Unsupervised Discriminative Feature Selection via Contrastive Graph Learning.

Due to many unmarked data, there has been tremendous interest in developing unsupervised feature selection methods, among which graph-guided feature selection is one of the most representative techniques. However, the existing feature selection methods have the following limitations: (1) All of them only remove redundant features shared by all classes and neglect the class-specific properties; thus, the selected features cannot well characterize the discriminative structure of the data. (2) The existing methods only consider the relationship between the data and the corresponding neighbor points by Euclidean distance while neglecting the differences with other samples. Thus, existing methods cannot encode discriminative information well. (3) They adaptively learn the graph in the original or embedding space. Thus, the learned graph cannot characterize the data's cluster structure. To solve these limitations, we present a novel unsupervised discriminative feature selection via contrastive graph learning, which integrates feature selection and graph learning into a uniform framework. Specifically, our model adaptively learns the affinity matrix, which helps characterize the data's intrinsic and cluster structures in the original space and the contrastive learning. We minimize l1,2 -norm regularization on the projection matrix to preserve class-specific features and remove redundant features shared by all classes. Thus, the selected features encode discriminative information well and characterize the discriminative structure of the data. Generous experiments indicate that our proposed model has state-of-the-art performance.

Learning deep representation and discriminative features for clustering of multi-layer networks.

The multi-layer network consists of the interactions between different layers, where each layer of the network is depicted as a graph, providing a comprehensive way to model the underlying complex systems. The layer-specific modules of multi-layer networks are critical to understanding the structure and function of the system. However, existing methods fail to characterize and balance the connectivity and specificity of layer-specific modules in networks because of the complicated inter- and intra-coupling of various layers. To address the above issues, a joint learning graph clustering algorithm (DRDF) for detecting layer-specific modules in multi-layer networks is proposed, which simultaneously learns the deep representation and discriminative features. Specifically, DRDF learns the deep representation with deep nonnegative matrix factorization, where the high-order topology of the multi-layer network is gradually and precisely characterized. Moreover, it addresses the specificity of modules with discriminative feature learning, where the intra-class compactness and inter-class separation of pseudo-labels of clusters are explored as self-supervised information, thereby providing a more accurate method to explicitly model the specificity of the multi-layer network. Finally, DRDF balances the connectivity and specificity of layer-specific modules with joint learning, where the overall objective of the graph clustering algorithm and optimization rules are derived. The experiments on ten multi-layer networks showed that DRDF not only outperforms eight baselines on graph clustering but also enhances the robustness of algorithms.

Efficient Multi-View K-Means for Image Clustering.

Nowadays, data in the real world often comes from multiple sources, but most existing multi-view K-Means perform poorly on linearly non-separable data and require initializing the cluster centers and calculating the mean, which causes the results to be unstable and sensitive to outliers. This paper proposes an efficient multi-view K-Means to solve the above-mentioned issues. Specifically, our model avoids the initialization and computation of clusters centroid of data. Additionally, our model use the Butterworth filters function to transform the adjacency matrix into a distance matrix, which makes the model is capable of handling linearly inseparable data and insensitive to outliers. To exploit the consistency and complementarity across multiple views, our model constructs a third tensor composed of discrete index matrices of different views and minimizes the tensor's rank by tensor Schatten p-norm. Experiments on two artificial datasets verify the superiority of our model on linearly inseparable data, and experiments on several benchmark datasets illustrate the performance.

Contrastive self-representation learning for data clustering.

This paper is concerned with self-representation subspace learning. It is one of the most representative subspace techniques, which has attracted considerable attention for clustering due to its good performance. Among these methods, low-rank representation (LRR) has achieved impressive results for subspace clustering. However, it only considers the similarity between the data itself, while neglecting the differences with other samples. Besides, it cannot well deal with noise and portray cluster-to-cluster relationships well. To solve these problems, we propose a Contrastive Self-representation model for Clustering (CSC). CSC simultaneously takes into account the similarity/dissimilarity between positive/negative pairs when learning the self-representation coefficient matrix of data while the form of the loss function can reduce the effect of noise on the results. Moreover, We use the ℓ1,2-norm regularizer on the coefficient matrix to achieve its sparsity to better characterize the cluster structure. Thus, the learned self-representation coefficient matrix well encodes both the discriminative information and cluster structure. Extensive experiments on seven benchmark databases indicate the superiority of our proposed method.

Sparse discriminant PCA based on contrastive learning and class-specificity distribution.

