Multi-view Clustering Algorithms Research Articles

Weighted Multi-View Spectral Clustering Based on Spectral Perturbation

Considering the diversity of the views, assigning the multiviews with different weights is important to multi-view clustering. Several multi-view clustering algorithms have been proposed to assign different weights to the views. However, the existing weighting schemes do not simultaneously consider the characteristic of multi-view clustering and the characteristic of related single-view clustering. In this paper, based on the spectral perturbation theory of spectral clustering, we propose a weighted multi-view spectral clustering algorithm which employs the spectral perturbation to model the weights of the views. The proposed weighting scheme follows the two basic principles: 1) the clustering results on each view should be close to the consensus clustering result, and 2) views with similar clustering results should be assigned similar weights. According to spectral perturbation theory, the largest canonical angle is used to measure the difference between spectral clustering results. In this way, the weighting scheme can be formulated into a standard quadratic programming problem. Experimental results demonstrate the superiority of the proposed algorithm.

Consensus Guided Multi-View Clustering

In recent decades, tremendous emerging techniques thrive the artificial intelligence field due to the increasing collected data captured from multiple sensors. These multi-view data provide more rich information than traditional single-view data. Fusing heterogeneous information for certain tasks is a core part of multi-view learning, especially for multi-view clustering. Although numerous multi-view clustering algorithms have been proposed, most scholars focus on finding the common space of different views, but unfortunately ignore the benefits from partition level by ensemble clustering. For ensemble clustering, however, there is no interaction between individual partitions from each view and the final consensus one. To fill the gap, we propose a Consensus Guided Multi-View Clustering (CMVC) framework, which incorporates the generation of basic partitions from each view and fusion of consensus clustering in an interactive way, i.e., the consensus clustering guides the generation of basic partitions, and high quality basic partitions positively contribute to the consensus clustering as well. We design a non-trivial optimization solution to formulate CMVC into two iterative k -means clusterings by an approximate calculation. In addition, the generalization of CMVC provides a rich feasibility for different scenarios, and the extension of CMVC with incomplete multi-view clustering further validates the effectiveness for real-world applications. Extensive experiments demonstrate the advantages of CMVC over other widely used multi-view clustering methods in terms of cluster validity, and the robustness of CMVC to some important parameters and incomplete multi-view data.

An active three-way clustering method via low-rank matrices for multi-view data

In recent years, multi-view clustering algorithms have shown promising performance by combining multiple sources or views of datasets. A problem that has not been addressed satisfactorily is the uncertain relationship between an object and a cluster. Thus, this paper investigates an active three-way clustering method via low-rank matrices that can improve clustering accuracy as clustering proceeds for the multi-view data of high dimensionality. We adopt a three-way clustering representation to reflect the three types of relationships between an object and a cluster, namely, belong-to definitely, uncertain and not belong-to definitely. We construct the consensus low-rank matrix from each weighted low-rank matrix by taking account of the diversity of views, and give the method to solve the optimization problem of objective function based on the improved augmented Lagrangian multiplier algorithm. We suggest an active learning strategy to learn important informative pairwise constraints after measuring the uncertainty of an object based on the entropy concept. The experimental results conducted on real-world datasets have validated the effectiveness of the proposed method.

Co-regularized weighting multiview clustering

This paper deals with clustering for multiview data. Multiview clustering has been a research hot spot in many domains or applications, such as information retrieval, biology, chemistry, and marketing. Exploring information from multiple views, one can hope to find a clustering that is more accurate than the ones obtained using the individual views. The aim is to search for clustering patterns that perform a consensus between the patterns from different views. Inspired by variable weighting and co-regularized strategy, this paper studies co-regularized weighting multiview clustering algorithms. Two co-regularized weighting multiview clustering algorithms are proposed from two aspects: pairwise co-regularization and centroid-based co-regularization. Experimental results obtained both on synthetic and real datasets show that the proposed algorithms outperform the main existing multiview clustering algorithms.

Multi-view clustering via multi-manifold regularized non-negative matrix factorization

Non-negative matrix factorization based multi-view clustering algorithms have shown their competitiveness among different multi-view clustering algorithms. However, non-negative matrix factorization fails to preserve the locally geometrical structure of the data space. In this paper, we propose a multi-manifold regularized non-negative matrix factorization framework (MMNMF) which can preserve the locally geometrical structure of the manifolds for multi-view clustering. MMNMF incorporates consensus manifold and consensus coefficient matrix with multi-manifold regularization to preserve the locally geometrical structure of the multi-view data space. We use two methods to construct the consensus manifold and two methods to find the consensus coefficient matrix, which leads to four instances of the framework. Experimental results show that the proposed algorithms outperform existing non-negative matrix factorization based algorithms for multi-view clustering.

Consensus Kernel K-Means Clustering for Incomplete Multiview Data.

Multiview clustering aims to improve clustering performance through optimal integration of information from multiple views. Though demonstrating promising performance in various applications, existing multiview clustering algorithms cannot effectively handle the view's incompleteness. Recently, one pioneering work was proposed that handled this issue by integrating multiview clustering and imputation into a unified learning framework. While its framework is elegant, we observe that it overlooks the consistency between views, which leads to a reduction in the clustering performance. In order to address this issue, we propose a new unified learning method for incomplete multiview clustering, which simultaneously imputes the incomplete views and learns a consistent clustering result with explicit modeling of between-view consistency. More specifically, the similarity between each view's clustering result and the consistent clustering result is measured. The consistency between views is then modeled using the sum of these similarities. Incomplete views are imputed to achieve an optimal clustering result in each view, while maintaining between-view consistency. Extensive comparisons with state-of-the-art methods on both synthetic and real-world incomplete multiview datasets validate the superiority of the proposed method.

