Multiview Spectral Clustering via Structured Low-Rank Matrix Factorization

UNAGI: Unified neighbor-aware graph neural network for multi-view clustering

Multi-view graph refining-based clustering (MGRC) methods aim to facilitate the clustering of data via Graph Neural Networks (GNNs) by learning optimal graphs that reflect the underlying topology of the data. However, current MGRC approaches are limited by their disjoint two-stage process, where the graph structure is learned in the first stage before the GNN messages are propagated in the subsequent stage. Additionally, current approaches neglect the importance of cross-view structural consistency and semantic-level information and only consider intra-view embeddings. To address these issues, we propose a Unified Neighbor-Aware Graph neural network for multi-vIew clustering (UNAGI). Specifically, we develop a novel framework that seamlessly merges the optimization of the graph topology and sample representations through a differentiable graph adapter, which enables a unified training paradigm. In addition, we propose a unique regularization to learn robust graphs and align the inter-view graph topology with the guidance of neighbor-aware pseudo-labels. Extensive experimental evaluation across seven datasets demonstrates UNAGI's ability to achieve superior clustering performance.

Parameter-Free Multiview K-Means Clustering With Coordinate Descent Method

Recently, more and more real-world datasets have been composed of heterogeneous but related features from diverse views. Multiview clustering provides a promising attempt at a solution for partitioning such data according to heterogeneous information. However, most existing methods suffer from hyper-parameter tuning trouble and high computational cost. Besides, there is still an opportunity for improvement in clustering performance. To this end, a novel multiview framework, called parameter-free multiview -means clustering with coordinate descent method (PFMVKM), is presented to address the above problems. Specifically, PFMVKM is completely parameter-free and learns the weights via a self-weighted scheme, which can avoid the intractable process of hyper-parameters tuning. Moreover, our model is capable of directly calculating the cluster indicator matrix, with no need to learn the cluster centroid matrix and the indicator matrix simultaneously as previous multiview methods have to do. What's more, we propose an efficient optimization algorithm utilizing the idea of coordinate descent, which can not only reduce the computational complexity but also improve the clustering performance. Extensive experiments on various types of real datasets illustrate that the proposed method outperforms existing state-of-the-art competitors and conforms well with the actual situation.

One-Step Multi-View Clustering With Diverse Representation

Multi-View clustering has attracted broad attention due to its capacity to utilize consistent and complementary information among views. Although tremendous progress has been made recently, most existing methods undergo high complexity, preventing them from being applied to large-scale tasks. Multi-View clustering via matrix factorization is a representative to address this issue. However, most of them map the data matrices into a fixed dimension, limiting the model's expressiveness. Moreover, a range of methods suffers from a two-step process, i.e., multimodal learning and the subsequent k-means, inevitably causing a suboptimal clustering result. In light of this, we propose a one-step multi-view clustering with diverse representation (OMVCDR) method, which incorporates multi-view learning and k-means into a unified framework. Specifically, we first project original data matrices into various latent spaces to attain comprehensive information and auto-weight them in a self-supervised manner. Then, we directly use the information matrices under diverse dimensions to obtain consensus discrete clustering labels. The unified work of representation learning and clustering boosts the quality of the final results. Furthermore, we develop an efficient optimization algorithm with proven convergence to solve the resultant problem. Comprehensive experiments on various datasets demonstrate the promising clustering performance of our proposed method. The code is publicly available at https://github.com/wanxinhang/OMVCDR.

Subgraph Propagation and Contrastive Calibration for Incomplete Multiview Data Clustering

The success of multiview raw data mining relies on the integrity of attributes. However, each view faces various noises and collection failures, which leads to a condition that attributes are only partially available. To make matters worse, the attributes in multiview raw data are composed of multiple forms, which makes it more difficult to explore the structure of the data especially in multiview clustering task. Due to the missing data in some views, the clustering task on incomplete multiview data confronts the following challenges, namely: 1) mining the topology of missing data in multiview is an urgent problem to be solved; 2) most approaches do not calibrate the complemented representations with common information of multiple views; and 3) we discover that the cluster distributions obtained from incomplete views have a cluster distribution unaligned problem (CDUP) in the latent space. To solve the above issues, we propose a deep clustering framework based on subgraph propagation and contrastive calibration (SPCC) for incomplete multiview raw data. First, the global structural graph is reconstructed by propagating the subgraphs generated by the complete data of each view. Then, the missing views are completed and calibrated under the guidance of the global structural graph and contrast learning between views. In the latent space, we assume that different views have a common cluster representation in the same dimension. However, in the unsupervised condition, the fact that the cluster distributions of different views do not correspond affects the information completion process to use information from other views. Finally, the complemented cluster distributions for different views are aligned by contrastive learning (CL), thus solving the CDUP in the latent space. Our method achieves advanced performance on six benchmarks, which validates the effectiveness and superiority of our SPCC.

