Several methods have been proposed to estimate the number of clusters in a dataset; the basic ideal behind all of them has been to study an index that measures inter-cluster separation and intra-cluster cohesion over a range of cluster numbers and report the number which gives an optimum value of the index. In this paper we propose a simple, parameter free approach that is like human cognition to form clusters, where closely lying points are easily identified to form a cluster and total number of clusters are revealed. To identify closely lying points, affinity of two points is defined as a function of distance and a threshold affinity is identified, above which two points in a dataset are likely to be in the same cluster. Well separated clusters are identified even in the presence of outliers, whereas for not so well separated dataset, final number of clusters are estimated and the detected clusters are merged to produce the final clusters. Experiments performed with several large dimensional synthetic and real datasets show good results with robustness to noise and density variation within dataset.
Sri Sathya Sai Institute of Higher Learning（斯里萨蒂亚赛高等研究院）
Spectral clustering has gained importance in recent years due to its ability to cluster complex data as it requires only pairwise similarity among data points with its ease of implementation. The central point in spectral clustering is the process of capturing pair-wise similarity. In the literature, many research techniques have been proposed for effective construction of affinity matrix with suitable pair- wise similarity. In this paper a general framework for capturing pairwise affinity using local features such as density, proximity and structural similarity is been proposed. Topological N…
Unsupervised hashing methods have attracted widespread attention with the explosive growth of large-scale data, which can greatly reduce storage and computation by learning compact binary codes. Existing unsupervised hashing methods attempt to exploit the valuable information from samples, which fails to take the local geometric structure of unlabeled samples into consideration. Moreover, hashing based on auto-encoders aims to minimize the reconstruction loss between the input data and binary codes, which ignores the potential consistency and complementarity of multiple sources data. To addres…
University of Electronic Science and Technology of China（电子科技大学）
A recently proposed clustering method, called the Nearest Descent (ND), can organize the whole dataset into a sparsely connected graph, called the In-tree. This ND-based Intree structure proves able to reveal the clustering structure underlying the dataset, except one imperfect place, that is, there are some undesired edges in this In-tree which require to be removed. Here, we propose an effective way to automatically remove the undesired edges in In-tree via an effective combination of the In-tree structure with affinity propagation (AP). The key for the combination is to add edges between th…
Laboratory for Intelligent and Safe Automobiles, UC San Diego（加州大学圣迭戈分校智能与安全汽车实验室）
This study presents an approach to lane detection involving the prediction of binary segmentation masks and per-pixel affinity fields. These affinity fields, along with the binary masks, can then be used to cluster lane pixels horizontally and vertically into corresponding lane instances in a post-processing step. This clustering is achieved through a simple row-by-row decoding process with little overhead; such an approach allows LaneAF to detect a variable number of lanes without assuming a fixed or maximum number of lanes. Moreover, this form of clustering is more interpretable in compariso…
Nankai Univeristy（南开大学）；Inception Institute of Artificial Intelligence（起源人工智能研究院）；Harbin Institute of Technology（哈尔滨工业大学）；Xi’an Jiaotong University（西安交通大学）；The Hong Kong Polytechnic University（香港理工大学）；The Chinese University of Hong Kong (Shenzhen)（香港中文大学（深圳））
The self-expressive property of data points, i.e., each data point can be linearly represented by the other data points in the same subspace, has proven effective in leading subspace clustering methods. Most self-expressive methods usually construct a feasible affinity matrix from a coefficient matrix, obtained by solving an optimization problem. However, the negative entries in the coefficient matrix are forced to be positive when constructing the affinity matrix via exponentiation, absolute symmetrization, or squaring operations. This consequently damages the inherent correlations among the …
