Multi-view Clustering Algorithm Research Articles

Fast correntropy-based multi-view clustering with prototype graph factorization

As a consequence of the ability to incorporate information from different perspectives, multi-view clustering has gained significant attention. Nevertheless, 1) its high computational cost, particularly when processing large-scale and high-dimensional multi-view data, restricts its applications in practice; and 2) complex noise in real-world data also challenges the robustness of existing algorithms. To tackle the above challenges, we develop a fast correntropy-based multi-view clustering algorithm with prototype graph factorization (FCMCPF). FCMCPF first adopts prototype graphs to effectively mitigate the complexity associated with graph construction, thereby reducing it from a quadratic complexity to a linear one. Then, it decomposes these prototype graphs under the correntropy criterion to robustly find the cluster indicator matrix without any post-processing. To solve the non-convex and non-linear model, we devise a fast half-quadratic-based strategy to first convert it into a convex formulation and then swiftly complete the optimization via the matrix properties of orthogonality and trace. The extensive experiments conducted on noisy and real-world datasets illustrate that FCMCPF is highly efficient and robust compared to other advanced algorithms, with comparable or even superior clustering effectiveness.

Research on multi-view clustering algorithm based on sequential three-way decision

Multi-view clustering has achieved many applications in recent years. But the existing multi-view clustering methods face two problems, firstly, the traditional multi-view clustering uses a hard clustering method, which cannot describe the uncertainty between the samples and the clusters, and secondly how to perform effective incremental learning on multi-view data when the number of views increases. Therefore to address the above two problems, we firstly propose a three-way fuzzy spectral clustering algorithm based on fuzzy clustering, which can perform three-way clustering on multi-views and get soft clustering results, thus describing the uncertainty between samples and clusters. Then based on the sequential decision making approach, an incremental learning mechanism is designed for multi-view clustering when the number of views increases. Finally, these two works are combined to propose a multi-view clustering algorithm based on sequential three-way decision making. The experimental results demonstrate that the method proposed in this paper has better clustering accuracy and efficiency compared to the traditional multi-view clustering algorithm.

Multi-view subspace clustering based on adaptive search

Multi-view clustering has been widely applied to image classification, information retrieval, medical pathology analysis, and other fields. So far, many multi-view subspace clustering algorithms based on self-representation learning have been developed. However, most of them use the original data as a dictionary to construct affinity graphs, and their clustering performance depends largely on the quality of the original data features. If the raw data is corrupted by noise, directly using these noisy data as a self-representing dictionary may pose a series of research challenges. Secondly, in the process of self-representation learning, the internal relationship between data points is actually continuously updated and changed, and fixed data points not only affect the selection of view feature diversity, but also may lead to clustering results that are unusually sensitive to the input data. Finally, the coefficient matrix obtained by self-representation learning may contain noise or data structures that are not relevant to multi-view clustering. To remedy these shortcomings, this work proposes a new multi-view clustering algorithm, namely, multi-view subspace clustering based on adaptive search. Specifically, first, we find its similar data matrix for each view’s original data and perform dictionary learning by using the similar data matrix as a dictionary. This not only facilitates identifying the continuously varied internal relationships between data points, but also alleviates the errors that occur when the raw data is directly selected as a dictionary. Second, we introduce robust principal component analysis (RPCA) and rank constraints into the construction of affinity matrices to obtain cleaner and more robust affinity matrices that explore the same clustering properties among different views. In addition, we develop an augmented Lagrange multiplier (ALM) based method to solve the objective function of the model. Finally, we conducted substantial experiments on six real multi-view datasets to demonstrate that the MSC-AS algorithm is more robust and effective than some other advanced clustering algorithms.