Partially multi-view clustering via re-alignment

Multi-view clustering learns consistent information from multi-view data, aiming to achieve more significant clustering characteristics. However, data in real-world scenarios often exhibit temporal or spatial asynchrony, leading to views with unaligned instances. Existing methods primarily address this issue by learning transformation matrices to align unaligned instances, but this process of learning differentiable transformation matrices is cumbersome. To address the challenge of partially unaligned instances, we propose Partially Multi-view Clustering via Re-alignment (PMVCR). Our approach integrates representation learning and data alignment through a two-stage training and a re-alignment process. Specifically, our training process consists of three stages: (i) In the coarse-grained alignment stage, we construct negative instance pairs for unaligned instances and utilize contrastive learning to preliminarily learn the view representations of the instances. (ii) In the re-alignment stage, we match unaligned instances based on the similarity of their view representations, aligning them with the primary view. (iii) In the fine-grained alignment stage, we further enhance the discriminative power of the view representations and the model's ability to differentiate between clusters. Compared to existing models, our method effectively leverages information between unaligned samples and enhances model generalization by constructing negative instance pairs. Clustering experiments on several popular multi-view datasets demonstrate the effectiveness and superiority of our method. Our code is publicly available at https://github.com/WenB777/PMVCR.git.

SOUL-Net: A Sparse and Low-Rank Unrolling Network for Spectral CT Image Reconstruction

Spectral computed tomography (CT) is an emerging technology, that generates a multienergy attenuation map for the interior of an object and extends the traditional image volume into a 4-D form. Compared with traditional CT based on energy-integrating detectors, spectral CT can make full use of spectral information, resulting in high resolution and providing accurate material quantification. Numerous model-based iterative reconstruction methods have been proposed for spectral CT reconstruction. However, these methods usually suffer from difficulties such as laborious parameter selection and expensive computational costs. In addition, due to the image similarity of different energy bins, spectral CT usually implies a strong low-rank prior, which has been widely adopted in current iterative reconstruction models. Singular value thresholding (SVT) is an effective algorithm to solve the low-rank constrained model. However, the SVT method requires a manual selection of thresholds, which may lead to suboptimal results. To relieve these problems, in this article, we propose a sparse and low-rank unrolling network (SOUL-Net) for spectral CT image reconstruction, that learns the parameters and thresholds in a data-driven manner. Furthermore, a Taylor expansion-based neural network backpropagation method is introduced to improve the numerical stability. The qualitative and quantitative results demonstrate that the proposed method outperforms several representative state-of-the-art algorithms in terms of detail preservation and artifact reduction.

Multiview Spectral Clustering Based on Consensus Neighbor Strategy

Multiview spectral clustering, renowned for its spatial learning capability, has garnered significant attention in the data mining field. However, existing methods assume that the optimal consensus adjacency matrix is confined within the space spanned by each view's adjacency matrix. This constraint restricts the feasible domain of the algorithm and hinders the exploration of the optimal consensus adjacency matrix. To address this limitation, we propose a novel and convex strategy, termed the consensus neighbor strategy, for learning the optimal consensus adjacency matrix. This approach constructs the optimal consensus adjacency matrix by capturing the consensus local structure of each sample across all views, thereby expanding the search space and facilitating the discovery of the optimal consensus adjacency matrix. Furthermore, we introduce the concept of a correlation measuring matrix to prevent trivial solution. We develop an efficient iterative algorithm to solve the resulting optimization problem, benefitting from the convex nature of our model, which ensures convergence to a global optimum. Experimental results on 16 multiview datasets demonstrate that our proposed algorithm surpasses state-of-the-art methods in terms of its robust consensus representation learning capability. The code of this article is uploaded to https://github.com/PhdJiayiTang/Consensus-Neighbor-Strategy.git.

A Dual-Masked Deep Structural Clustering Network With Adaptive Bidirectional Information Delivery

Structured clustering networks, which alleviate the oversmoothing issue by delivering hidden features from autoencoder (AE) to graph convolutional networks (GCNs), involve two shortcomings for the clustering task. For one thing, they used vanilla structure to learn clustering representations without considering feature and structure corruption; for another thing, they exhibit network degradation and vanishing gradient issues after stacking multilayer GCNs. In this article, we propose a clustering method called dual-masked deep structural clustering network (DMDSC) with adaptive bidirectional information delivery (ABID). Specifically, DMDSC enables generative self-supervised learning to mine deeper interstructure and interfeature correlations by simultaneously reconstructing corrupted structures and features. Furthermore, DMDSC develops an ABID module to establish an information transfer channel between each pairwise layer of AE and GCNs to alleviate the oversmoothing and vanishing gradient problems. Numerous experiments on six benchmark datasets have shown that the proposed DMDSC outperforms the most advanced deep clustering algorithms.

