College of Intelligence and Computing, Tianjin University（天津大学智能与计算学部）；Haihe Lab of ITAI（海河人工智能与自主智能实验室）；University at Albany, State University of New York（纽约州立大学奥尔巴尼分校）
Pengfei Zhu, Xinjie Yao, Yu Wang, Binyuan Hui, Dawei Du, Qinghua Hu
Multi-view subspace clustering aims to discover the inherent structure of data by fusing multiple views of complementary information. Most existing methods first extract multiple types of handcrafted features and then learn a joint affinity matrix for clustering. The disadvantage of this approach lies in two aspects: 1) multi-view relations are not embedded into feature learning, and 2) the end-to-end learning manner of deep learning is not suitable for multi-view clustering. Even when deep features have been extracted, it is a nontrivial problem to choose a proper backbone for clustering on different datasets. To address these issues, we propose the Multi-view Deep Subspace Clustering Networks (MvDSCN), which learns a multi-view self-representation matrix in an end-to-end manner. The MvDSCN consists of two sub-networks, \ie, a diversity network (Dnet) and a universality network (Unet). A latent space is built using deep convolutional autoencoders, and a self-representation matrix is learned in the latent space using a fully connected layer. Dnet learns view-specific self-representation matrices, whereas Unet learns a common self-representation matrix for all views. To exploit the complementarity of multi-view representations, the Hilbert--Schmidt independence criterion (HSIC) is introduced as a diversity regularizer that captures the nonlinear, high-order inter-view relations. Because different views share the same label space, the self-representation matrices of each view are aligned to the common one by universality regularization. The MvDSCN also unifies multiple backbones to boost clustering performance and avoid the need for model selection. Experiments demonstrate the superiority of the MvDSCN.
Hyperspectral image (HSI) clustering is a challenging task due to the high complexity of HSI data. Subspace clustering has been proven to be powerful for exploiting the intrinsic relationship between data points. Despite the impressive performance in the HSI clustering, traditional subspace clustering methods often ignore the inherent structural information among data. In this paper, we revisit the subspace clustering with graph convolution and present a novel subspace clustering framework called Graph Convolutional Subspace Clustering (GCSC) for robust HSI clustering. Specifically, the framew…
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;…
Deep Subspace Clustering Networks (DSC) provide an efficient solution to the problem of unsupervised subspace clustering by using an undercomplete deep auto-encoder with a fully-connected layer to exploit the self expressiveness property. This method uses undercomplete representations of the input data which makes it not so robust and more dependent on pre-training. To overcome this, we propose a simple yet efficient alternative method - Overcomplete Deep Subspace Clustering Networks (ODSC) where we use overcomplete representations for subspace clustering. In our proposed method, we fuse the f…
Sparse subspace clustering methods, such as Sparse Subspace Clustering (SSC) \cite{ElhamifarV13} and $\ell^{1}$-graph \cite{YanW09,ChengYYFH10}, are effective in partitioning the data that lie in a union of subspaces. Most of those methods use $\ell^{1}$-norm or $\ell^{2}$-norm with thresholding to impose the sparsity of the constructed sparse similarity graph, and certain assumptions, e.g. independence or disjointness, on the subspaces are required to obtain the subspace-sparse representation, which is the key to their success. Such assumptions are not guaranteed to hold in practice and they …
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…
Many clustering problems in computer vision and other contexts are also classification problems, where each cluster shares a meaningful label. Subspace clustering algorithms in particular are often applied to problems that fit this description, for example with face images or handwritten digits. While it is straightforward to request human input on these datasets, our goal is to reduce this input as much as possible. We present a pairwise-constrained clustering algorithm that actively selects queries based on the union-of-subspaces model. The central step of the algorithm is in querying points…
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…
China University of Petroleum, Beijing（中国石油大学（北京））
In this paper, we propose a novel Attentive Multi-View Deep Subspace Nets (AMVDSN), which deeply explores underlying consistent and view-specific information from multiple views and fuse them by considering each view's dynamic contribution obtained by attention mechanism. Unlike most multi-view subspace learning methods that they directly reconstruct data points on raw data or only consider consistency or complementarity when learning representation in deep or shallow space, our proposed method seeks to find a joint latent representation that explicitly considers both consensus and view-specif…
We propose Deep Closed-Form Subspace Clustering (DCFSC), a new embarrassingly simple model for subspace clustering with learning non-linear mapping. Compared with the previous deep subspace clustering (DSC) techniques, our DCFSC does not have any parameters at all for the self-expressive layer. Instead, DCFSC utilizes the implicit data-driven self-expressive layer derived from closed-form shallow auto-encoder. Moreover, DCFSC also has no complicated optimization scheme, unlike the other subspace clustering methods. With its extreme simplicity, DCFSC has significant memory-related benefits over…
University of California, Berkeley（加州大学伯克利分校）；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 methods based on expressing each data point as a linear combination of other data points have achieved great success in computer vision applications such as motion segmentation, face and digit clustering. In face clustering, the subspaces are linear and subspace clustering methods can be applied directly. In motion segmentation, the subspaces are affine and an additional affine constraint on the coefficients is often enforced. However, since affine subspaces can always be embedded into linear subspaces of one extra dimension, it is unclear if the affine constraint is really…
Anchor-based Multi-view Subspace Clustering with Hierarchical Feature Descent
College of Computer, National University of Defense Technology（国防科技大学计算机学院）；Intelligent Game and Decision Lab（智能游戏与决策实验室）；College of Intelligence Science and Technology, National University of Defense Technology（国防科技大学智能科学学院）