Much mathematical effort has been devoted to developing Principal Component Analysis (PCA), which is the most popular feature extraction method. To suppress the negative effect of noise on PCA performance, there have been extensive studies and applications of a large number of robust PCAs achieving outstanding results. However, existing methods suffer from at least two shortcomings: (1) They expressed PCA as a reconstruction model measured by Euclidean distance, which only considers the relationship between the data and its reconstruction and ignores the differences between different data points; (2) They did not consider the class-specificity distribution information contained in the data itself, thus lacking discriminative properties. To overcome the above problems, we propose a Sparse Discriminant Principal Components Analysis (SDPCA) model based on contrastive learning and class-specificity distribution. Specifically, we use contrastive learning to measure the relationship between samples and their reconstructions, which fully takes the discriminative information between data into account in PCA. In order to make the extracted low-dimensional features profoundly reflect the class-specificity distribution of the data, we minimize the squared ℓ1,2-norm of the low-dimensional embedding. In addition, to reduce the effects of redundant features and noise and to improve the interpretability of PCA at the same time, we impose sparsity constraints on the projection matrix using the squared ℓ1,2-norm. Our experimental results on different types of benchmark databases demonstrate that our model has state-of-the-art performance.

Active learning based on similarity level histogram and adaptive-scale sampling for very high resolution image classification.

In remote sensing image classification, active learning aims to obtain an excellent classification model by selecting informative or representative training samples. However, due to the complexity of remote sensing images, the same class of ground objects usually have different spectral representations. The existing active learning methods may not take into account diverse representations of the same targets, which leads to a possible lack of intra-class diversity in the collected samples. To alleviate this problem, we propose an active learning method based on similarity level histogram (SLH) and adaptive-scale sampling to improve very high resolution remote sensing image classification. Specifically, we construct a SLH for each class of ground objects to effectively consider the intra-class diversity of the same target. To avoid the problem of sample imbalance caused by over-sampling or under-sampling, we design an adaptive-scale sampling strategy. Then, we utilize active learning to mine representative samples from each SLH warehouse according to adaptive-scale sampling strategies until the iteration condition is satisfied. Experiments show that the proposed algorithm can achieve better classification performance with limited training samples and is competitive with other methods based on four sets of publicly available data.

Low-rank discrete multi-view spectral clustering.

Spectral clustering has attracted intensive attention in multimedia applications due to its good performance on arbitrary shaped clusters and well-defined mathematical framework. However, most existing multi-view spectral clustering methods still have the following demerits: (1) They ignore useful complementary information embedded in indicator matrices of different views. (2) The conventional post-processing methods based on the relax and discrete strategy inevitably result in the sub-optimal discrete solution. To tackle the aforementioned drawbacks, we propose a low-rank discrete multi-view spectral clustering model. Drawing inspiration from the fact that the difference between indicator matrices of different views provides useful complementary information for clustering, our model exploits the complementary information embedded in indicator matrices with tensor Schatten p-norm constraint. Further, we integrate low-rank tensor learning and discrete label recovering into a uniform framework, which avoids the uncertainty of the relaxed and discrete strategy. Extensive experiments on benchmark datasets have demonstrated the effectiveness and superiority of the proposed method.

Joint feature selection and optimal bipartite graph learning for subspace clustering.

Recently, there has been tremendous interest in developing graph-based subspace clustering in high-dimensional data, which does not require a priori knowledge of the number of dimensions and subspaces. The general steps of such algorithms are dictionary representation and spectral clustering. Traditional methods use the dataset itself as a dictionary when performing dictionary representation. There are some limitations that the redundant information present in the dictionary and features may make the constructed graph structure unclear and require post-processing to obtain labels. To address these problems, we propose a novel subspace clustering model that first introduces feature selection to process the input data, randomly selects some samples to construct a dictionary to remove redundant information and learns the optimal bipartite graph with K-connected components under the constraint of the (normalized) Laplacian rank. Finally, the labels are obtained directly from the graphs. The experimental results on motion segmentation and face recognition datasets demonstrate the superior effectiveness and stability of our algorithm.

Graph Embedding Contrastive Multi-Modal Representation Learning for Clustering.

Multi-modal clustering (MMC) aims to explore complementary information from diverse modalities for clustering performance facilitating. This article studies challenging problems in MMC methods based on deep neural networks. On one hand, most existing methods lack a unified objective to simultaneously learn the inter- and intra-modality consistency, resulting in a limited representation learning capacity. On the other hand, most existing processes are modeled for a finite sample set and cannot handle out-of-sample data. To handle the above two challenges, we propose a novel Graph Embedding Contrastive Multi-modal Clustering network (GECMC), which treats the representation learning and multi-modal clustering as two sides of one coin rather than two separate problems. In brief, we specifically design a contrastive loss by benefiting from pseudo-labels to explore consistency across modalities. Thus, GECMC shows an effective way to maximize the similarities of intra-cluster representations while minimizing the similarities of inter-cluster representations at both inter- and intra-modality levels. So, the clustering and representation learning interact and jointly evolve in a co-training framework. After that, we build a clustering layer parameterized with cluster centroids, showing that GECMC can learn the clustering labels with given samples and handle out-of-sample data. GECMC yields superior results than 14 competitive methods on four challenging datasets. Codes and datasets are available: https://github.com/xdweixia/GECMC.