Multimodal Emotion Recognition Based on EEG and EOG Signals Evoked by the Video-Odor Stimuli

Affective data is the basis of emotion recognition, which is mainly acquired through extrinsic elicitation. To investigate the enhancing effects of multi-sensory stimuli on emotion elicitation and emotion recognition, we designed an experimental paradigm involving visual, auditory, and olfactory senses. A multimodal emotional dataset (OVPD-II) that employed the video-only or video-odor patterns as the stimuli materials, and recorded the electroencephalogram (EEG) and electrooculogram (EOG) signals, was created. The feedback results reported by subjects after each trial demonstrated that the video-odor pattern outperformed the video-only pattern in evoking individuals' emotions. To further validate the efficiency of the video-odor pattern, the transformer was employed to perform the emotion recognition task, where the highest accuracy reached 86.65% (66.12%) for EEG (EOG) modality with the video-odor pattern, which improved by 1.42% (3.43%) compared with the video-only pattern. What's more, the hybrid fusion (HF) method combined with the transformer and joint training was developed to improve the performance of the emotion recognition task, which achieved classify accuracies of 89.50% and 88.47% for the video-odor and video-only patterns, respectively.

Efficient and Effective One-Step Multiview Clustering

Multiview clustering algorithms have attracted intensive attention and achieved superior performance in various fields recently. Despite the great success of multiview clustering methods in realistic applications, we observe that most of them are difficult to apply to large-scale datasets due to their cubic complexity. Moreover, they usually use a two-stage scheme to obtain the discrete clustering labels, which inevitably causes a suboptimal solution. In light of this, an efficient and effective one-step multiview clustering (E2OMVC) method is proposed to directly obtain clustering indicators with a small-time burden. Specifically, according to the anchor graphs, the smaller similarity graph of each view is constructed, from which the low-dimensional latent features are generated to form the latent partition representation. By introducing a label discretization mechanism, the binary indicator matrix can be directly obtained from the unified partition representation which is formed by fusing all latent partition representations from different views. In addition, by coupling the fusion of all latent information and the clustering task into a joint framework, the two processes can help each other and obtain a better clustering result. Extensive experimental results demonstrate that the proposed method can achieve comparable or better performance than the state-of-the-art methods. The demo code of this work is publicly available at https://github.com/WangJun2023/EEOMVC.

Deep Multiview Adaptive Clustering With Semantic Invariance

Multiview clustering has attracted significant attention in various fields, due to the superiority in mining patterns of multiview data. However, previous methods are still confronted with two challenges. First, they do not fully consider the semantic invariance of multiview data in aggregating complementary information, degrading semantic robustness of fusion representations. Second, they rely on predefined clustering strategies to mine patterns, lacking adequate explorations of data structures. To address the challenges, deep multiview adaptive clustering via semantic invariance (DMAC-SI) is proposed, which learns an adaptive clustering strategy on semantics-robust fusion representations to fully explore structures in mining patterns. Specifically, a mirror fusion architecture is devised to explore interview invariance and intrainstance invariance hidden in multiview data, which captures invariant semantics of complementary information to learn semantics-robust fusion representations. Then, a Markov decision process of multiview data partitions is proposed within the reinforcement learning framework, which learns an adaptive clustering strategy on semantics-robust fusion representations to guarantee the structure explorations in mining patterns. The two components seamlessly collaborate in an end-to-end manner to accurately partition multiview data. Finally, extensive experiment results on five benchmark datasets demonstrate that DMAC-SI outperforms the state-of-the-art methods.

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.

Multi-View Graph Learning by Joint Modeling of Consistency and Inconsistency

Graph learning has emerged as a promising technique for multi-view clustering due to its ability to learn a unified and robust graph from multiple views. However, existing graph learning methods mostly focus on the multi-view consistency issue, yet often neglect the inconsistency between views, which makes them vulnerable to possibly low-quality or noisy datasets. To overcome this limitation, we propose a new multi-view graph learning framework, which for the first time simultaneously and explicitly models multi-view consistency and inconsistency in a unified objective function, through which the consistent and inconsistent parts of each single-view graph as well as the unified graph that fuses the consistent parts can be iteratively learned. Though optimizing the objective function is NP-hard, we design a highly efficient optimization algorithm that can obtain an approximate solution with linear time complexity in the number of edges in the unified graph. Furthermore, our multi-view graph learning approach can be applied to both similarity graphs and dissimilarity graphs, which lead to two graph fusion-based variants in our framework. Experiments on 12 multi-view datasets have demonstrated the robustness and efficiency of the proposed approach. The code is available at https://github.com/youweiliang/Multi-view_Graph_Learning.

