Recently, with the assumption that samples can be reconstructed by themselves, subspace clustering (SC) methods have achieved great success. Generally, SC methods contain some parameters to be tuned, ...and different affinity matrices can obtain with different parameter values. In this paper, for the first time, we study a method for fusing these different affinity matrices to promote clustering performance and provide the corresponding solution from a multi-view clustering (MVC) perspective. That is, we argue that the different affinity matrices are consistent and complementary, which is similar to the fundamental assumption of MVC methods. Based on this observation, in this paper, we use least squares regression (LSR), which is a typical SC method, as an example since it can be efficiently optimized and has shown good clustering performance and we propose a novel robust least squares regression method from an MVC perspective (RLSR/MVCP). Specifically, we first utilize LSR with different parameter values to obtain different affinity matrices. Then, to fully explore the information contained in these different affinity matrices and to remove noise, we further fuse these affinity matrices into a tensor, which is constrained by the tensor low-rank constraint, i.e., the tensor nuclear norm (TNN). The two steps are combined into a framework that is solved by the augmented Lagrange multiplier (ALM) method. The experimental results on several datasets indicate that RLSR/MVCP has very encouraging clustering performance and is superior to state-of-the-art SC methods.
In recent years, researchers have proposed many graph-based multi-view clustering (GMC) algorithms to solve the multi-view clustering (MVC) problem. However, there are still some limitations in the ...existing GMC algorithm. In these algorithms, a graph is usually constructed to represent the relationship between the samples in a view; however, it cannot represent the relationship very well since it is often preconstructed. In addition, these algorithms ignore the robustness problem of each graph and high-level information between different graphs. Then, in the paper, we propose a novel MVC method, i.e., robust and optimal neighborhood graph learning for MVC (RONGL/MVC). Specifically, we first build an initial graph for each view. However, these initial graphs cannot represent the relationship between the samples in each view well, so we look for the optimal graph with k connected components in the neighborhood of each initial graph, where k is the number of clusters. Then, to improve the robustness of RONGL/MVC, we reconstruct the optimal graph with the self-representation matrix. Furthermore, we stack all the self-representation matrices into a tensor and impose the tensor low-rank constraint, which can maximize consistent features and explore the high-order relationship between optimal graphs. In addition, we provide an optimization strategy by utilizing the Augmented Lagrange Multiplier (ALM) method. Experimental results on several datasets indicate that RONGL/MVC outperforms state-of-the-art methods.
Dealing with partial occlusion or illumination is one of the most challenging problems in image representation and classification. In this problem, the characterization of the representation error ...plays a crucial role. In most current approaches, the error matrix needs to be stretched into a vector and each element is assumed to be independently corrupted. This ignores the dependence between the elements of error. In this paper, it is assumed that the error image caused by partial occlusion or illumination changes is a random matrix variate and follows the extended matrix variate power exponential distribution. This has the heavy tailed regions and can be used to describe a matrix pattern of l × m dimensional observations that are not independent. This paper reveals the essence of the proposed distribution: it actually alleviates the correlations between pixels in an error matrix E and makes E approximately Gaussian. On the basis of this distribution, we derive a Schatten p-norm-based matrix regression model with L q regularization. Alternating direction method of multipliers is applied to solve this model. To get a closed-form solution in each step of the algorithm, two singular value function thresholding operators are introduced. In addition, the extended Schatten p-norm is utilized to characterize the distance between the test samples and classes in the design of the classifier. Extensive experimental results for image reconstruction and classification with structural noise demonstrate that the proposed algorithm works much more robustly than some existing regression-based methods.
Recently, subspace clustering (SC) has received an increasing amount of attention. Generally, SC methods are implemented on sample data in matrix form. Even for multiway or tensor data, which is ...prevalent in reality, traditional SC methods should convert each sample to a vector and then form a data matrix. However, the vectorization process will damage the underlying inherent spatial structure of the data. To address this problem, in this paper, we propose a novel consensus tensor low-rank representation (CTLRR) method, which is directly implemented on tensor data. First, the tensor nuclear norm (TNN) and t-product, which is defined as the multiplication of two tensors, are employed to model the data and obtain the low-rank representation tensor. Second, spectral clustering is unified into CTLRR to explore the consensus information among the low-rank representation tensor, which helps obtain the final fusion similarity matrix with the k connected components, where k is the number of clusters. Third, the cluster structure is characterized, and the clustering performance is substantially improved. Last, an optimization procedure for CTLRR is presented. Experimental results on certain challenging datasets show that the proposed CTLRR method outperforms the state-of-the-art methods.
Beneficial effects of metformin on cancer risk and mortality have been proved by epidemiological and clinical studies, thus attracting research interest in elucidating the underlying mechanisms. ...Recently, tumour‐associated macrophages (TAMs) appeared to be implicated in metformin‐induced antitumour activities. However, how metformin inhibits TAMs‐induced tumour progression remains ill‐defined. Here, we report that metformin‐induced antitumour and anti‐angiogenic activities were not or only partially contributed by its direct inhibition of functions of tumour and endothelial cells. By skewing TAM polarization from M2‐ to M1‐like phenotype, metformin inhibited both tumour growth and angiogenesis. Depletion of TAMs by clodronate liposomes eliminated M2‐TAMs‐induced angiogenic promotion, while also abrogating M1‐TAMs‐mediated anti‐angiogenesis, thus promoting angiogenesis in tumours from metformin treatment mice. Further in vitro experiments using TAMs‐conditioned medium and a coculture system were performed, which demonstrated an inhibitory effect of metformin on endothelial sprouting and tumour cell proliferation promoted by M2‐polarized RAW264.7 macrophages. Based on these results, metformin‐induced inhibition of tumour growth and angiogenesis is greatly contributed by skewing of TAMs polarization in microenvironment, thus offering therapeutic opportunities for metformin in cancer treatment.