A Similarity Matrix Low-Rank Approximation and Inconsistency Separation Fusion Approach for Multiview Clustering

In recent years, multi-view clustering algorithms have achieved promising performance by exploiting the com-plementarity and consistency of different views. However, many multi-view spectral clustering methods only focus on the con-sistent information of views, and the time cost of feature decomposition is expensive. Moreover, these methods also require post-processing (e.g., k-means) to obtain the final clustering results. To overcome these limitations simultaneously, we propose a novel multi-view clustering algorithm. Firstly, the method removes the inconsistent information of the views through cross-view measurement to maintain consistent information. These inconsistencies may be caused by noise, corruptions, or view-specific properties and will affect the quality of the similarity matrix. Then, we learn a consensus embedding matrix with non-negative constraints by performing a low-rank decomposition of the consistency information. In this way, we can replace the eigendecomposition of the n × n Laplacian matrix in spectral clustering with the singular value decomposition of a n × c low-rank matrix to reduce the computational burden, where c ≪ n. Furthermore, due to the non-negative constraint, we can directly obtain the clustering results. Also, to consider the diversity of views, adaptive weighting is applied to different view data. Compared to state-of-the-art multi-view clustering methods on five benchmark multi-view datasets, we demonstrate the superiority and effectiveness of our approach. We release the source code at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/hulu88/FAMvC</uri> .

Multi-view [formula omitted]-means clustering algorithm based on redundant and sparse feature learning

In recent years, multi-view clustering has been widely concerned and studied. Being its data generally has high dimension and noise, how to effectively deal with redundant features in data from various views and improve the clustering effect is an important issue in multi-view clustering. In this paper, a robust multi-view clustering algorithm Multi-view K-means clustering algorithm based on redundant and sparse feature learning (RSFMVKM) considering redundancy and sparse feature learning is proposed, which can effectively reduce the dimensions of data from different views. Firstly, the K-means algorithm is extended to multi-view clustering, and the importance of each views is represented by learning the weight of each view. Secondly, the sparse feature representation is obtained by applying the norm constraint to the projection matrix in a single view, and the cosine similarity is used to depict the redundancy matrix, which can remove the redundant information and improve the clustering effect. Moreover, the proposed algorithm can effectively avoid the generation of empty classes, and the clustering index matrix is discrete, so the clustering results can be obtained directly. Finally, the proposed algorithm is compared with six state-of-the-art multi-view clustering algorithms on six public datasets, and the experimental results show that the algorithm is effective.

Latent information-guided one-step multi-view fuzzy clustering based on cross-view anchor graph

Although graph-inspired clustering methods have achieved impressive success in the area of multi-view data analysis, current methods still face several challenges. First, classical graph construction approaches are computationally expensive in terms of both time and space for large-scale data. Second, fusing graphs from different views remains a challenge. Third, most existing methods require additional post-processing steps to generate the label assignment matrix. To address the above challenges, this paper proposes a novel multi-view clustering algorithm, called latent information-guided one-step multi-view fuzzy clustering based on cross-view anchor graph. Specifically, we introduce an efficient cross-view anchor graph learning approach to construct the similarity matrix of multi-view data and extract latent information from the graph, which reduces the computational complexity of graph learning and inspires the optimization of the consensus membership matrix. Following that, our one-step multi-view fuzzy clustering algorithm can directly generate the final clustering result in an effective and straightforward manner. Furthermore, during the optimization process, the proposed method balances consensus matrix learning and view-specified membership exploration via a self-tuned weighting mechanism. The comprehensive experimental analysis demonstrates the superiority of our approach over the state-of-the-art approaches.

A multi-view clustering algorithm based on deep semi-NMF

Multi-view clustering (MVC) aims to fuse the information among multiple views to achieve effective clustering. Many MVC algorithms based on semi-nonnegative matrix factorization (SNMF) typically have two issues: (1) their optimization schemes are not flexible enough; and (2) the variables are updated only rely on the data but not guided by learning rate. These problems can result in very poor clusters generated. In this paper, we present a multi-view clustering algorithm based on deep SNMF (MCDS) to resolve these issues. Specifically, we first design two types of activation functions to restrict the value domain of the element in the low-dimensional matrix to eliminate the constraint. Then, the SGD algorithm is used to implement element update guided by the learning rate. After obtaining the corresponding weight matrix and bias matrix, we combine them with the activation functions to construct a deep SNMF (DSNMF) network. This network is to update the element in the corresponding low-dimensional matrix for each view and obtain the consensus matrix. To validate the proposed algorithm, numerous experiments are performed on six multi-view datasets including both normal and large-scale datasets. The results demonstrate that MCDS can achieve excellent clustering results and outperform other competitive methods.