Autoencoder in Autoencoder Networks

Modeling complex correlations on multiview data is still challenging, especially for high-dimensional features with possible noise. To address this issue, we propose a novel unsupervised multiview representation learning (UMRL) algorithm, termed autoencoder in autoencoder networks (AE2-Nets). The proposed framework effectively encodes information from high-dimensional heterogeneous data into a compact and informative representation with the proposed bidirectional encoding strategy. Specifically, the proposed AE2-Nets conduct encoding in two directions: the inner-AE-networks extract view-specific intrinsic information (forward encoding), while the outer-AE-networks integrate this view-specific intrinsic information from different views into a latent representation (backward encoding). For the nested architecture, we further provide a probabilistic explanation and extension from hierarchical variational autoencoder. The forward-backward strategy flexibly addresses high-dimensional (noisy) features within each view and encodes complementarity across multiple views in a unified framework. Extensive results on benchmark datasets validate the advantages compared to the state-of-the-art algorithms.

Latent Low-Rank Representation With Weighted Distance Penalty for Clustering

Latent low-rank representation (LatLRR) is a critical self-representation technique that improves low-rank representation (LRR) by using observed and unobserved samples. It can simultaneously learn the low-dimensional structure embedded in the data space and capture the salient features. However, LatLRR ignores the local geometry structure and can be affected by the noise and redundancy in the original data space. To solve the above problems, we propose a latent LRR with weighted distance penalty (LLRRWD) for clustering in this article. First, a weighted distance is proposed to enhance the original Euclidean distance by enlarging the distance among the unconnected samples, which can enhance the discriminitation of the distance among the samples. By leveraging on the weighted distance, a weighted distance penalty is introduced to the LatLRR model to enable the method to preserve both the local geometric information and global information, improving discrimination of the learned affinity matrix. Moreover, a weight matrix is imposed on the sparse error norm to reduce the effect of noise and redundancy. Experimental results based on several benchmark databases show the effectiveness of our method in clustering.

Balance guided incomplete multi-view spectral clustering

There is a large volume of incomplete multi-view data in the real-world. How to partition these incomplete multi-view data is an urgent realistic problem since almost all of the conventional multi-view clustering methods are inapplicable to cases with missing views. In this paper, a novel graph learning-based incomplete multi-view clustering (IMVC) method is proposed to address this issue. Different from existing works, our method aims at learning a common consensus graph from all incomplete views and obtaining a clustering indicator matrix in a unified framework. To achieve a stable clustering result, a relaxed spectral clustering model is introduced to obtain a probability consensus representation with all positive elements that reflect the data clustering result. Considering the different contributions of views to the clustering task, a weighted multi-view learning mechanism is introduced to automatically balance the effects of different views in model optimization. In this way, the intrinsic information of the incomplete multi-view data can be fully exploited. The experiments on several incomplete multi-view datasets show that our method outperforms the compared state-of-the-art clustering methods, which demonstrates the effectiveness of our method for IMVC.

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.

Bi-Nuclear Tensor Schatten-p Norm Minimization for Multi-View Subspace Clustering

Multi-view subspace clustering aims to integrate the complementary information contained in different views to facilitate data representation. Currently, low-rank representation (LRR) serves as a benchmark method. However, we observe that these LRR-based methods would suffer from two issues: limited clustering performance and high computational cost since (1) they usually adopt the nuclear norm with biased estimation to explore the low-rank structures; (2) the singular value decomposition of large-scale matrices is inevitably involved. Moreover, LRR may not achieve low-rank properties in both intra-views and inter-views simultaneously. To address the above issues, this paper proposes the Bi-nuclear tensor Schatten- p norm minimization for multi-view subspace clustering (BTMSC). Specifically, BTMSC constructs a third-order tensor from the view dimension to explore the high-order correlation and the subspace structures of multi-view features. The Bi-Nuclear Quasi-Norm (BiN) factorization form of the Schatten- p norm is utilized to factorize the third-order tensor as the product of two small-scale third-order tensors, which not only captures the low-rank property of the third-order tensor but also improves the computational efficiency. Finally, an efficient alternating optimization algorithm is designed to solve the BTMSC model. Extensive experiments with ten datasets of texts and images illustrate the performance superiority of the proposed BTMSC method over state-of-the-art methods.