Domain adaptation deals with training models using large scale labeled data from a specific source domain and then adapting the knowledge to certain target domains that have few or no labels. Many prior works learn domain agnostic feature representations for this purpose using a global distribution alignment objective which does not take into account the finer class specific structure in the source and target domains. We address this issue in our work and propose an instance affinity based criterion for source to target transfer during adaptation, called ILA-DA. We first propose a reliable and…
Bottom-up approaches for image-based multi-person pose estimation consist of two stages: (1) keypoint detection and (2) grouping of the detected keypoints to form person instances. Current grouping approaches rely on learned embedding from only visual features that completely ignore the spatial configuration of human poses. In this work, we formulate the grouping task as a graph partitioning problem, where we learn the affinity matrix with a Graph Neural Network (GNN). More specifically, we design a Geometry-aware Association GNN that utilizes spatial information of the keypoints and learns lo…
Sichuan University（四川大学）；National University of Singapore（新加坡国立大学）；OmniVision Technologies Singapore Pte. Ltd.（豪威科技新加坡私人有限公司）；Tsinghua University（清华大学）；Artificial Intelligence Institute（360人工智能研究院）
In this paper, we present a deep extension of Sparse Subspace Clustering, termed Deep Sparse Subspace Clustering (DSSC). Regularized by the unit sphere distribution assumption for the learned deep features, DSSC can infer a new data affinity matrix by simultaneously satisfying the sparsity principle of SSC and the nonlinearity given by neural networks. One of the appealing advantages brought by DSSC is: when original real-world data do not meet the class-specific linear subspace distribution assumption, DSSC can employ neural networks to make the assumption valid with its hierarchical nonlinea…
GLC++: Source-Free Universal Domain Adaptation through Global-Local Clustering and Contrastive Affinity Learning
School of Computer Science and Technology, Tongji University（同济大学计算机科学与技术学院）；School of Automotive Engineering, Tongji University（同济大学汽车工程学院）；Faculty of Computer Science, Chemnitz University of Technology（化学工业大学计算机科学学院）；Department of Computer Science, Shanghai Jiao Tong University（上海交通大学计算机科学系）；College of Computing and Data Science, Nanyang Technological University（南洋理工大学计算与数据科学学院）；School of Computer Science and Technology, Key Laboratory of Embedded System and Service Computing, Ministry of Education, Tongji University（同济大学计算机科学与技术学院、教育部嵌入式系统与服务计算重点实验室）
Beijing University of Posts and Telecommunications（北京邮电大学）；Johns Hopkins University（约翰斯·霍普金斯大学）
Subspace clustering refers to the problem of segmenting data drawn from a union of subspaces. State-of-the-art approaches for solving this problem follow a two-stage approach. In the first step, an affinity matrix is learned from the data using sparse or low-rank minimization techniques. In the second step, the segmentation is found by applying spectral clustering to this affinity. While this approach has led to state-of-the-art results in many applications, it is sub-optimal because it does not exploit the fact that the affinity and the segmentation depend on each other. In this paper, we pro…
Algebraic Subspace Clustering (ASC) is a simple and elegant method based on polynomial fitting and differentiation for clustering noiseless data drawn from an arbitrary union of subspaces. In practice, however, ASC is limited to equi-dimensional subspaces because the estimation of the subspace dimension via algebraic methods is sensitive to noise. This paper proposes a new ASC algorithm that can handle noisy data drawn from subspaces of arbitrary dimensions. The key ideas are (1) to construct, at each point, a decreasing sequence of subspaces containing the subspace passing through that point;…
We propose a data-driven approach to detect conversational groups by identifying spatial arrangements typical of these focused social encounters. Our approach uses a novel Deep Affinity Network (DANTE) to predict the likelihood that two individuals in a scene are part of the same conversational group, considering their social context. The predicted pair-wise affinities are then used in a graph clustering framework to identify both small (e.g., dyads) and large groups. The results from our evaluation on multiple, established benchmarks suggest that combining powerful deep learning methods with …
