspace-level hierarchical strategy. Feature-level method concatenates all kinds of latent representations from multiple views, and the original problem therefore degenerates to a single-view subspace clustering process. Subspace-level hierarchical method performs different self-expressive reconstruction processes on the corresponding complementary and consistent latent representations coming from each view, i.e. the prior constraints imposed on different types of subspace representations are related to the appropriate input factors. Finally, extensive experimental results on real-world datasets demonstrate the superiority of our proposed methods by comparing against some state-of-the-art subspace clustering algorithms.
In this paper, we propose a novel Attentive Multi-View Deep Subspace Nets (AMVDSN), which deeply explores underlying consistent and view-specific information from multiple views and fuse them by considering each view's dynamic contribution obtained by attention mechanism. Unlike most multi-view subspace learning methods that they directly reconstruct data points on raw data or only consider consistency or complementarity when learning representation in deep or shallow space, our proposed method seeks to find a joint latent representation that explicitly considers both consensus and view-specific information among multiple views, and then performs subspace clustering on learned joint latent representation.Besides, different views contribute differently to representation learning, we therefore introduce attention mechanism to derive dynamic weight for each view, which performs much better than previous fusion methods in the field of multi-view subspace clustering. The proposed algorithm is intuitive and can be easily optimized just by using Stochastic Gradient Descent (SGD) because of the neural network framework, which also provides strong non-linear characterization capability compared with traditional subspace clustering approaches. The experimental results on seven real-world data sets have demonstrated the effectiveness of our proposed algorithm against some state-of-the-art subspace learning approaches.
In recent years, multi-view subspace clustering has achieved impressive performance due to the exploitation of complementary imformation across multiple views. However, multi-view data can be very complicated and are not easy to cluster in real-world applications. Most existing methods operate on raw data and may not obtain the optimal solution. In this work, we propose a novel multi-view clustering method named smoothed multi-view subspace clustering (SMVSC) by employing a novel technique, i.e., graph filtering, to obtain a smooth representation for each view, in which similar data points have similar feature values. Specifically, it retains the graph geometric features through applying a low-pass filter. Consequently, it produces a ``clustering-friendly" representation and greatly facilitates the downstream clustering task. Extensive experiments on benchmark datasets validate the superiority of our approach. Analysis shows that graph filtering increases the separability of classes.
Incomplete multi-view clustering is an important technique to deal with real-world incomplete multi-view data. Previous works assume that all views have the same incompleteness, i.e., balanced incompleteness. However, different views often have distinct incompleteness, i.e., unbalanced incompleteness, which results in strong views (low-incompleteness views) and weak views (high-incompleteness views). The unbalanced incompleteness prevents us from directly using the previous methods for clustering. In this paper, inspired by the effective biological evolution theory, we design the novel scheme of view evolution to cluster strong and weak views. Moreover, we propose an Unbalanced Incomplete Multi-view Clustering method (UIMC), which is the first effective method based on view evolution for unbalanced incomplete multi-view clustering. Compared with previous methods, UIMC has two unique advantages: 1) it proposes weighted multi-view subspace clustering to integrate these unbalanced incomplete views, which effectively solves the unbalanced incomplete multi-view problem; 2) it designs the low-rank and robust representation to recover the data, which diminishes the impact of the incompleteness and noises. Extensive experimental results demonstrate that UIMC improves the clustering performance by up to 40% on three evaluation metrics over other state-of-the-art methods.