As a challenging problem, incomplete multi-view clustering (MVC) has drawn much attention in recent years. Most of the existing methods contain the feature recovering step inevitably to obtain the ...clustering result of incomplete multi-view datasets. The extra target of recovering the missing feature in the original data space or common subspace is difficult for unsupervised clustering tasks and could accumulate mistakes during the optimization. Moreover, the biased error is not taken into consideration in the previous graph-based methods. The biased error represents the unexpected change of incomplete graph structure, such as the increase in the intra-class relation density and the missing local graph structure of boundary instances. It would mislead those graph-based methods and degrade their final performance. In order to overcome these drawbacks, we propose a new graph-based method named Graph Structure Refining for Incomplete MVC (GSRIMC). GSRIMC avoids recovering feature steps and just fully explores the existing subgraphs of each view to produce superior clustering results. To handle the biased error, the biased error separation is the core step of GSRIMC. In detail, GSRIMC first extracts basic information from the precomputed subgraph of each view and then separates refined graph structure from biased error with the help of tensor nuclear norm. Besides, cross-view graph learning is proposed to capture the missing local graph structure and complete the refined graph structure based on the complementary principle. Extensive experiments show that our method achieves better performance than other state-of-the-art baselines.
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.
A retrospective study.
The purpose of this study was to identify the independent risk factors for postoperative surgical site infection (SSI) after posterior lumbar spinal surgery based on the ...perioperative factors analysis.
SSI is one of the most common complications after spinal surgery. Previous studies have identified different risk factors for postoperative SSI after lumbar spinal surgery. However, most of the studies were focused on the patient and procedure-related factors. Few studies reported the correlation between laboratory tests and postoperative SSI.
A retrospective study was carried out in a single institution. Patients who underwent posterior lumbar spinal surgery between January 2010 and August 2016 were included in this study. All patients' medical records were reviewed and patients with postoperative SSI were identified. Perioperative variables were included to determine the risk factors for SSI by univariate and multivariate regression analysis.
A total of 2715 patients undergoing posterior lumbar spinal surgery were included in this study. Of these patients, 64 (2.4%) were detected with postoperative SSI, including 46 men and 18 women. Diabetes mellitus (P = 0.026), low preoperative serum level of calcium (P = 0.009), low preoperative and postoperative albumin (P = 0.025 and 0.035), high preoperative serum glucose (P = 0.029), multiple fusion segments (P < 0.001), increased surgical time and estimated blood loss (P = 0.023 and 0.005), decreased postoperative hemoglobin (P = 0.008), and prolonged drainage duration (P = 0.016) were found to be the independent risk factors for SSI. Multilevel fusion and a history of diabetes mellitus were the two strongest risk factors (odds ratio = 2.329 and 2.227) for SSI.
Based on a large population analysis, previous reported risk factors for SSI were confirmed in this study while some new independent risk factors were identified significantly associated with SSI following lumbar spinal surgery, including preoperative low serum level of calcium, decreased preoperative and postoperative albumin, and decreased postoperative hemoglobin.
4.
Although many multi-view clustering approaches have been developed recently, one common shortcoming of most of them is that they generally rely on the original feature space or consider the two ...components of the similarity-based clustering separately (i.e., similarity matrix construction and cluster indicator matrix calculation), which may negatively affect the clustering performance. To tackle this shortcoming, in this paper, we propose a new method termed Multi-view Clustering in Latent Embedding Space (MCLES), which jointly recovers a comprehensive latent embedding space, a robust global similarity matrix and an accurate cluster indicator matrix in a unified optimization framework. In this framework, each variable boosts each other in an interplay manner to achieve the optimal solution. To avoid the optimization problem of quadratic programming, we further propose to relax the constraint of the global similarity matrix, based on which an improved version termed Relaxed Multi-view Clustering in Latent Embedding Space (R-MCLES) is proposed. Compared with MCLES, R-MCLES achieves lower computational complexity with more correlations between pairs of data points. Extensive experiments conducted on both image and document datasets have demonstrated the superiority of the proposed methods when compared with the state-of-the-art.
•We propose two novel multi-view clustering methods.•The three key matrixes can be learned in a unified framework.•Extensive experiments are conducted.
Multiview subspace clustering has attracted an increasing amount of attention in recent years. However, most of the existing multiview subspace clustering methods assume linear relations between ...multiview data points when learning the affinity representation by means of the self-expression or fail to preserve the locality property of the original feature space in the learned affinity representation. To address the above issues, in this article, we propose a new multiview subspace clustering method termed smoothness regularized multiview subspace clustering with kernel learning (SMSCK). To capture the nonlinear relations between multiview data points, the proposed model maps the concatenated multiview observations into a high-dimensional kernel space, in which the linear relations reflect the nonlinear relations between multiview data points in the original space. In addition, to explicitly preserve the locality property of the original feature space in the learned affinity representation, the smoothness regularization is deployed in the subspace learning in the kernel space. Theoretical analysis has been provided to ensure that the optimal solution of the proposed model meets the grouping effect. The unique optimal solution of the proposed model can be obtained by an optimization strategy and the theoretical convergence analysis is also conducted. Extensive experiments are conducted on both image and document data sets, and the comparison results with state-of-the-art methods demonstrate the effectiveness of our method.