Dual-graph regularized concept factorization for multi-view clustering

Matrix factorization is an important technology that obtains the latent representation of data by mining the potential structure of data. As two popular matrix factorization techniques, concept factorization (CF) and non-negative matrix factorization (NMF) have achieved excellent results in multi-view clustering tasks. Compared with multi-view NMF, multi-view CF not only removes the non-negative constraint but also utilizes the idea of the kernel to learn the latent representation of data. However, both of them ignore the local geometric structure in the nonlinear low-dimensional manifold. Furthermore, most of the existing CF-based methods are designed for single-view tasks, which cannot be directly applied to multi-view clustering tasks. To tackle the above shortcomings, we present a new multi-view clustering algorithm, called dual-graph regularized concept factorization for multi-view clustering (MVDGCF). Specifically, we first extend conventional single-view CF to a multi-view version, which can explore the complementary information of multi-view data more effectively. Then we develop a novel dual-graph regularization strategy, which can simultaneously capture the local structure information of the data space and feature space, respectively. Moreover, an adaptive weight vector is introduced to balance the importance of different views. Finally, extensive experiments are carried out on seven datasets. The results show that our method is superior to several popular multi-view clustering methods.

Incomplete multi-view clustering based on low-rank representation with adaptive graph regularization

Incomplete multi-view clustering has attracted attention due to its ability to deal with clustering problems with incomplete information. However, most existing methods either ignore the local structure of the data or fail to consider the importance of different views. In addition, some methods based on mean filling may easily introduce useless information when the data has a large missing rate. To address these issues, this paper proposes an incomplete multi-view clustering algorithm based on graph regularized low-rank representations without using filling method. Specifically, we combine a distance regularization term and low-rank representation-based non-negativity constraints to directly learn graphs with global and local data structures from raw data. Furthermore, we introduce a novel weighted fusion mechanism in the model to learn a consistent representation of all views, which effectively avoids bad views from affecting the quality of the final fused consensus graph. Experimental results on six incomplete multi-view datasets demonstrate that our proposed method achieves the best performance compared with the existing state-of-the-art methods.

Clustering Analysis of Online Teaching Cases and Evaluation of Teaching Results

To facilitate front-line teachers to provide more efficient cases for classroom teaching activities in limited teaching time, it is necessary to conduct clustering analysis of online teaching cases. The existing clustering study on text-based teaching resources focuses on the representation and fusion of different views of texts and the discovery of consistent clustering allocation, and ignores the high-dimensional sparsity of text data. To this end, this paper studies clustering analysis of online teaching cases and evaluation of teaching results. This paper gives the design flow of online teaching with case teaching as the core and proposes a text multi-view clustering algorithm based on case subject alignment, and presents a clustering model structure based on subject alignment. Based on the grey system theory, this paper compares online classroom teaching results before and after teachers use clustering algorithm to process teaching cases. Finally, the experimental setup is given, and the effectiveness of the proposed algorithm is verified by experiment.

A Generalized Deep Learning Algorithm Based on NMF for Multi-View Clustering

Multi-view clustering research is a hot topic in the field of data mining, where complementary information between views can better describe data objects and improve the clustering performance. Non-negative matrix factorization (NMF) based multi-view clustering algorithm suffers from weak feature extraction, slow convergence speed and low accuracy. To solve these problems, this paper proposes a generalized deep learning multi-view clustering (GDLMC) algorithm based on NMF. Firstly, via decoupling the elements in the matrix, the matrix elements are non-negatively restricted using an activation function with a non-negative value domain, and the elements are updated employing stochastic gradient descent with learning rate guidance. Then, the corresponding gradients when the elements update are transformed into generalized weights and generalized biases, followed by combining the generalized weights and generalized biases with activation functions to construct generalized deep learning (GDL). Further, GDL is adopted to learn the corresponding low-dimensional matrix of each view and consensus matrix for obtaining the GDLMC algorithm. In addition, the detailed reasoning of the GDLMC algorithm are given. Finally, extensive experiments are conducted on four public datasets including regular and large-scale datasets, and the experimental results show that GDLMC has significant advantages.

