Fuzzy clustering-based microaggregation for multi-view data with constraints

Multi-view subspace clustering has been an important and powerful tool for partitioning multi-view data, especially multi-view high-dimensional data. Despite great success, most of the existing multi-view subspace clustering methods still suffer from three limitations. First, they often recover the subspace structure in the original space, which can not guarantee the robustness when handling multi-view data with nonlinear structure. Second, these methods mostly regard subspace clustering and affinity matrix learning as two independent steps, which may not well discover the latent relationships among data samples. Third, many of them ignore the different importance of multiple views, whose performance may be badly affected by the low-quality views in multi-view data. To overcome these three limitations, this paper develops a novel subspace clustering method for multi-view data, termed Kernelized Multi-view Subspace Clustering via Auto-weighted Graph Learning (KMSC-AGL). Specifically, the proposed method implicitly maps the multi-view data from linear space into nonlinear space via kernel-induced functions, so as to exploit the nonlinear structure hidden in data. Furthermore, our method aims to enhance the clustering performance by learning a set of view-specific representations and their affinity matrix in a general framework. By integrating the view weighting strategy into this framework, our method can automatically assign the weights to different views, while learning an optimal affinity matrix that is well-adapted to the subsequent spectral clustering. Extensive experiments are conducted on a variety of multi-view data sets, which have demonstrated the superiority of the proposed method.

Multiview clustering (MVC), which aims to explore the underlying cluster structure shared by multiview data, has drawn more research efforts in recent years. To exploit the complementary information among multiple views, existing methods mainly learn a common latent subspace or develop a certain loss across different views, while ignoring the higher level information such as basic partitions (BPs) generated by the single-view clustering algorithm. In light of this, we propose a novel marginalized multiview ensemble clustering (M2VEC) method in this paper. Specifically, we solve MVC in an EC way, which generates BPs for each view individually and seeks for a consensus one. By this means, we naturally leverage the complementary information of multiview data upon the same partition space. In order to boost the robustness of our approach, the marginalized denoising process is adopted to mimic the data corruptions and noises, which provides robust partition-level representations for each view by training a single-layer autoencoder. A low-rank and sparse decomposition is seamlessly incorporated into the denoising process to explicitly capture the consistency information and meanwhile compensate the distinctness between heterogeneous features. Spectral consensus graph partitioning is also involved by our model to make M2VEC as a unified optimization framework. Moreover, a multilayer M2VEC is eventually delivered in a stacked fashion to encapsulate nonlinearity into partition-level representations for handling complex data. Experimental results on eight real-world data sets show the efficacy of our approach compared with several state-of-the-art multiview and EC methods. We also showcase our method performs well with partial multiview data.

This article studies a new problem of data stream clustering, namely, multiview data stream (MVStream) clustering. Although many data stream clustering algorithms have been developed, they are restricted to the single-view streaming data, and clustering MVStreams still remains largely unsolved. In addition to the many issues encountered by the conventional single-view data stream clustering, such as capturing cluster evolution and discovering clusters of arbitrary shapes under the limited computational resources, the main challenge of MVStream clustering lies in integrating information from multiple views in a streaming manner and abstracting summary statistics from the integrated features simultaneously. In this article, we propose a novel MVStream clustering algorithm for the first time. The main idea is to design a multiview support vector domain description (MVSVDD) model, by which the information from multiple insufficient views can be integrated, and the outputting support vectors (SVs) are utilized to abstract the summary statistics of the historical multiview data objects. Based on the MVSVDD model, a new multiview cluster labeling method is designed, whereby clusters of arbitrary shapes can be discovered for each view. By tracking the cluster labels of SVs in each view, the cluster evolution associated with concept drift can be captured. Since the SVs occupy only a small portion of data objects, the proposed MVStream algorithm is quite efficient with the limited computational resources. Extensive experiments are conducted to demonstrate the effectiveness and efficiency of the proposed method.