In this work, we propose an approach for detecting conversation groups in social scenarios like cocktail parties and networking events, from overhead camera recordings. We posit the detection of conversation groups as a learning problem that could benefit from leveraging the spatial context of the surroundings, and the inherent temporal context in interpersonal dynamics which is reflected in the temporal dynamics in human behavior signals, an aspect that has not been addressed in recent prior works. This motivates our approach which consists of a dynamic LSTM-based deep learning model that pre…
Nanjing University（南京大学）；Huazhong University of Science and Technology（华中科技大学）
This paper proposes an affinity fusion graph framework to effectively connect different graphs with highly discriminating power and nonlinearity for natural image segmentation. The proposed framework combines adjacency-graphs and kernel spectral clustering based graphs (KSC-graphs) according to a new definition named affinity nodes of multi-scale superpixels. These affinity nodes are selected based on a better affiliation of superpixels, namely subspace-preserving representation which is generated by sparse subspace clustering based on subspace pursuit. Then a KSC-graph is built via a novel ke…
Universitat Autonoma de Barcelona（巴塞罗那自治大学）；Nanjing University of Science and Technology（南京理工大学）；Huawei Kirin Solution（华为麒麟解决方案）
Domain adaptation (DA) aims to alleviate the domain shift between source domain and target domain. Most DA methods require access to the source data, but often that is not possible (e.g. due to data privacy or intellectual property). In this paper, we address the challenging source-free domain adaptation (SFDA) problem, where the source pretrained model is adapted to the target domain in the absence of source data. Our method is based on the observation that target data, which might no longer align with the source domain classifier, still forms clear clusters. We capture this intrinsic structu…
School of Computer Science and Technology, Zhejiang University（浙江大学计算机科学与技术学院）
Recently a new clustering algorithm called 'affinity propagation' (AP) has been proposed, which efficiently clustered sparsely related data by passing messages between data points. However, we want to cluster large scale data where the similarities are not sparse in many cases. This paper presents two variants of AP for grouping large scale data with a dense similarity matrix. The local approach is partition affinity propagation (PAP) and the global method is landmark affinity propagation (LAP). PAP passes messages in the subsets of data first and then merges them as the number of initial step…
Many state-of-the-art subspace clustering methods follow a two-step process by first constructing an affinity matrix between data points and then applying spectral clustering to this affinity. Most of the research into these methods focuses on the first step of generating the affinity, which often exploits the self-expressive property of linear subspaces, with little consideration typically given to the spectral clustering step that produces the final clustering. Moreover, existing methods often obtain the final affinity that is used in the spectral clustering step by applying ad-hoc or arbitr…
Spectral clustering is one of the most popular clustering approaches with the capability to handle some challenging clustering problems. Most spectral clustering methods provide a nonlinear map from the data manifold to a subspace. Only a little work focuses on the explicit linear map which can be viewed as the unsupervised distance metric learning. In practice, the selection of the affinity matrix exhibits a tremendous impact on the unsupervised learning. While much success of affinity learning has been achieved in recent years, some issues such as noise reduction remain to be addressed. In t…
Subspace clustering refers to the problem of clustering high-dimensional data that lie in a union of low-dimensional subspaces. State-of-the-art subspace clustering methods are based on the idea of expressing each data point as a linear combination of other data points while regularizing the matrix of coefficients with L1, L2 or nuclear norms for a sparse solution. L1 regularization is guaranteed to give a subspace-preserving affinity (i.e., there are no connections between points from different subspaces) under broad theoretical conditions, but the clusters may not be fully connected. L2 and …
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…
NEC Labs America（NEC美国实验室）；Australian Centre for Robotic Vision（澳大利亚机器人视觉中心）；Australian National University（澳大利亚国立大学）；University of Adelaide（阿德莱德大学）；Monash University（莫纳什大学）