Multi-view clustering (MVC) has attracted more and more attention in the recent few years by making full use of complementary and consensus information between multiple views to cluster objects into ...different partitions. Although there have been two existing works for MVC survey, neither of them jointly takes the recent popular deep learning-based methods into consideration. Therefore, in this paper, we conduct a comprehensive survey of MVC from the perspective of representation learning. It covers a quantity of multi-view clustering methods including the deep learning-based models, providing a novel taxonomy of the MVC algorithms. Furthermore, the representation learning-based MVC methods can be mainly divided into two categories, i.e., shallow representation learning-based MVC and deep representation learning-based MVC, where the deep learning-based models are capable of handling more complex data structure as well as showing better expression. In the shallow category, according to the means of representation learning, we further split it into two groups, i.e., multi-view graph clustering and multi-view subspace clustering. To be more comprehensive, basic research materials of MVC are provided for readers, containing introductions of the commonly used multi-view datasets with the download link and the open source code library. In the end, some open problems are pointed out for further investigation and development.
Multiview clustering plays an important part in unsupervised learning. Although the existing methods have shown promising clustering performances, most of them assume that the data is completely ...coupled between different views, which is unfortunately not always ensured in real-world applications. The clustering performance of these methods drops dramatically when handling the uncoupled data. The main reason is that: 1) cross-view correlation of uncoupled data is unclear, which limits the existing multiview clustering methods to explore the complementary information between views and 2) features from different views are uncoupled with each other, which may mislead the multiview clustering methods to partition data into wrong clusters. To address these limitations, we propose a tensor approach for uncoupled multiview clustering (T-UMC) in this article. Instead of pairwise correlation, T-UMC chooses a most reliable view by view-specific silhouette coefficient (VSSC) at first, and then couples the self-representation matrix of each view with it by pairwise cross-view coupling learning. After that, by integrating recoupled self-representation matrices into a third-order tensor, the high-order correlations of all views are explored with tensor singular value decomposition (t-SVD)-based tensor nuclear norm (TNN). And the view-specific local structures of each individual view are also preserved with the local structure learning scheme with manifold learning. Besides, the physical meaning of view-specific coupling matrix is also discussed in this article. Extensive experiments on six commonly used benchmark datasets have demonstrated the superiority of the proposed method compared with the state-of-the-art multiview clustering methods.
Most existing large-scale multiview clustering algorithms attempt to capture data distribution in multiple views by selecting view-wise anchor representations beforehand with ...<inline-formula><tex-math notation="LaTeX">k</tex-math></inline-formula>-means, or by direct matrix factorization on the original observations. Despite impressive performance, few of them have paid attention to the semantic correlations between anchor bases and cluster centroids, or even the underlying relations between clusters and data samples. In view of this, we propose a C oncept F actorization based M ultiview C lustering for Large-scale Data (CFMC) method with nearly linear complexity. The anchor bases learning, coefficient expression with clear semantic cues and partitioning are integrated together in this unified model. Meanwhile, explicit connections among multiview data, anchor bases and clusters are modeled via coefficient representations with semantic meanings. A four-step alternate minimizing algorithm is designed to handle the optimization problem, which is proved to have linear time complexity w.r.t. the sample size. Extensive experiments conducted on several challenging large-scale datasets confirm the superiority of the method compared with the state-of-the-art methods.
Multiview attribute graph clustering aims to cluster nodes into disjoint categories by taking advantage of the multiview topological structures and the node attribute values. However, the existing ...works fail to explicitly discover the inherent relationships in multiview topological graph matrices while considering different properties between the graphs. Besides, they cannot well handle the sparse structure of some graphs in the learning procedure of graph embeddings. Therefore, in this article, we propose a novel contrastive multiview attribute graph clustering (CMAGC) with adaptive encoders method. Within this framework, the adaptive encoders concerning different properties of distinct topological graphs are chosen to integrate multiview attribute graph information by checking whether there exists high-order neighbor information or not. Meanwhile, the number of layers of the GCN encoders is selected according to the prior knowledge related to the characteristics of different topological graphs. In particular, the feature-level and cluster-level contrastive learning are conducted on the multiview soft assignment representations, where the union of the first-order neighbors from the corresponding graph pairs is regarded as the positive pairs for data augmentation and the sparse neighbor information problem in some graphs can be well dealt with. To the best of our knowledge, it is the first time to explicitly deal with the inherent relationships from the interview and intraview perspectives. Extensive experiments are conducted on several datasets to verify the superiority of the proposed CMAGC method compared with the state-of-the-art methods.
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.