With the popularity of multimedia technology, information is always represented or transmitted from multiple views. Most of the existing algorithms are graph-based ones to learn the complex structures within multiview data but overlooked the information within data representations. Furthermore, many existing works treat multiple views discriminatively by introducing some hyperparameters, which is undesirable in practice. To this end, abundant multiview based methods have been proposed for dimension reduction. However, there are still no research to leverage the existing work into a unified framework. To address this issue, in this paper, we propose a general framework for multiview data dimension reduction, named Kernelized Multiview Subspace Analysis (KMSA). It directly handles the multi-view feature representation in the kernel space, which provides a feasible channel for direct manipulations on multiview data with different dimensions. Meanwhile, compared with those graph-based methods, KMSA can fully exploit information from multiview data with nothing to lose. Furthermore, since different views have different influences on KMSA, we propose a self-weighted strategy to treat different views discriminatively according to their contributions. A co-regularized term is proposed to promote the mutual learning from multi-views. KMSA combines self-weighted learning with the co-regularized term to learn appropriate weights for all views. We also discuss the influence of the parameters in KMSA regarding the weights of multi-views. We evaluate our proposed framework on 6 multiview datasets for classification and image retrieval. The experimental results validate the advantages of our proposed method.

Graph-oriented multi-view clustering methods have achieved impressive performances by employing relationships and complex structures hidden in multi-view data. However, most of them still suffer from the following two common problems. (1) They target at studying a common representation or pairwise correlations between views, neglecting the comprehensiveness and deeper higher-order correlations among multiple views. (2) The prior knowledge of view-specific representation can not be taken into account to obtain the consensus indicator graph in a unified graph construction and clustering framework. To deal with these problems, we propose a novel Low-rank Tensor Based Proximity Learning (LTBPL) approach for multi-view clustering, where multiple low-rank probability affinity matrices and consensus indicator graph reflecting the final performances are jointly studied in a unified framework. Specifically, multiple affinity representations are stacked in a low-rank constrained tensor to recover their comprehensiveness and higher-order correlations. Meanwhile, view-specific representation carrying different adaptive confidences is jointly linked with the consensus indicator graph. Extensive experiments on nine real-world datasets indicate the superiority of LTBPL compared with the state-of-the-art methods.

Recently, numerous multi-view clustering (MVC) and multi-view graph clustering (MVGC) methods have been proposed. Despite significant progress, they still face two issues: I) MVC and MVGC are often developed independently for multi-view and multi-graph data. They have redundancy but lack a unified methodology to combine their strengths. II) Contrastive learning is usually adopted to explore the associations across multiple views. However, traditional contrastive losses ignore the neighbor relationship in multi-view scenarios and easily lead to false associations in sample pairs. To address these issues, we propose Graph Embedded Contrastive Learning for Multi-View Clustering. Concretely, we propose a process of view-specific pre-training with adaptive graph convolution to make our method compatible with both multi-view and multi-graph data, which aggregates the graph information into data and leverages autoencoders to learn view-specific representations. Furthermore, to explore the view-cross associations, we introduce the process of view-cross contrastive learning and clustering, where we propose the graph-guided contrastive learning that can generate global graph to mitigate the false association issue as well as the cluster-guided contrastive clustering for improving the model robustness. Finally, extensive experiments demonstrate that our method achieves superior performance on both MVC and MVGC tasks.

Multi-view clustering has become a widely studied problem in the area of unsupervised learning. It aims to integrate multiple views by taking advantages of the consensus and complimentary information from multiple views. Most of the existing works in multi-view clustering utilize the vector-based representation for features in each view. However, in many real-world applications, instances are represented by graphs, where those vector-based models cannot fully capture the structure of the graphs from each view. To solve this problem, in this paper we propose a Multi-view Clustering framework on graph instances with Graph Embedding (MCGE). Specifically, we model the multi-view graph data as tensors and apply tensor factorization to learn the multi-view graph embeddings, thereby capturing the local structure of graphs. We build an iterative framework by incorporating multi-view graph embedding into the multi-view clustering task on graph instances, jointly performing multi-view clustering and multi-view graph embedding simultaneously. The multi-view clustering results are used for refining the multi-view graph embedding, and the updated multi-view graph embedding results further improve the multi-view clustering. Extensive experiments on two real brain network datasets (i.e., HIV and Bipolar) demonstrate the superior performance of the proposed MCGE approach in multi-view connectome analysis for clinical investigation and application.

