This paper explores the problem of multi-view spectral clustering (MVSC) based on tensor low-rank modeling. Unlike the existing methods that all adopt an off-the-shelf tensor low-rank norm without considering the special characteristics of the tensor in MVSC, we design a novel structured tensor low-rank norm tailored to MVSC. Specifically, we explicitly impose a symmetric low-rank constraint and a structured sparse low-rank constraint on the frontal and horizontal slices of the tensor to characterize the intra-view and inter-view relationships, respectively. Moreover, the two constraints could be jointly optimized to achieve mutual refinement. On the basis of the novel tensor low-rank norm, we formulate MVSC as a convex low-rank tensor recovery problem, which is then efficiently solved with an augmented Lagrange multiplier based method iteratively. Extensive experimental results on five benchmark datasets show that the proposed method outperforms state-of-the-art methods to a significant extent. Impressively, our method is able to produce perfect clustering. In addition, the parameters of our method can be easily tuned, and the proposed model is robust to different datasets, demonstrating its potential in practice.
A low-rank transformation learning framework for subspace clustering and classification is here proposed. Many high-dimensional data, such as face images and motion sequences, approximately lie in a union of low-dimensional subspaces. The corresponding subspace clustering problem has been extensively studied in the literature to partition such high-dimensional data into clusters corresponding to their underlying low-dimensional subspaces. However, low-dimensional intrinsic structures are often violated for real-world observations, as they can be corrupted by errors or deviate from ideal models…
Southeast University（东南大学）；City University of Hong Kong（香港城市大学）
This paper explores the problem of clustering ensemble, which aims to combine multiple base clusterings to produce better performance than that of the individual one. The existing clustering ensemble methods generally construct a co-association matrix, which indicates the pairwise similarity between samples, as the weighted linear combination of the connective matrices from different base clusterings, and the resulting co-association matrix is then adopted as the input of an off-the-shelf clustering algorithm, e.g., spectral clustering. However, the co-association matrix may be dominated by po…
Low-Rank Representation (LRR) highly suffers from discarding the locality information of data points in subspace clustering, as it may not incorporate the data structure nonlinearity and the non-uniform distribution of observations over the ambient space. Thus, the information of the observational density is lost by the state-of-art LRR models, as they take a constant number of adjacent neighbors into account. This, as a result, degrades the subspace clustering accuracy in such situations. To cope with deficiency, in this paper, we propose to consider a hypergraph model to facilitate having a …
On Unifying Multi-View Self-Representations for Clustering by Tensor Multi-Rank Minimization
Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；University of Technology, Sydney（悉尼科技大学）；The Hong Kong Polytechnic University（香港理工大学）；Xiamen University（厦门大学）
Multi-view clustering methods have been a focus in recent years because of their superiority in clustering performance. However, typical traditional multi-view clustering algorithms still have shortcomings in some aspects, such as removal of redundant information, utilization of various views and fusion of multi-view features. In view of these problems, this paper proposes a new multi-view clustering method, low-rank subspace multi-view clustering based on adaptive graph regularization. We construct two new data matrix decomposition models into a unified optimization model. In this framework, …
Southeast University（东南大学）；Caritas Institute of Higher Education（明爱专上学院）；City University of Hong Kong（香港城市大学）
In this letter, we propose a novel semi-supervised subspace clustering method, which is able to simultaneously augment the initial supervisory information and construct a discriminative affinity matrix. By representing the limited amount of supervisory information as a pairwise constraint matrix, we observe that the ideal affinity matrix for clustering shares the same low-rank structure as the ideal pairwise constraint matrix. Thus, we stack the two matrices into a 3-D tensor, where a global low-rank constraint is imposed to promote the affinity matrix construction and augment the initial pair…