Incomplete multi-view clustering via kernelized graph learning

A fundamental assumption underpinning the recent progress in multi-view clustering is the full observation of all views, which rarely holds for real-world data as they often suffer from the absence of some instances in individual views. Such incompleteness generally disables the traditional multi-view clustering models in practical applications. This paper proposes a Kernelized Graph-based Incomplete Multi-view Clustering (KGIMC) algorithm to overcome this limitation. The key novelty of our model is that its subtasks, e.g. similarity learning, clustering analysis, and kernel completion, are optimized in a mutual reinforcement manner to achieve an overall optimal clustering result as follows: 1) Similarity learning is directed by clustering analysis to construct a graph with as many connected components just as the number of clusters. 2) The well-constructed similarity graph in the last iteration is employed to guide the process of kernel completion. 3) The updated kernels are in turn used to conduct subsequent similarity learning. We extend our model into multi-kernel settings to alleviate the difficulty of kernel selection. We provide an alternating iterative algorithm to solve KGIMC with convergence guaranteed and complexity analyzed. Extensive experiments are conducted on several popular datasets, and the results demonstrate that KGIMC outperforms the state-of-the-art approaches in general.

Multi-View Clustering-Based Time Series Empirical Tropospheric Delay Correction

Tropospheric delays (TDs) still hinder the millimeter-scale measurement accuracy of interferometric synthetic aperture radar (InSAR). Towards the higher accuracy, this letter presents a new time series TDs correction method. The rationale behind the proposed method is that multi-view clustering (MvC) is introduced to identify the spatiotemporal TDs behaviors, particularly, in which one-pass multi-view clustering (OPMC) algorithm is employed to perform window segmentation rather than sticking to the commonly used boxcar windows. Next, a phase-elevation network correction model in each cluster is constructed by fully considering the spatiotemporal phase information. Besides, an iterative weighted scheme is designed to further enhance the robustness of the estimated model parameters. The Sentinel-1 datasets covering the southwest mountainous area, China, confirm the effectiveness of the new method.

A multi-view clustering algorithm for attributed weighted multi-edge directed networks

A multi-view clustering algorithm for attributed weighted multi-edge directed networks

Streamline Selection around Critical Points of 3D Flow Fields by the Multi-View Clustering

When visualizing streamlines around critical points, the complex and diverse characteristics of the flow field and the possible existence of common points or symmetries among streamlines may lead to the failure of conventional geometric or similarity-based selection methods. Therefore, a data-driven streamline selection method around critical points, MvCcp, is proposed. It is a method based on multi-view clustering algorithm. By voxelizing the flow field with different granularity, the location distribution view and the geometric feature view data based on the histogram of their distance fields are generated, and the streamlines are selected by the multi-view clustering algorithm. The qualitative visualization of the 3D flow field around six typical critical points such as HalfCylinder was compared with three other typical selection methods, and the comparison experiments based on quantitative metrics such as MSE, PSNR, SSIM, AAD showed that MvCcp had more excellent and more stable performance in all experimental 3D flow fields.

Reciprocal consistency graph learning by aligning multi-semantic spaces for multi-view clustering

Graph-based multi-view clustering can effectively reveal the latent cluster structure of multi-view data, however, it remains challenging to construct high-quality graphs by exploring the discriminant information from data. Most of the existing graph-based methods usually construct the graph in the original space or subspace, which may not take the differences of semantic information in different spaces into considerations. Moreover, existing approaches generally measure the relevance of the pair-wise views, which may result in insufficient information exploitation and limited graph representation. To remedy these issues, we proposed an innovative multi-view clustering algorithm called reciprocal consistency graph learning (RCGL), which learns consistency representation by aligning the semantic information from three spaces simultaneously to uncover latent complementarity and consistency among different views. Specifically, we construct the low-dimensional space based on linear projection to preserve essential semantic information. Furthermore, RCGL maps the low-dimension representation from linear space into nonlinear space via Hilbert–Schmidt independence criterion, to explore the nonlinear information hidden in data. Moreover, multiple graphs in kernel space are extended to tensor space for learning a high-order graph, which is helpful to better measure the correlation between multiple views. Finally, the objective function is solved by an alternating optimization scheme. Extensive experiments on five benchmark multi-view datasets demonstrate that RCGL outperforms state-of-the-art baselines markedly.