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.

Adversarial Multiview Clustering Networks With Adaptive Fusion.

The existing deep multiview clustering (MVC) methods are mainly based on autoencoder networks, which seek common latent variables to reconstruct the original input of each view individually. However, due to the view-specific reconstruction loss, it is challenging to extract consistent latent representations over multiple views for clustering. To address this challenge, we propose adversarial MVC (AMvC) networks in this article. The proposed AMvC generates each view's samples conditioning on the fused latent representations among different views to encourage a more consistent clustering structure. Specifically, multiview encoders are used to extract latent descriptions from all the views, and the corresponding generators are used to generate the reconstructed samples. The discriminative networks and the mean squared loss are jointly utilized for training the multiview encoders and generators to balance the distinctness and consistency of each view's latent representation. Moreover, an adaptive fusion layer is developed to obtain a shared latent representation, on which a clustering loss and the l1,2 -norm constraint are further imposed to improve clustering performance and distinguish the latent space. Experimental results on video, image, and text datasets demonstrate that the effectiveness of our AMvC is over several state-of-the-art deep MVC methods.

Tensorized Bipartite Graph Learning for Multi-View Clustering.

Despite the impressive clustering performance and efficiency in characterizing both the relationship between the data and cluster structure, most existing graph-based multi-view clustering methods still have the following drawbacks. They suffer from the expensive time burden due to both the construction of graphs and eigen-decomposition of Laplacian matrix. Moreover, none of them simultaneously considers the similarity of inter-view and similarity of intra-view. In this article, we propose a variance-based de-correlation anchor selection strategy for bipartite construction. The selected anchors not only cover the whole classes but also characterize the intrinsic structure of data. Following that, we present a tensorized bipartite graph learning for multi-view clustering (TBGL). Specifically, TBGL exploits the similarity of inter-view by minimizing the tensor Schatten p-norm, which well exploits both the spatial structure and complementary information embedded in the bipartite graphs of views. We exploit the similarity of intra-view by using the [Formula: see text]-norm minimization regularization and connectivity constraint on each bipartite graph. So the learned graph not only well encodes discriminative information but also has the exact connected components which directly indicates the clusters of data. Moreover, we solve TBGL by an efficient algorithm which is time-economical and has good convergence. Extensive experimental results demonstrate that TBGL is superior to the state-of-the-art methods. Codes and datasets are available: https://github.com/xdweixia/TBGL-MVC.

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.

Fast multiple graphs learning for multi-view clustering.

Graph-based multi-view clustering has become an active topic due to the efficiency in characterizing both the complex structure and relationship between multimedia data. However, existing methods have the following shortcomings: (1) They are inefficient or even fail for graph learning in large scale due to the graph construction and eigen-decomposition. (2) They cannot well exploit both the complementary information and spatial structure embedded in graphs of different views. To well exploit complementary information and tackle the scalability issue plaguing graph-based multi-view clustering, we propose an efficient multiple graph learning model via a small number of anchor points and tensor Schatten p-norm minimization. Specifically, we construct a hidden and tractable large graph by anchor graph for each view and well exploit complementary information embedded in anchor graphs of different views by tensor Schatten p-norm regularizer. Finally, we develop an efficient algorithm, which scales linearly with the data size, to solve our proposed model. Extensive experimental results on several datasets indicate that our proposed method outperforms some state-of-the-art multi-view clustering algorithms.

View-Consistency Learning for Incomplete Multiview Clustering.

In this article, we present a novel general framework for incomplete multi-view clustering by integrating graph learning and spectral clustering. In our model, a tensor low-rank constraint are introduced to learn a stable low-dimensional representation, which encodes the complementary information and takes into account the cluster structure between different views. A corresponding algorithm associated with augmented Lagrangian multipliers is established. In particular, tensor Schatten p -norm is used as a tighter approximation to the tensor rank function. Besides, both consistency and specificity are jointly exploited for subspace representation learning. Extensive experiments on benchmark datasets demonstrate that our model outperforms several baseline methods in incomplete multi-view clustering.

Multiview Spectral Clustering With Bipartite Graph.