Multi-Task Multi-View Clustering

Multi-task clustering and multi-view clustering have severally found wide applications and received much attention in recent years. Nevertheless, there are many clustering problems that involve both multi-task clustering and multi-view clustering, i.e., the tasks are closely related and each task can be analyzed from multiple views. In this paper, we introduce a multi-task multi-view clustering framework which integrates within-view-task clustering, multi-view relationship learning, and multi-task relationship learning. Under this framework, we propose two multi-task multi-view clustering algorithms, the bipartite graph based multi-task multi-view clustering algorithm, and the semi-nonnegative matrix tri-factorization based multi-task multi-view clustering algorithm. The former one can deal with the multi-task multi-view clustering of nonnegative data, the latter one is a general multi-task multi-view clustering method, i.e., it can deal with the data with negative feature values. Experimental results on publicly available data sets in web page mining and image mining show the superiority of the proposed multi-task multi-view clustering algorithms over either multi-task clustering algorithms or multi-view clustering algorithms for multi-task clustering of multi-view data.

A novel multi-view clustering method via low-rank and matrix-induced regularization

Multi-view clustering algorithms have shown promising performance in various applications over the last few decades. Most of them, however, do not adequately take noises and correlation among multiple views into account, which may degrade the clustering performance. In this paper, we propose a novel multi-view clustering method to address these issues. In specific, we construct a low-rank consensus matrix and a sparse error matrix from each similarity matrix corresponding to each view. Furthermore, a matrix-induced regularization term is incorporated to reduce the redundancy and enhance the diversity among different views. The augmented Lagrangian multiplier algorithm is adopted to solve the resultant optimization problem. Comprehensive experiments are conducted to verify the effectiveness of the proposed algorithm. Results demonstrate that our algorithm outperforms several state-of-the-art ones on both synthetic and benchmark data sets.

Multi-View Clustering Based on Belief Propagation

The availability of many heterogeneous but related views of data has arisen in numerous clustering problems. Different views encode distinct representations of the same data, which often admit the same underlying cluster structure. The goal of multi-view clustering is to properly combine information from multiple views so as to generate high quality clustering results that are consistent across different views. Based on max-product belief propagation, we propose a novel multi-view clustering algorithm termed multi-view affinity propagation (MVAP). The basic idea is to establish a multi-view clustering model consisting of two components, which measure the within-view clustering quality and the explicit clustering consistency across different views, respectively. Solving this model is NP-hard, and a multi-view affinity propagation is proposed, which works by passing messages both within individual views and across different views. However, the exemplar consistency constraint makes the optimization almost impossible. To this end, by using some previously designed mathematical techniques, the messages as well as the cluster assignment vector computations are simplified to get simple yet functionally equivalent computations. Experimental results on several real-world multi-view datasets show that MVAP outperforms existing multi-view clustering algorithms. It is especially suitable for clustering more than two views.

MVDA: a multi-view genomic data integration methodology.

BackgroundMultiple high-throughput molecular profiling by omics technologies can be collected for the same individuals. Combining these data, rather than exploiting them separately, can significantly increase the power of clinically relevant patients subclassifications.ResultsWe propose a multi-view approach in which the information from different data layers (views) is integrated at the levels of the results of each single view clustering iterations. It works by factorizing the membership matrices in a late integration manner. We evaluated the effectiveness and the performance of our method on six multi-view cancer datasets. In all the cases, we found patient sub-classes with statistical significance, identifying novel sub-groups previously not emphasized in literature. Our method performed better as compared to other multi-view clustering algorithms and, unlike other existing methods, it is able to quantify the contribution of single views on the final results.ConclusionOur observations suggest that integration of prior information with genomic features in the subtyping analysis is an effective strategy in identifying disease subgroups. The methodology is implemented in R and the source code is available online at http://neuronelab.unisa.it/a-multi-view-genomic-data-integration-methodology/.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-015-0680-3) contains supplementary material, which is available to authorized users.

Constrained NMF-Based Multi-View Clustering on Unmapped Data

Existing multi-view clustering algorithms require thatthe data is completely or partially mapped betweeneach pair of views. However, this requirement couldnot be satisfied in most practical settings. In this paper,we tackle the problem of multi-view clustering for unmappeddata in the framework of NMF based clustering.With the help of inter-view constraints, we definethe disagreement between each pair of views by the factthat the indicator vectors of two instances from two differentviews should be similar if they belong to the samecluster and dissimilar otherwise. The overall objectiveof our algorithm is to minimize the loss function of NMFin each view as well as the disagreement betweeneach pair of views. Experimental results show that, witha small number of constraints, the proposed algorithmgets good performance on unmapped data, and outperformsexisting algorithms on partially mapped data andcompletely mapped data.

Collaborative fuzzy clustering from multiple weighted views.

Clustering with multiview data is becoming a hot topic in data mining, pattern recognition, and machine learning. In order to realize an effective multiview clustering, two issues must be addressed, namely, how to combine the clustering result from each view and how to identify the importance of each view. In this paper, based on a newly proposed objective function which explicitly incorporates two penalty terms, a basic multiview fuzzy clustering algorithm, called collaborative fuzzy c-means (Co-FCM), is firstly proposed. It is then extended into its weighted view version, called weighted view collaborative fuzzy c-means (WV-Co-FCM), by identifying the importance of each view. The WV-Co-FCM algorithm indeed tackles the above two issues simultaneously. Its relationship with the latest multiview fuzzy clustering algorithm Collaborative Fuzzy K-Means (Co-FKM) is also revealed. Extensive experimental results on various multiview datasets indicate that the proposed WV-Co-FCM algorithm outperforms or is at least comparable to the existing state-of-the-art multitask and multiview clustering algorithms and the importance of different views of the datasets can be effectively identified.