Subspace clustering algorithms are notorious for their scalability issues because building and processing large affinity matrices are demanding. In this paper, we introduce a method that simultaneously learns an embedding space along subspaces within it to minimize a notion of reconstruction error, thus addressing the problem of subspace clustering in an end-to-end learning paradigm. To achieve our goal, we propose a scheme to update subspaces within a deep neural network. This in turn frees us from the need of having an affinity matrix to perform clustering. Unlike previous attempts, our meth…
We propose a simple yet effective proposal-free architecture for lidar panoptic segmentation. We jointly optimize both semantic segmentation and class-agnostic instance classification in a single network using a pillar-based bird's-eye view representation. The instance classification head learns pairwise affinity between pillars to determine whether the pillars belong to the same instance or not. We further propose a local clustering algorithm to propagate instance ids by merging semantic segmentation and affinity predictions. Our experiments on nuScenes dataset show that our approach outperfo…
Washington University in St. Louis（圣路易斯华盛顿大学）；Simon Fraser University（西蒙弗雷泽大学）
We propose a new approach for 3D instance segmentation based on sparse convolution and point affinity prediction, which indicates the likelihood of two points belonging to the same instance. The proposed network, built upon submanifold sparse convolution [3], processes a voxelized point cloud and predicts semantic scores for each occupied voxel as well as the affinity between neighboring voxels at different scales. A simple yet effective clustering algorithm segments points into instances based on the predicted affinity and the mesh topology. The semantic for each instance is determined by the…
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；University of Oregon（俄勒冈大学）
Most of the modern instance segmentation approaches fall into two categories: region-based approaches in which object bounding boxes are detected first and later used in cropping and segmenting instances; and keypoint-based approaches in which individual instances are represented by a set of keypoints followed by a dense pixel clustering around those keypoints. Despite the maturity of these two paradigms, we would like to report an alternative affinity-based paradigm where instances are segmented based on densely predicted affinities and graph partitioning algorithms. Such affinity-based appro…
Sri Sathya Sai Institute of Higher Learning（斯里·萨提亚·赛高等教育学院）
Spectral Clustering(SC) is a prominent data clustering technique of recent times which has attracted much attention from researchers. It is a highly data-driven method and makes no strict assumptions on the structure of the data to be clustered. One of the central pieces of spectral clustering is the construction of an affinity matrix based on a similarity measure between data points. The way the similarity measure is defined between data points has a direct impact on the performance of the SC technique. Several attempts have been made in the direction of strengthening the pairwise similarity …
Video co-segmentation refers to the task of jointly segmenting common objects appearing in a given group of videos. In practice, high-dimensional data such as videos can be conceptually thought as being drawn from a union of subspaces corresponding to categories rather than from a smooth manifold. Therefore, segmenting data into respective subspaces --- subspace clustering --- finds widespread applications in computer vision, including co-segmentation. State-of-the-art methods via subspace clustering seek to solve the problem in two steps: First, an affinity matrix is built from data, with app…
The key in agglomerative clustering is to define the affinity measure between two sets. A novel agglomerative clustering method is proposed by utilizing the path integral to define the affinity measure. Firstly, the path integral descriptor of an edge, a node and a set is computed by path integral and exponent generating function. Then, the affinity measure between two sets is obtained by path integral descriptor of sets. Several good properties of the path integral descriptor is proposed in this paper. In addition, we give the physical interpretation of the proposed path integral descriptor o…
School of IoT Engineering, Jiangnan University（江南大学物联网工程学院）
Recently, sparse subspace clustering has been a valid tool to deal with high-dimensional data. There are two essential steps in the framework of sparse subspace clustering. One is solving the coefficient matrix of data, and the other is constructing the affinity matrix from the coefficient matrix, which is applied to the spectral clustering. This paper investigates the factors which affect clustering performance from both clustering accuracy and stability of the approaches based on existing algorithms. We select four methods to solve the coefficient matrix and use four different ways to constr…