In the era of big data, data may come from multiple sources, known as multi-view data. Multi-view clustering aims at generating better clusters by exploiting complementary and consistent information from multiple views rather than relying on the individual view. Due to inevitable system errors caused by data-captured sensors or others, the data in each view may be erroneous. Various types of errors behave differently and inconsistently in each view. More precisely, error could exhibit as noise and corruptions in reality. Unfortunately, none of the existing multi-view clustering approaches handle all of these error types. Consequently, their clustering performance is dramatically degraded. In this paper, we propose a novel Markov chain method for Error-Robust Multi-View Clustering (EMVC). By decomposing each view into a shared transition probability matrix and error matrix and imposing structured sparsity-inducing norms on error matrices, we characterize and handle typical types of errors explicitly. To solve the challenging optimization problem, we propose a new efficient algorithm based on Augmented Lagrangian Multipliers and prove its convergence rigorously. Experimental results on various synthetic and real-world datasets show the superiority of the proposed EMVC method over the baseline methods and its robustness against different types of errors.

Nowadays, multi-view dataset have become ubiquitous along with more and more data are gathered from different measuring technologies or various sources, in which various aspects of dataset are formalized as multiple views. Although a variety of multi-view clustering analysis approaches have been put forward to uncover the cluster structure hidden in the data, most of these existing methods are based on such a hypothesis: the relationship between objects and clusters are definite. However, most of the data in our real life may have no clear cluster boundaries but have indistinct or overlapping boundaries. How to effectively reveal the uncertain cluster structure under multiview data is still a big challenge for multi-view clustering analysis. Inspired by the powerful uncertain information modeling and analysis capabilities of rough and fuzzy sets, this paper proposes a new multi-view clustering method to discover the uncertain cluster information. A rough set concept based cluster centroid updating strategy is designed to efficiently describe the uncertain construction of clusters. A view weight is introduced to capture the different importance of various views. A fuzzy-based iterative optimization objective function is developed to fuse different view information. Finally, an efficient iterative optimization algorithm is devised to solve the proposed rough fuzzy objective function. Experiments on widely used benchmark datasets prove that our proposed method is always superior to several latest clustering approaches.

With the development of multimedia time, one sample can always be described from multiple views which contain compatible and complementary information. Most algorithms cannot take information from multiple views into considerations and fail to achieve desirable performance in most situations. For many applications, such as image retrieval, face recognition, etc., an appropriate distance metric can better reflect the similarities between various samples. Therefore, how to construct a good distance metric learning methods which can deal with multiview data has been an important topic during the last decade. In this paper, we proposed a novel algorithm named Self-weighted Multiview Metric Learning (SM <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> L) which can finish this task by maximizing the cross correlations between different views. Furthermore, because multiple views have different contributions to the learning procedure of SM <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> L, we adopt a self-weighted learning framework to assign multiple views with different weights. Various experiments on benchmark datasets can verify the performance of our proposed method.

A novel multi-view dimensionality reduction and recognition framework with applications to face recognition

Adaptive multi-view subspace learning based on distributed optimization

Nowadays, non-negative matrix factorization (NMF) based cluster analysis for multi-view data shows impressive behavior in machine learning. Usually, multi-view data have complementary information from various views. The main concern behind the NMF is how to factorize the data to achieve a significant clustering solution from these complementary views. However, NMF does not focus to conserve the geometrical structures of the data space. In this article, we intensify on the above issue and evolve a new NMF clustering method with manifold regularization for multi-view data. The manifold regularization factor is exploited to retain the locally geometrical structure of the data space and gives extensively common clustering solution from multiple views. The weight control term is adopted to handle the distribution of each view weight. An iterative optimization strategy depended on multiplicative update rule is applied on the objective function to achieve optimization. Experimental analysis on the real-world datasets are exhibited that the proposed approach achieves better clustering performance than some state-of-the-art algorithms.

Boosting one-class transfer learning for multiple view uncertain data

The existing multiview clustering models learn a consistent low-dimensional embedding either from multiple feature matrices or multiple similarity matrices, which ignores the interaction between the two procedures and limits the improvement of clustering performance on multiview data. To address this issue, a bidirectional probabilistic subspaces approximation (BPSA) model is developed in this article to learn a consistently orthogonal embedding from multiple feature matrices and multiple similarity matrices simultaneously via the disturbed probabilistic subspace modeling and approximation. A skillful bidirectional fusion strategy is designed to guarantee the parameter-free property of the BPSA model. Two adaptively weighted learning mechanisms are introduced to ensure the inconsistencies among multiple views and the inconsistencies between bidirectional learning processes. To solve the optimization problem involved in the BPSA model, an iterative solver is derived, and a rigorous convergence guarantee is provided. Extensive experimental results on both toy and real-world datasets demonstrate that our BPSA model achieves state-of-the-art performance even if it is parameter-free.