Spectral Clustering With Adaptive Neighbors for Deep Learning

Spectral clustering is a well-known clustering algorithm for unsupervised learning, and its improved algorithms have been successfully adapted for many real-world applications. However, traditional spectral clustering algorithms are still facing many challenges to the task of unsupervised learning for large-scale datasets because of the complexity and cost of affinity matrix construction and the eigen-decomposition of the Laplacian matrix. From this perspective, we are looking forward to finding a more efficient and effective way by adaptive neighbor assignments for affinity matrix construction to address the above limitation of spectral clustering. It tries to learn an affinity matrix from the view of global data distribution. Meanwhile, we propose a deep learning framework with fully connected layers to learn a mapping function for the purpose of replacing the traditional eigen-decomposition of the Laplacian matrix. Extensive experimental results have illustrated the competitiveness of the proposed algorithm. It is significantly superior to the existing clustering algorithms in the experiments of both toy datasets and real-world datasets.

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 ℓ_1,2 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.

Hyper-Laplacian Regularized Multi-View Clustering with Exclusive L21 Regularization and Tensor Log-Determinant Minimization Approach

Multi-view clustering aims to capture the multiple views inherent information by identifying the data clustering that reflects distinct features of datasets. Being a consensus in literature that different views of a dataset share a common latent structure, most existing multi-view subspace learning methods rely on the nuclear norm to seek the low-rank representation of the underlying subspace. However, the nuclear norm often fails to distinguish the variance of features for each cluster due to its convexity nature and data tends to fall in multiple non-linear subspaces for multi-dimensional datasets. To address these problems, we propose a new and novel multi-view clustering method (HL-L21-TLD-MSC) that unifies the Hyper-Laplacian (HL) and exclusive ℓ 2, 1 (L21) regularization with Tensor Log-Determinant Rank Minimization (TLD) setting. Specifically, the hyper-Laplacian regularization maintains the local geometrical structure that makes the estimation prune to nonlinearities, and the mixed ℓ 2, 1 and ℓ 1, 2 regularization provides the joint sparsity within-cluster as well as the exclusive sparsity between-cluster. Furthermore, a log-determinant function is used as a tighter tensor rank approximation to discriminate the dimension of features. An efficient alternating algorithm is then derived to optimize the proposed model, and the construction of a convergent sequence to the Karush-Kuhn-Tucker (KKT) critical point solution is mathematically validated in detail. Extensive experiments are conducted on ten well-known datasets to demonstrate that the proposed approach outperforms the existing state-of-the-art approaches with various scenarios, in which, six of them achieve perfect results under our framework developed in this paper, demonstrating highly effectiveness for the proposed approach.

Adaptive Feature Projection With Distribution Alignment for Deep Incomplete Multi-View Clustering

Incomplete multi-view clustering (IMVC) analysis, where some views of multi-view data usually have missing data, has attracted increasing attention. However, existing IMVC methods still have two issues: 1) they pay much attention to imputing or recovering the missing data, without considering the fact that the imputed values might be inaccurate due to the unknown label information, 2) the common features of multiple views are always learned from the complete data, while ignoring the feature distribution discrepancy between the complete and incomplete data. To address these issues, we propose an imputation-free deep IMVC method and consider distribution alignment in feature learning. Concretely, the proposed method learns the features for each view by autoencoders and utilizes an adaptive feature projection to avoid the imputation for missing data. All available data are projected into a common feature space, where the common cluster information is explored by maximizing mutual information and the distribution alignment is achieved by minimizing mean discrepancy. Additionally, we design a new mean discrepancy loss for incomplete multi-view learning and make it applicable in mini-batch optimization. Extensive experiments demonstrate that our method achieves the comparable or superior performance compared with state-of-the-art methods.

Multiview Clustering via Proximity Learning in Latent Representation Space

Most existing multiview clustering methods are based on the original feature space. However, the feature redundancy and noise in the original feature space limit their clustering performance. Aiming at addressing this problem, some multiview clustering methods learn the latent data representation linearly, while performance may decline if the relation between the latent data representation and the original data is nonlinear. The other methods which nonlinearly learn the latent data representation usually conduct the latent representation learning and clustering separately, resulting in that the latent data representation might be not well adapted to clustering. Furthermore, none of them model the intercluster relation and intracluster correlation of data points, which limits the quality of the learned latent data representation and therefore influences the clustering performance. To solve these problems, this article proposes a novel multiview clustering method via proximity learning in latent representation space, named multiview latent proximity learning (MLPL). For one thing, MLPL learns the latent data representation in a nonlinear manner which takes the intercluster relation and intracluster correlation into consideration simultaneously. For another, through conducting the latent representation learning and consensus proximity learning simultaneously, MLPL learns a consensus proximity matrix with k connected components to output the clustering result directly. Extensive experiments are conducted on seven real-world datasets to demonstrate the effectiveness and superiority of the MLPL method compared with the state-of-the-art multiview clustering methods.