Most existing approaches address multi-view subspace clustering problem by constructing the affinity matrix on each view separately and afterwards propose how to extend spectral clustering algorithm to handle multi-view data. This paper presents an approach to multi-view subspace clustering that learns a joint subspace representation by constructing affinity matrix shared among all views. Relying on the importance of both low-rank and sparsity constraints in the construction of the affinity matrix, we introduce the objective that balances between the agreement across different views, while at …
City University of Hong Kong（香港城市大学）；Caritas Institute of Higher Education（明爱专上学院）；Southeast University（东南大学）
Deep self-expressiveness-based subspace clustering methods have demonstrated effectiveness. However, existing works only consider the attribute information to conduct the self-expressiveness, which may limit the clustering performance. In this paper, we propose a novel adaptive attribute and structure subspace clustering network (AASSC-Net) to simultaneously consider the attribute and structure information in an adaptive graph fusion manner. Specifically, we first exploit an auto-encoder to represent input data samples with latent features for the construction of an attribute matrix. We also c…
Beijing University of Posts and Telecommunications（北京邮电大学）；Johns Hopkins University（约翰斯·霍普金斯大学）
Sparse subspace clustering (SSC) is a state-of-the-art method for segmenting a set of data points drawn from a union of subspaces into their respective subspaces. It is now well understood that SSC produces subspace-preserving data affinity under broad geometric conditions but suffers from a connectivity issue. In this paper, we develop a novel geometric analysis for a variant of SSC, named affine SSC (ASSC), for the problem of clustering data from a union of affine subspaces. Our contributions include a new concept called affine independence for capturing the arrangement of a collection of af…
Subspace clustering is to find underlying low-dimensional subspaces and cluster the data points correctly. In this paper, we propose a novel multi-view subspace clustering method. Most existing methods suffer from two critical issues. First, they usually adopt a two-stage framework and isolate the processes of affinity learning, multi-view information fusion and clustering. Second, they assume the data lies in a linear subspace which may fail in practice as most real-world datasets may have non-linearity structures. To address the above issues, in this paper we propose a novel Enriched Robust …
Automatic Ultrasound Curve Angle Measurement via Affinity Clustering for Adolescent Idiopathic Scoliosis Evaluation
The Hong Kong Polytechnic University（香港理工大学）；The Chinese University of Hong Kong（香港中文大学）；Joint Scoliosis Research Center of the Chinese University of Hong Kong and Nanjing University（香港中文大学与南京大学联合脊柱侧弯研究中心）；Nanjing University（南京大学）
Nanjing University of Science and Technology（南京理工大学）
Due to the few annotated labels of 3D point clouds, how to learn discriminative features of point clouds to segment object instances is a challenging problem. In this paper, we propose a simple yet effective 3D instance segmentation framework that can achieve good performance by annotating only one point for each instance. Specifically, to tackle extremely few labels for instance segmentation, we first oversegment the point cloud into superpoints in an unsupervised manner and extend the point-level annotations to the superpoint level. Then, based on the superpoint graph, we propose an inter-su…
Subspace clustering methods based on $\ell_1$, $\ell_2$ or nuclear norm regularization have become very popular due to their simplicity, theoretical guarantees and empirical success. However, the choice of the regularizer can greatly impact both theory and practice. For instance, $\ell_1$ regularization is guaranteed to give a subspace-preserving affinity (i.e., there are no connections between points from different subspaces) under broad conditions (e.g., arbitrary subspaces and corrupted data). However, it requires solving a large scale convex optimization problem. On the other hand, $\ell_2…
Inception Institute of Artificial Intelligence（人工智能 inception 研究院）；University of Canberra（堪培拉大学）；Australian National University（澳大利亚国立大学）；Beijing Institute of Technology（北京理工大学）