Iterative Views Agreement: An Iterative Low-Rank based Structured Optimization Method to Multi-View Spectral Clustering
The University of New South Wales（新南威尔士大学）；The University of Adelaide（阿德莱德大学）；Australian Centre for Robotic Vision（澳大利亚机器人视觉中心）；The University of Melbourne（墨尔本大学）；University of Technology Sydney（悉尼科技大学）
One-step Multi-view Clustering With Adaptive Low-rank Anchor-graph Learning
National Key Laboratory of Human–Machine Hybrid Augmented Intelligence（人机混合增强智能国家重点实验室）；National Engineering Research Center for Visual Information and Applications（视觉信息与应用国家工程研究中心）；Institute of Artificial Intelligence and Robotics（人工智能与机器人研究所）；Xi’an Jiaotong University（西安交通大学）；School of Electrical and Electronic Engineering（电子工程学院）；Nanyang Technological University（南洋理工大学）
Institute of Information Science, Beijing Jiaotong University（北京交通大学信息科学研究所）；Beijing Key Laboratory of Advanced Information Science and Network Technology（北京先进信息科学与网络技术重点实验室）；Department of Computer Science and Technology, Tsinghua University（清华大学计算机科学与技术系）
In this paper, a novel unsupervised low-rank representation model, i.e., Auto-weighted Low-Rank Representation (ALRR), is proposed to construct a more favorable similarity graph (SG) for clustering. In particular, ALRR enhances the discriminability of SG by capturing the multi-subspace structure and extracting the salient features simultaneously. Specifically, an auto-weighted penalty is introduced to learn a similarity graph by highlighting the effective features, and meanwhile, overshadowing the disturbed features. Consequently, ALRR obtains a similarity graph that can preserve the intrinsic…
Sorbonne Paris Nord University（索邦巴黎北大学）；University of Versailles（凡尔赛大学）；Université Paris-Saclay（巴黎萨克雷大学）
Several methods for triclustering three-dimensional data require the cluster size or the number of clusters in each dimension to be specified. To address this issue, the Multi-Slice Clustering (MSC) for 3-order tensor finds signal slices that lie in a low dimensional subspace for a rank-one tensor dataset in order to find a cluster based on the threshold similarity. We propose an extension algorithm called MSC-DBSCAN to extract the different clusters of slices that lie in the different subspaces from the data if the dataset is a sum of r rank-one tensor (r > 1). Our algorithm uses the same inp…
DaSCI Andalusian Institute（DaSCI安达卢西亚研究所）；University of Granada（格拉纳达大学）；Ghent University - imec（根特大学-imec）；University of Jaén（哈恩大学）
Clustering is a well-known unsupervised machine learning approach capable of automatically grouping discrete sets of instances with similar characteristics. Constrained clustering is a semi-supervised extension to this process that can be used when expert knowledge is available to indicate constraints that can be exploited. Well-known examples of such constraints are must-link (indicating that two instances belong to the same group) and cannot-link (two instances definitely do not belong together). The research area of constrained clustering has grown significantly over the years with a large …
IBM Thomas J. Watson Research Center（IBM托马斯·J·沃森研究中心）
Spectral clustering has shown a superior performance in analyzing the cluster structure. However, its computational complexity limits its application in analyzing large-scale data. To address this problem, many low-rank matrix approximating algorithms are proposed, including the Nystrom method - an approach with proven approximate error bounds. There are several algorithms that provide recipes to construct Nystrom approximations with variable accuracies and computing times. This paper proposes a scalable Nystrom-based clustering algorithm with a new sampling procedure, Centroid Minimum Sum of …
Spectral clustering techniques are valuable tools in signal processing and machine learning for partitioning complex data sets. The effectiveness of spectral clustering stems from constructing a non-linear embedding based on creating a similarity graph and computing the spectral decomposition of the Laplacian matrix. However, spectral clustering methods fail to scale to large data sets because of high computational cost and memory usage. A popular approach for addressing these problems utilizes the Nystrom method, an efficient sampling-based algorithm for computing low-rank approximations to l…
As a hot research topic, many multi-view clustering approaches are proposed over the past few years. Nevertheless, most existing algorithms merely take the consensus information among different views into consideration for clustering. Actually, it may hinder the multi-view clustering performance in real-life applications, since different views usually contain diverse statistic properties. To address this problem, we propose a novel Tensor-based Intrinsic Subspace Representation Learning (TISRL) for multi-view clustering in this paper. Concretely, the rank preserving decomposition is proposed f…