Deep Multiview Collaborative Clustering

The clustering methods have absorbed even-increasing attention in machine learning and computer vision communities in recent years. In this article, we focus on the real-world applications where a sample can be represented by multiple views. Traditional methods learn a common latent space for multiview samples without considering the diversity of multiview representations and use K -means to obtain the final results, which are time and space consuming. On the contrary, we propose a novel end-to-end deep multiview clustering model with collaborative learning to predict the clustering results directly. Specifically, multiple autoencoder networks are utilized to embed multi-view data into various latent spaces and a heterogeneous graph learning module is employed to fuse the latent representations adaptively, which can learn specific weights for different views of each sample. In addition, intraview collaborative learning is framed to optimize each single-view clustering task and provide more discriminative latent representations. Simultaneously, interview collaborative learning is employed to obtain complementary information and promote consistent cluster structure for a better clustering solution. Experimental results on several datasets show that our method significantly outperforms several state-of-the-art clustering approaches.

Unsupervised Feature Selection via Orthogonal Basis Clustering and Local Structure Preserving

Due to the "curse of dimensionality" issue, how to discard redundant features and select informative features in high-dimensional data has become a critical problem, hence there are many research studies dedicated to solving this problem. Unsupervised feature selection technique, which does not require any prior category information to conduct with, has gained a prominent place in preprocessing high-dimensional data among all feature selection techniques, and it has been applied to many neural networks and learning systems related applications, e.g., pattern classification. In this article, we propose an efficient method for unsupervised feature selection via orthogonal basis clustering and reliable local structure preserving, which is referred to as OCLSP briefly. Our OCLSP method consists of an orthogonal basis clustering together with an adaptive graph regularization, which realizes the functionality of simultaneously achieving excellent cluster separation and preserving the local information of data. Besides, we exploit an efficient alternative optimization algorithm to solve the challenging optimization problem of our proposed OCLSP method, and we perform a theoretical analysis of its computational complexity and convergence. Eventually, we conduct comprehensive experiments on nine real-world datasets to test the validity of our proposed OCLSP method, and the experimental results demonstrate that our proposed OCLSP method outperforms many state-of-the-art unsupervised feature selection methods in terms of clustering accuracy and normalized mutual information, which indicates that our proposed OCLSP method has a strong ability in identifying more important features.

Multiview Subspace Clustering Using Low-Rank Representation

Multiview subspace clustering is one of the most widely used methods for exploiting the internal structures of multiview data. Most previous studies have performed the task of learning multiview representations by individually constructing an affinity matrix for each view without simultaneously exploiting the intrinsic characteristics of multiview data. In this article, we propose a multiview low-rank representation (MLRR) method to comprehensively discover the correlation of multiview data for multiview subspace clustering. MLRR considers symmetric low-rank representations (LRRs) to be an approximately linear spatial transformation under the new base, that is, the multiview data themselves, to fully exploit the angular information of the principal directions of LRRs, which is adopted to construct an affinity matrix for multiview subspace clustering, under a symmetric condition. MLRR takes full advantage of LRR techniques and a diversity regularization term to exploit the diversity and consistency of multiple views, respectively, and this method simultaneously imposes a symmetry constraint on LRRs. Hence, the angular information of the principal directions of rows is consistent with that of columns in symmetric LRRs. The MLRR model can be efficiently calculated by solving a convex optimization problem. Moreover, we present an intuitive fusion strategy for symmetric LRRs from the perspective of spectral clustering to obtain a compact representation, which can be shared by multiple views and comprehensively represents the intrinsic features of multiview data. Finally, the experimental results based on benchmark datasets demonstrate the effectiveness and robustness of MLRR compared with several state-of-the-art multiview subspace clustering algorithms.

Dynamic Graph Reasoning for Conversational Open-Domain Question Answering

In recent years, conversational agents have provided a natural and convenient access to useful information in people’s daily life, along with a broad and new research topic, conversational question answering (QA). On the shoulders of conversational QA, we study the conversational open-domain QA problem, where users’ information needs are presented in a conversation and exact answers are required to extract from the Web. Despite its significance and value, building an effective conversational open-domain QA system is non-trivial due to the following challenges: (1) precisely understand conversational questions based on the conversation context; (2) extract exact answers by capturing the answer dependency and transition flow in a conversation; and (3) deeply integrate question understanding and answer extraction. To address the aforementioned issues, we propose an end-to-end Dynamic Graph Reasoning approach to Conversational open-domain QA (DGRCoQA for short). DGRCoQA comprises three components, i.e., a dynamic question interpreter (DQI), a graph reasoning enhanced retriever (GRR), and a typical Reader, where the first one is developed to understand and formulate conversational questions while the other two are responsible to extract an exact answer from the Web. In particular, DQI understands conversational questions by utilizing the QA context, sourcing from predicted answers returned by the Reader, to dynamically attend to the most relevant information in the conversation context. Afterwards, GRR attempts to capture the answer flow and select the most possible passage that contains the answer by reasoning answer paths over a dynamically constructed context graph . Finally, the Reader, a reading comprehension model, predicts a text span from the selected passage as the answer. DGRCoQA demonstrates its strength in the extensive experiments conducted on a benchmark dataset. It significantly outperforms the existing methods and achieves the state-of-the-art performance.