Multi-view spectral clustering has become appealing due to its good performance in capturing the correlations among all views. However, on one hand, many existing methods usually require a quadratic or cubic complexity for graph construction or eigenvalue decomposition of Laplacian matrix; on the other hand, they are inefficient and unbearable burden to be applied to large scale data sets, which can be easily obtained in the era of big data. Moreover, the existing methods cannot encode the complementary information between adjacency matrices, i.e., similarity graphs of views and the low-rank spatial structure of adjacency matrix of each view. To address these limitations, we develop a novel multi-view spectral clustering model. Our model well encodes the complementary information by Schatten p -norm regularization on the third tensor whose lateral slices are composed of the adjacency matrices of the corresponding views. To further improve the computational efficiency, we leverage anchor graphs of views instead of full adjacency matrices of the corresponding views, and then present a fast model that encodes the complementary information embedded in anchor graphs of views by Schatten p -norm regularization on the tensor bipartite graph. Finally, an efficient alternating algorithm is derived to optimize our model. The constructed sequence was proved to converge to the stationary KKT point. Extensive experimental results indicate that our method has good performance.

Attributes learning network for generalized zero-shot learning.

In the absence of unseen training data, zero-shot learning algorithms utilize the semantic knowledge shared by the seen and unseen classes to establish the connection between the visual space and the semantic space, so as to realize the recognition of the unseen classes. However, in real applications, the original semantic representation cannot well characterize both the class-specificity structure and discriminative information in dimension space, which leads to unseen classes being easily misclassified into seen classes. To tackle this problem, we propose a Salient Attributes Learning Network (SALN) to generate discriminative and expressive semantic representation under the supervision of the visual features. Meanwhile, ℓ1,2-norm constraint is employed to make the learned semantic representation well characterize the class-specificity structure and discriminative information in dimension space. Then feature alignment network projects the learned semantic representation into visual space and a relation network is adopted for classification. The performance of the proposed approach has made progress on the five benchmark datasets in generalized zero-shot learning task, and in-depth experiments indicate the effectiveness and excellence of our method.

Tensor Completion-Based Incomplete Multiview Clustering.

Incomplete multiview clustering is a challenging problem in the domain of unsupervised learning. However, the existing incomplete multiview clustering methods only consider the similarity structure of intraview while neglecting the similarity structure of interview. Thus, they cannot take advantage of both the complementary information and spatial structure embedded in similarity matrices of different views. To this end, we complete the incomplete graph with missing data referring to tensor complete and present a novel and effective model to handel the incomplete multiview clustering task. To be specific, we consider the similarity of the interview graphs via the tensor Schatten p -norm-based completion technique to make use of both the complementary information and spatial structure. Meanwhile, we employ the connectivity constraint for similarity matrices of different views such that the connected components approximately represent clusters. Thus, the learned entire graph not only has the low-rank structure but also well characterizes the relationship between unmissing data. Extensive experiments show the promising performance of the proposed method comparing with several incomplete multiview approaches in the clustering tasks.

Multiview Subspace Clustering by an Enhanced Tensor Nuclear Norm.

Despite the promising preliminary results, tensor-singular value decomposition (t-SVD)-based multiview subspace is incapable of dealing with real problems, such as noise and illumination changes. The major reason is that tensor-nuclear norm minimization (TNNM) used in t-SVD regularizes each singular value equally, which does not make sense in matrix completion and coefficient matrix learning. In this case, the singular values represent different perspectives and should be treated differently. To well exploit the significant difference between singular values, we study the weighted tensor Schatten p -norm based on t-SVD and develop an efficient algorithm to solve the weighted tensor Schatten p -norm minimization (WTSNM) problem. After that, applying WTSNM to learn the coefficient matrix in multiview subspace clustering, we present a novel multiview clustering method by integrating coefficient matrix learning and spectral clustering into a unified framework. The learned coefficient matrix well exploits both the cluster structure and high-order information embedded in multiview views. The extensive experiments indicate the efficiency of our method in six metrics.

Multi-view graph embedding clustering network: Joint self-supervision and block diagonal representation.

Multi-view clustering has become an active topic in artificial intelligence. Yet, similar investigation for graph-structured data clustering has been absent so far. To fill this gap, we present a Multi-View Graph embedding Clustering network (MVGC). Specifically, unlike traditional multi-view construction methods, which are only suitable to describe Euclidean structure data, we leverage Euler transform to augment the node attribute, as a new view descriptor, for non-Euclidean structure data. Meanwhile, we impose block diagonal representation constraint, which is measured by the ℓ1,2-norm, on self-expression coefficient matrix to well explore the cluster structure. By doing so, the learned view-consensus coefficient matrix well encodes the discriminative information. Moreover, we make use of the learned clustering labels to guide the learnings of node representation and coefficient matrix, where the latter is used in turn to conduct the subsequent clustering. In this way, clustering and representation learning are seamlessly connected, with the aim to achieve better clustering performance. Extensive experimental results indicate that MVGC is superior to 11 state-of-the-art methods on four benchmark datasets. In particular, MVGC achieves an Accuracy of 96.17% (53.31%) on the ACM (IMDB) dataset, which is an up to 2.85% (1.97%) clustering performance improvement compared with the strongest baseline.