Rutgers University（罗格斯大学）；Booz Allen Hamilton（博思艾伦咨询公司）；U.S. Army Research Laboratory（美国陆军研究实验室）
Representation of human actions as a sequence of human body movements or action attributes enables the development of models for human activity recognition and summarization. We present an extension of the low-rank representation (LRR) model, termed the clustering-aware structure-constrained low-rank representation (CS-LRR) model, for unsupervised learning of human action attributes from video data. Our model is based on the union-of-subspaces (UoS) framework, and integrates spectral clustering into the LRR optimization problem for better subspace clustering results. We lay out an efficient li…
A low-rank non-convex norm method for multiview graph clustering
The UM6P Vanguard Center, Mohammed VI Polytechnic University, Green City, Morocco（摩洛哥绿色城穆莱·易斯二世理工大学UM6P先锋中心）；Université du Littoral Cote d’Opale, LMPA（滨海阿尔卑斯大学LMPA）
Clustering based on Stochastic Dominance with application for risk averters and risk seekers
School of Science, Changchun University, Changchun, China（长春大学科学学院，中国长春）；School of Mathematics and Science, Northeast Normal University, Changchun, China（东北师范大学数学与科学学院，中国长春）
Université Lumière-Lyon-II（里昂第二大学）；The Alan Turing Institute（艾伦·图灵研究所）；The National Physical Laboratory（英国国家物理实验室）；Inria Lille - Nord Europe research centre（法国国家信息与自动化研究所里尔-北欧研究中心）；University College London（伦敦大学学院）
This paper studies clustering for possibly high dimensional data (e.g. images, time series, gene expression data, and many other settings), and rephrase it as low rank matrix estimation in the PAC-Bayesian framework. Our approach leverages the well known Burer-Monteiro factorisation strategy from large scale optimisation, in the context of low rank estimation. Moreover, our Burer-Monteiro factors are shown to lie on a Stiefel manifold. We propose a new generalized Bayesian estimator for this problem and prove novel prediction bounds for clustering. We also devise a componentwise Langevin sampl…
FL-TAC: Enhanced Fine-Tuning in Federated Learning via Low-Rank, Task-Specific Adapter Clustering
Tsinghua-Berkeley Shenzhen Institute（清华-伯克利深圳学院）；Tsinghua Shenzhen International Graduate School（清华大学深圳国际研究生院）；Tsinghua University（清华大学）；Institute for AI Industry Research (AIR), Tsinghua University（清华大学人工智能产业研究院）；Shanghai AI Lab（上海人工智能实验室）；RISC-V International Open Source Laboratory（RISC-V国际开源实验室）；Ryerson University（瑞尔森大学）
Graph Convolutional Networks (GCNs) have proven to be successful tools for semi-supervised classification on graph-based datasets. We propose a new GCN variant whose three-part filter space is targeted at dense graphs. Examples include Gaussian graphs for 3D point clouds with an increased focus on non-local information, as well as hypergraphs based on categorical data. These graphs differ from the common sparse benchmark graphs in terms of the spectral properties of their graph Laplacian. Most notably we observe large eigengaps, which are unfavorable for popular existing GCN architectures. Our…
China University of Petroleum, Beijing Campus (CUP)（中国石油大学（北京））
Multi-view learning can cover all features of data samples more comprehensively, so multi-view learning has attracted widespread attention. Traditional subspace clustering methods, such as sparse subspace clustering (SSC) and low-ranking subspace clustering (LRSC), cluster the affinity matrix for a single view, thus ignoring the problem of fusion between views. In our article, we propose a new Multiview Subspace Adaptive Learning based on Attention and Autoencoder (MSALAA). This method combines a deep autoencoder and a method for aligning the self-representations of various views in Multi-view…
South China Agricultural University（华南农业大学）；Sun Yat-sen University（中山大学）
Multi-view subspace clustering aims to discover the hidden subspace structures from multiple views for robust clustering, and has been attracting considerable attention in recent years. Despite significant progress, most of the previous multi-view subspace clustering algorithms are still faced with two limitations. First, they usually focus on the consistency (or commonness) of multiple views, yet often lack the ability to capture the cross-view inconsistencies in subspace representations. Second, many of them overlook the local structures of multiple views and cannot jointly leverage multiple…