Multiview Subspace Clustering via Co-Training Robust Data Representation

Taking the assumption that data samples are able to be reconstructed with the dictionary formed by themselves, recent multiview subspace clustering (MSC) algorithms aim to find a consensus reconstruction matrix via exploring complementary information across multiple views. Most of them directly operate on the original data observations without preprocessing, while others operate on the corresponding kernel matrices. However, they both ignore that the collected features may be designed arbitrarily and hard guaranteed to be independent and nonoverlapping. As a result, original data observations and kernel matrices would contain a large number of redundant details. To address this issue, we propose an MSC algorithm that groups samples and removes data redundancy concurrently. In specific, eigendecomposition is employed to obtain the robust data representation of low redundancy for later clustering. By utilizing the two processes into a unified model, clustering results will guide eigendecomposition to generate more discriminative data representation, which, as feedback, helps obtain better clustering results. In addition, an alternate and convergent algorithm is designed to solve the optimization problem. Extensive experiments are conducted on eight benchmarks, and the proposed algorithm outperforms comparative ones in recent literature by a large margin, verifying its superiority. At the same time, its effectiveness, computational efficiency, and robustness to noise are validated experimentally.

Robust Rank-Constrained Sparse Learning: A Graph-Based Framework for Single View and Multiview Clustering

Graph-based clustering aims to partition the data according to a similarity graph, which has shown impressive performance on various kinds of tasks. The quality of similarity graph largely determines the clustering results, but it is difficult to produce a high-quality one, especially when data contain noises and outliers. To solve this problem, we propose a robust rank constrained sparse learning (RRCSL) method in this article. The L_2,1 -norm is adopted into the objective function of sparse representation to learn the optimal graph with robustness. To preserve the data structure, we construct an initial graph and search the graph within its neighborhood. By incorporating a rank constraint, the learned graph can be directly used as the cluster indicator, and the final results are obtained without additional postprocessing. In addition, the proposed method cannot only be applied to single-view clustering but also extended to multiview clustering. Plenty of experiments on synthetic and real-world datasets have demonstrated the superiority and robustness of the proposed framework.

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.

Large-Scale Subspace Clustering by Independent Distributed and Parallel Coding

Subspace clustering is a popular method to discover underlying low-dimensional structures of high-dimensional multimedia data (e.g., images, videos, and texts). In this article, we consider a large-scale subspace clustering (LS²C) problem, that is, partitioning million data points with a millon dimensions. To address this, we explore an independent distributed and parallel framework by dividing big data/variable matrices and regularization by both columns and rows. Specifically, LS²C is independently decomposed into many subproblems by distributing those matrices into different machines by columns since the regularization of the code matrix is equal to a sum of that of its submatrices (e.g., square-of-Frobenius/ l₁ -norm). Consensus optimization is designed to solve these subproblems in a parallel way for saving communication costs. Moreover, we provide theoretical guarantees that LS²C can recover consensus subspace representations of high-dimensional data points under broad conditions. Compared with the state-of-the-art LS²C methods, our approach achieves better clustering results in public datasets, including a million images and videos.

Weighted Error Entropy-Based Information Theoretic Learning for Robust Subspace Representation

In most of the existing representation learning frameworks, the noise contaminating the data points is often assumed to be independent and identically distributed (i.i.d.), where the Gaussian distribution is often imposed. This assumption, though greatly simplifies the resulting representation problems, may not hold in many practical scenarios. For example, the noise in face representation is usually attributable to local variation, random occlusion, and unconstrained illumination, which is essentially structural, and hence, does not satisfy the i.i.d. property or the Gaussianity. In this article, we devise a generic noise model, referred to as independent and piecewise identically distributed (i.p.i.d.) model for robust presentation learning, where the statistical behavior of the underlying noise is characterized using a union of distributions. We demonstrate that our proposed i.p.i.d. model can better describe the complex noise encountered in practical scenarios and accommodate the traditional i.i.d. one as a special case. Assisted by the proposed noise model, we then develop a new information-theoretic learning framework for robust subspace representation through a novel minimum weighted error entropy criterion. Thanks to the superior modeling capability of the i.p.i.d. model, our proposed learning method achieves superior robustness against various types of noise. When applying our scheme to the subspace clustering and image recognition problems, we observe significant performance gains over the existing approaches.