Real-world object classes appear in imbalanced ratios. This poses a significant challenge for classifiers which get biased towards frequent classes. We hypothesize that improving the generalization capability of a classifier should improve learning on imbalanced datasets. Here, we introduce the first hybrid loss function that jointly performs classification and clustering in a single formulation. Our approach is based on an `affinity measure' in Euclidean space that leads to the following benefits: (1) direct enforcement of maximum margin constraints on classification boundaries, (2) a tractab…
LoomSC: Scalable Deep Subspace Clustering with Projector Factorization and Exact Spectral Reduction
École de technologie supérieure (ÉTS)（高等技术学院）；University of Bahrain (UOB)（巴林大学）；Université du Québec à Montréal (UQAM)（魁北克大学蒙特利尔分校）；COMSATS University Islamabad（伊斯兰堡COMSATS大学）
Nanjing University of Posts and Telecommunications（南京邮电大学）；University of Trento（特伦托大学）；Texas State University（得克萨斯州立大学）；Wuhan University（武汉大学）；Minjiang University（闽江学院）
Multi-view subspace clustering aims to divide a set of multisource data into several groups according to their underlying subspace structure. Although the spectral clustering based methods achieve promotion in multi-view clustering, their utility is limited by the separate learning manner in which affinity matrix construction and cluster indicator estimation are isolated. In this paper, we propose to jointly learn the self-representation, continue and discrete cluster indicators in an unified model. Our model can explore the subspace structure of each view and fusion them to facilitate cluster…
We propose a new clustering algorithm, Extended Affinity Propagation, based on pairwise similarities. Extended Affinity Propagation is developed by modifying Affinity Propagation such that the desirable features of Affinity Propagation, e.g., exemplars, reasonable computational complexity and no need to specify number of clusters, are preserved while the shortcomings, e.g., the lack of global structure discovery, that limit the applicability of Affinity Propagation are overcome. Extended Affinity Propagation succeeds not only in achieving this goal but can also provide various additional insig…
Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Horizon Robotics, Inc（地平线机器人公司）；CAS Center for Excellence in Brain Science and Intelligence Technology（中国科学院脑科学与智能技术卓越创新中心）
Recently, proposal-free instance segmentation has received increasing attention due to its concise and efficient pipeline. Generally, proposal-free methods generate instance-agnostic semantic segmentation labels and instance-aware features to group pixels into different object instances. However, previous methods mostly employ separate modules for these two sub-tasks and require multiple passes for inference. We argue that treating these two sub-tasks separately is suboptimal. In fact, employing multiple separate modules significantly reduces the potential for application. The mutual benefits …
The Chinese University of Hong Kong（香港中文大学）；SenseTime Group Limited（商汤集团有限公司）；Nanyang Technological University（南洋理工大学）
Face recognition sees remarkable progress in recent years, and its performance has reached a very high level. Taking it to a next level requires substantially larger data, which would involve prohibitive annotation cost. Hence, exploiting unlabeled data becomes an appealing alternative. Recent works have shown that clustering unlabeled faces is a promising approach, often leading to notable performance gains. Yet, how to effectively cluster, especially on a large-scale (i.e. million-level or above) dataset, remains an open question. A key challenge lies in the complex variations of cluster pat…
An algorithm to improve performance parameter for unsupervised decision forest clustering and density estimation is presented. Specifically, a dual assignment parameter is introduced as a density estimator by combining Random Forest and Gaussian Mixture Model. The Random Forest method has been specifically applied to construct a robust affinity graph that provides information on the underlying structure of data objects used in clustering. The proposed algorithm differs from the commonly used spectral clustering methods where the computed distance metric is used to find similarities between dat…
We propose Clustering Mask Transformer (CMT-DeepLab), a transformer-based framework for panoptic segmentation designed around clustering. It rethinks the existing transformer architectures used in segmentation and detection; CMT-DeepLab considers the object queries as cluster centers, which fill the role of grouping the pixels when applied to segmentation. The clustering is computed with an alternating procedure, by first assigning pixels to the clusters by their feature affinity, and then updating the cluster centers and pixel features. Together, these operations comprise the Clustering Mask …