Graph-based incomplete multi-view clustering (IMVC) methods have drawn considerable attention due to their good performance in exploring the nonlinear structure of data. However, they still have the ...following shortcomings. First, graph construction and eigen decomposition of the Laplacian matrix included in the IMVC methods generally have high computational complexity. Second, most methods do not consider the impact of missing views and neglect the potential relationships between different views. Third, few algorithms consider both intra-view and inter-view information for clustering. Therefore, we innovatively propose a scalable incomplete multi-view clustering via the tensor Schatten p-norm and tensorized bipartite graph (SIMVC/TSTBG) method, which combines tensorized bipartite graph, graph completion, and tensor low-rank constraint into a joint framework. Concretely, we first construct bipartite graphs based on the selected m anchor points and the n data points, reducing the size of the graph from n×n to n×m(m<<n), which considerably reduces the computational complexity. Second, we adaptively complete the missing bipartite graph, which reduces the effect of missing view information on the clustering results. Third, to explore connections between missing views and mine high-order information between views, we splice the bipartite graphs into a tensor and impose a tensor low-rank constraint, i.e., the tensor Schatten p-norm, on it. At the same time, we also design an efficient algorithm to solve SIMVC/TSTBG. To our knowledge, we are the first successful practice to integrate the tensor technique with the scalable IMVC method. Compared with other IMVC methods, the results on seven datasets fully show the high efficiency and effectiveness of SIMVC/TSTBG.
In this paper, we present a novel low-rank matrix factorization algorithm with adaptive graph regularizer (LMFAGR). We extend the recently proposed low-rank matrix with manifold regularization (MMF) ...method with an adaptive regularizer. Different from MMF, which constructs an affinity graph in advance, LMFAGR can simultaneously seek graph weight matrix and low-dimensional representations of data. That is, graph construction and low-rank matrix factorization are incorporated into a unified framework, which results in an automatically updated graph rather than a predefined one. The experimental results on some data sets demonstrate that the proposed algorithm outperforms the state-of-the-art low-rank matrix factorization methods.
The similarity of data plays an important role in clustering task, and good clustering performance often requires a reliable similarity matrix. A variety of metrics are used to define a similarity ...matrix in the past, and great achievements are obtained. However, due to the noise and outliers of data in the real world, the quality of the similarity matrix is often poor. Besides, the similarity matrix is often inflexible, which will degrade the clustering performance. To solve this problem, in this paper, we proposed a novel Multi-view Clustering Indicator Learning with Scaled Similarity (MCILSS). Our model uses the self-representation method to reconstruct the data matrix, and then obtain the similarity matrix by minimizing the reconstruction error. More importantly, in our model, we can adjust s
0
<
s
≤
1
to constrain the similarity matrix to gain the best clustering indicator matrix. In addition, the rank constraint is further used to improve the clustering performance. Finally, the indicator matrix is applied to obtain clustering results by k-means. Considering the nonlinear relationship in the data, we also proposed the kernel MCILSS which maps the original data to the kernel space. To solve the proposed models, two efficient optimization algorithms based on Augmented Lagrange Method (ALM) are also designed. The experimental results on some data sets show that our algorithm has better clustering performance than some representative algorithms.
How to design effective multi-view subspace clustering (MVSC) algorithms has recently become a research hotspot. In this paper, we propose a new MVSC algorithm, termed latent multi-view ...self-representation for clustering via the tensor nuclear norm (LMVS/TNN), which can seamlessly unify multi-view clustering and dimensionality reduction into a framework. Specifically, for each view data, LMVS/TNN learns the transformed data from the original space, which can maintain the original manifold structure, and
each subspace representation matrix from the transformed latent space simultaneously. Furthermore, to use the high-order correlations and complementary information from multi-view data,
LMVS/TNN
constructs a
third-order tensor by taking the representation matrix
extracted from the transformed latent space
as the frontal slice of the third-order tensor and the tensor is constrained by a new
low-rank tensor constraint, i.e., the tensor nuclear norm (TNN). In addition, based on the augmented Lagrangian scheme, we develop an efficient procedure to solve
LMVS/TNN
. To verify the performance of
LMVS/TNN, we conduct experiments on public datasets and find that
LMVS/TNN outperforms some representative clustering algorithms.
•Our model captures local and global structural information of the samples.•Data derive from linear or nonlinear subspaces can be accurately clustered.•Robust affinity matrices and weighted tensor ...nuclear norm are used to handle noise.•Experimental performance outperforms several state-of-the-art counter-parts.
Multi-view subspace clustering achieves impressive performance for high-dimensional data. However, many of these models do not sufficiently mine the intrinsic information among samples and consider the robustness problem of the affinity matrices, resulting in the degradation of clustering performance. To address these problems, we propose a novel high-order manifold regularized multi-view subspace clustering with robust affinity matrices and a weighted tensor nuclear norm (TNN) model (termed HMRMSC) to characterize real-world data. Specifically, all the similarity matrices of different views are first stacked into a third-order tensor. However, the constructed tensor may contain an additional inter-class representation since the data are usually noisy. Then, we use a technique similar to tensor principal component analysis (TPCA) to obtain a more robust similarity tensor, which is constrained by the so-called weighted TNN since the original TNN treats each singular value equally and usually considers no prior information of singular values. In addition, a high-order manifold regularized term is also added to utilize the manifold information of data. Finally, all the steps are unified into a framework, which is resolved by the augmented Lagrange multiplier (ALM) method. Experimental results on six representative datasets show that our model outperforms several state-of-the-art counterparts.
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