Multiview Subspace Clustering With Grouping Effect

Multiview subspace clustering (MVSC) is a recently emerging technique that aims to discover the underlying subspace in multiview data and thereby cluster the data based on the learned subspace. Though quite a few MVSC methods have been proposed in recent years, most of them cannot explicitly preserve the locality in the learned subspaces and also neglect the subspacewise grouping effect, which restricts their ability of multiview subspace learning. To address this, in this article, we propose a novel MVSC with grouping effect (MvSCGE) approach. Particularly, our approach simultaneously learns the multiple subspace representations for multiple views with smooth regularization, and then exploits the subspacewise grouping effect in these learned subspaces by means of a unified optimization framework. Meanwhile, the proposed approach is able to ensure the cross-view consistency and learn a consistent cluster indicator matrix for the final clustering results. Extensive experiments on several benchmark datasets have been conducted to validate the superiority of the proposed approach.

Rank Consistency Induced Multiview Subspace Clustering via Low-Rank Matrix Factorization

Multiview subspace clustering has been demonstrated to achieve excellent performance in practice by exploiting multiview complementary information. One of the strategies used in most existing methods is to learn a shared self-expressiveness coefficient matrix for all the view data. Different from such a strategy, this article proposes a rank consistency induced multiview subspace clustering model to pursue a consistent low-rank structure among view-specific self-expressiveness coefficient matrices. To facilitate a practical model, we parameterize the low-rank structure on all self-expressiveness coefficient matrices through the tri-factorization along with orthogonal constraints. This specification ensures that self-expressiveness coefficient matrices of different views have the same rank to effectively promote structural consistency across multiviews. Such a model can learn a consistent subspace structure and fully exploit the complementary information from the view-specific self-expressiveness coefficient matrices, simultaneously. The proposed model is formulated as a nonconvex optimization problem. An efficient optimization algorithm with guaranteed convergence under mild conditions is proposed. Extensive experiments on several benchmark databases demonstrate the advantage of the proposed model over the state-of-the-art multiview clustering approaches.

Surface Defect Segmentation Algorithm of Steel Plate Based on Geometric Median Filter Pruning

Problems such as redundancy of detection model parameters make it difficult to apply to factory embedded device applications. This paper focuses on the analysis of different existing deep learning model compression algorithms and proposes a model pruning algorithm based on geometric median filtering for structured pruning and compression of defect segmentation detection networks on the basis of structured pruning. Through experimental comparisons and optimizations, the proposed optimization algorithm can greatly reduce the network parameters and computational effort to achieve effective pruning of the defect detection algorithm for steel plate surfaces.

Multiview Spectral Clustering via Robust Subspace Segmentation

Multiview clustering refers to partition data according to its multiple views, where information from different perspectives can be jointly used in some certain complementary manner to produce more sensible clusters. It is believed that most of the existing multiview clustering methods technically suffer from possibly corrupted data, resulting in a dramatically decreased clustering performance. To overcome this challenge, we propose a multiview spectral clustering method based on robust subspace segmentation in this article. Our proposed algorithm is composed of three modules, that is: 1) the construction of multiple feature matrices from all views; 2) the formulation of a shared low-rank latent matrix by a low rank and sparse decomposition; and 3) the use of the Markov-chain-based spectral clustering method for producing the final clusters. To solve the optimization problem for a low rank and sparse decomposition, we develop an optimization procedure based on the scheme of the augmented Lagrangian method of multipliers. The experimental results on several benchmark datasets indicate that the proposed method outperforms favorably compared to several state-of-the-art multiview clustering techniques.

Efficient Unsupervised Dimension Reduction for Streaming Multiview Data

Multiview learning has received substantial attention over the past decade due to its powerful capacity in integrating various types of information. Conventional unsupervised multiview dimension reduction (UMDR) methods are usually conducted in an offline manner and may fail in many real-world applications, where data arrive sequentially and the data distribution changes periodically. Moreover, satisfying the requirements of high memory consumption and expensive retraining of the time cost in large-scale scenarios are difficult. To remedy these drawbacks, we propose an online UMDR (OUMDR) framework. OUMDR aims to seek a low-dimensional and informative consensus representation for streaming multiview data. View-specific weights are also learned in this article to reflect the contributions of different views to the final consensus presentation. A specific model called OUMDR-E is developed by introducing the exclusive group LASSO (EG-LASSO) to explore the intraview and interview correlations. Then, we develop an efficient iterative algorithm with limited memory and time cost requirements for optimization, where the convergence of each update is theoretically guaranteed. We evaluate the proposed approach in video-based expression recognition applications. The experimental results demonstrate the superiority of our approach in terms of both effectiveness and efficiency.