Australian National University（澳大利亚国立大学）；Motovis Intelligent Technologies（魔视智能科技）；NEC Labs America（NEC美国实验室）；Monash University（莫纳什大学）；Tencent AI Lab（腾讯人工智能实验室）
We introduce the Neural Collaborative Subspace Clustering, a neural model that discovers clusters of data points drawn from a union of low-dimensional subspaces. In contrast to previous attempts, our model runs without the aid of spectral clustering. This makes our algorithm one of the kinds that can gracefully scale to large datasets. At its heart, our neural model benefits from a classifier which determines whether a pair of points lies on the same subspace or not. Essential to our model is the construction of two affinity matrices, one from the classifier and the other from a notion of subs…
Xiamen University（厦门大学）；Chinese Academy of Sciences（中国科学院）
Color and intensity are two important components in an image. Usually, groups of image pixels, which are similar in color or intensity, are an informative representation for an object. They are therefore particularly suitable for computer vision tasks, such as saliency detection and object proposal generation. However, image pixels, which share a similar real-world color, may be quite different since colors are often distorted by intensity. In this paper, we reinvestigate the affinity matrices originally used in image segmentation methods based on spectral clustering. A new affinity matrix, wh…
Bootstrap Deep Spectral Clustering with Optimal Transport
College of Electronic and Information Engineering, Tongji University（同济大学电子与信息工程学院）；College of Electronic and Information Engineering, Shanghai Institute of Intelligent Science and Technology, Tongji University（上海智能科学与技术研究院，同济大学电子与信息工程学院）；Shanghai Research Institute for Intelligent Autonomous Systems, Tongji University（上海智能自主系统研究院，同济大学）；Faculty of Data Science, City University of Macau（澳门城市大学数据科学学院）；Faculty of Computer Science, University of Vienna（维也纳大学计算机科学学院）；Singapore Institute of Technology（新加坡理工学院）
National University of Singapore（新加坡国立大学）；Peking University（北京大学）
This paper studies the subspace segmentation problem. Given a set of data points drawn from a union of subspaces, the goal is to partition them into their underlying subspaces they were drawn from. The spectral clustering method is used as the framework. It requires to find an affinity matrix which is close to block diagonal, with nonzero entries corresponding to the data point pairs from the same subspace. In this work, we argue that both sparsity and the grouping effect are important for subspace segmentation. A sparse affinity matrix tends to be block diagonal, with less connections between…
In this paper, we propose a low-rank representation with symmetric constraint (LRRSC) method for robust subspace clustering. Given a collection of data points approximately drawn from multiple subspaces, the proposed technique can simultaneously recover the dimension and members of each subspace. LRRSC extends the original low-rank representation algorithm by integrating a symmetric constraint into the low-rankness property of high-dimensional data representation. The symmetric low-rank representation, which preserves the subspace structures of high-dimensional data, guarantees weight consiste…
Johns Hopkins University（约翰斯·霍普金斯大学）；Beijing University of Posts and Telecommunications（北京邮电大学）
State-of-the-art subspace clustering methods are based on expressing each data point as a linear combination of other data points while regularizing the matrix of coefficients with $\ell_1$, $\ell_2$ or nuclear norms. $\ell_1$ regularization is guaranteed to give a subspace-preserving affinity (i.e., there are no connections between points from different subspaces) under broad theoretical conditions, but the clusters may not be connected. $\ell_2$ and nuclear norm regularization often improve connectivity, but give a subspace-preserving affinity only for independent subspaces. Mixed $\ell_1$, …
Hubei University of Technology（湖北工业大学）；Huazhong University of Science and Technology（华中科技大学）；Nanjing University（南京大学）
Affinity graph-based segmentation methods have become a major trend in computer vision. The performance of these methods relies on the constructed affinity graph, with particular emphasis on the neighborhood topology and pairwise affinities among superpixels. Due to the advantages of assimilating different graphs, a multi-scale fusion graph has a better performance than a single graph with single-scale. However, these methods ignore the noise from images which influences the accuracy of pairwise similarities. Multi-scale combinatorial grouping and graph fusion also generate a higher computatio…