An improved multi-view spectral clustering based on tissue-like P systems

Multi-view spectral clustering is one of the multi-view clustering methods widely studied by numerous scholars. The first step of multi-view spectral clustering is to construct the similarity matrix of each view. Consequently, the clustering performance will be greatly affected by the quality of the similarity matrix of each view. To solve this problem well, an improved multi-view spectral clustering based on tissue-like P systems is proposed in this paper. The optimal per-view similarity matrix is generated in an iterative manner. In addition, spectral clustering is combined with the symmetric nonnegative matrix factorization method to directly output the clustering results to avoid the secondary operation, such as k-means or spectral rotation. Furthermore, improved multi-view spectral clustering is integrated with the tissue-like P system to enhance the computational efficiency of the multi-view clustering algorithm. Extensive experiments verify the effectiveness of this algorithm over other state-of-the-art algorithms.

Efficient and Robust MultiView Clustering With Anchor Graph Regularization

Multi-view clustering has received widespread attention owing to its effectiveness by integrating multi-view data appropriately, but traditional algorithms have limited applicability to large-scale real-world data due to their high computational complexity and low robustness. Focusing on the aforementioned issues, we propose an efficient and robust multi-view clustering algorithm with anchor graph regularization (ERMC-AGR). In this work, a novel anchor graph regularization (ARG) is designed to improve the quality of the learned embedded anchor graph (EAG), and the obtained EAG is decomposed by nonnegative matrix factorization (NMF) under correntropy criterion to acquire clustering results directly. Different from the traditional graph regularization that needs to construct a large-scale Laplacian matrix pertaining to the all-sample graph, our lightweight AGR, constructed from the perspective of anchors, can reduce the computational complexity significantly while improving the EAG quality. Moreover, a factor matrix of NMF is constrained to be the cluster indicator matrix to omit additional k-means after optimization. Subsequently, correntropy is utilized to improve the effectiveness and robustness of ERMC-AGR owing to its promising performance to complex noises and outliers. Extensive experiments on real-world datasets and noisy datasets show that ERMC-ARG can improve the clustering efficiency and robustness while ensuring comparable or even better effectiveness.

A Multi-view Kernel Clustering framework for Categorical sequences

Multi-view clustering, which optimally integrates complementary information from different views to improve clustering performance, has drawn considerable attention in recent years. Despite recent advances, issues remain when dealing with data of high dimensionality and heterogeneity, especially in categorical sequences. These unique challenges and properties have motivated us to develop a novel Multi-view Kernel Clustering framework for Categorical sequences (MKCC), where views are expressed in terms of kernel matrices and a weighted combination of the instances is learned in parallel to the partitioning. Concretely, MKCC adaptively constructs the kernel matrix without the need of defining the kernel function. Nonetheless, the computational cost of storing the kernel matrix is O(N2). To address this issue, we integrate a simple and efficient method for approximating the kernel matrix. A new multi-view clustering algorithm and a cluster validity index for categorical sequences are also proposed based on the framework. An empirical analysis on synthetic data sets and several commonly used real-world data sets demonstrates the appropriateness of the proposal, with the results showing the method’s outstanding performance.

Multi-View Clustering With the Cooperation of Visible and Hidden Views

Multi-view data are becoming common in real-world modeling tasks and many multi-view data clustering algorithms have thus been proposed. The existing algorithms usually focus on the cooperation of different views in the original space but neglect the influence of the hidden information among these different visible views, or they only consider the hidden information between the views. The algorithms are therefore not efficient since the available information is not fully excavated, particularly the otherness information in different views and the consistency information between them. In practice, the otherness and consistency information in multi-view data are both very useful for effective clustering analyses. In this study, a Multi-View clustering algorithm developed with the Cooperation of Visible and Hidden views, i.e., MV-Co-VH, is proposed. The MV-Co-VH algorithm first projects the multiple views from different visible spaces to the common hidden space by using the non-negative matrix factorization (NMF) strategy to obtain the common hidden view data. Collaborative learning is then implemented in the clustering procedure based on the visible views and the shared hidden view. The results of extensive experiments on UCI multi-view datasets and real-world image multi-view datasets show that the clustering performance of the proposed algorithm is competitive with or even better than that of the existing algorithms.