University of Electronic Science and Technology of China（电子科技大学）
Finding a suitable data representation for a specific task has been shown to be crucial in many applications. The success of subspace clustering depends on the assumption that the data can be separated into different subspaces. However, this simple assumption does not always hold since the raw data might not be separable into subspaces. To recover the ``clustering-friendly'' representation and facilitate the subsequent clustering, we propose a graph filtering approach by which a smooth representation is achieved. Specifically, it injects graph similarity into data features by applying a low-pa…
Delhi Technical University（德里技术大学）；Indraprastha Institute of Information Technology Delhi（德里因陀罗普拉斯塔信息技术学院）
Subspace clustering techniques have shown promise in hyperspectral image segmentation. The fundamental assumption in subspace clustering is that the samples belonging to different clusters/segments lie in separable subspaces. What if this condition does not hold? We surmise that even if the condition does not hold in the original space, the data may be nonlinearly transformed to a space where it will be separable into subspaces. In this work, we propose a transformation based on the tenets of deep dictionary learning (DDL). In particular, we incorporate the sparse subspace clustering (SSC) los…
South China Agricultural University（华南农业大学）；Pazhou Lab（琶洲实验室）；Sun Yat-sen University（中山大学）；Guangdong Key Laboratory of Information Security Technology（广东省信息安全技术重点实验室）；Key Laboratory of Machine Intelligence and Advanced Computing, Ministry of Education（教育部机器智能与先进计算重点实验室）；Nanyang Technological University（南洋理工大学）
The rapid emergence of high-dimensional data in various areas has brought new challenges to current ensemble clustering research. To deal with the curse of dimensionality, recently considerable efforts in ensemble clustering have been made by means of different subspace-based techniques. However, besides the emphasis on subspaces, rather limited attention has been paid to the potential diversity in similarity/dissimilarity metrics. It remains a surprisingly open problem in ensemble clustering how to create and aggregate a large population of diversified metrics, and furthermore, how to jointly…
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…
We propose a low-rank transformation-learning framework to robustify subspace clustering. Many high-dimensional data, such as face images and motion sequences, lie in a union of low-dimensional subspaces. The 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. We propose to address this by learning a l…
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…
Beijing University of Posts and Telecommunications（北京邮电大学）
Subspace clustering refers to the problem of segmenting high dimensional data drawn from a union of subspaces into the respective subspaces. In some applications, partial side-information to indicate "must-link" or "cannot-link" in clustering is available. This leads to the task of subspace clustering with side-information. However, in prior work the supervision value of the side-information for subspace clustering has not been fully exploited. To this end, in this paper, we present an enhanced approach for constrained subspace clustering with side-information, termed Constrained Sparse Subspa…
University of Adelaide（阿德莱德大学）；Australian National University（澳大利亚国立大学）；EPFL（洛桑联邦理工学院）
In this paper, we present a kernel subspace clustering method that can handle non-linear models. In contrast to recent kernel subspace clustering methods which use predefined kernels, we propose to learn a low-rank kernel matrix, with which mapped data in feature space are not only low-rank but also self-expressive. In this manner, the low-dimensional subspace structures of the (implicitly) mapped data are retained and manifested in the high-dimensional feature space. We evaluate the proposed method extensively on both motion segmentation and image clustering benchmarks, and obtain superior re…
This paper proposes a novel deep subspace clustering approach which uses convolutional autoencoders to transform input images into new representations lying on a union of linear subspaces. The first contribution of our work is to insert multiple fully-connected linear layers between the encoder layers and their corresponding decoder layers to promote learning more favorable representations for subspace clustering. These connection layers facilitate the feature learning procedure by combining low-level and high-level information for generating multiple sets of self-expressive and informative re…
Curtin University（科廷大学）；University of St Andrews（圣安德鲁斯大学）；Deakin University（迪肯大学）
We propose an effective subspace selection scheme as a post-processing step to improve results obtained by sparse subspace clustering (SSC). Our method starts by the computation of stable subspaces using a novel random sampling scheme. Thus constructed preliminary subspaces are used to identify the initially incorrectly clustered data points and then to reassign them to more suitable clusters based on their goodness-of-fit to the preliminary model. To improve the robustness of the algorithm, we use a dominant nearest subspace classification scheme that controls the level of sensitivity against…
Guangdong University of Technology（广东工业大学）；Commonwealth Scientific and Industrial Research Organisation（联邦科学与工业研究组织）；The University of Sydney（悉尼大学）
Sparse subspace clustering (SSC), as one of the most successful subspace clustering methods, has achieved notable clustering accuracy in computer vision tasks. However, SSC applies only to vector data in Euclidean space. As such, there is still no satisfactory approach to solve subspace clustering by ${\it self-expressive}$ principle for symmetric positive definite (SPD) matrices which is very useful in computer vision. In this paper, by embedding the SPD matrices into a Reproducing Kernel Hilbert Space (RKHS), a kernel subspace clustering method is constructed on the SPD manifold through an a…
Subspace clustering is an important unsupervised clustering approach. It is based on the assumption that the high-dimensional data points are approximately distributed around several low-dimensional linear subspaces. The majority of the prominent subspace clustering algorithms rely on the representation of the data points as linear combinations of other data points, which is known as a self-expressive representation. To overcome the restrictive linearity assumption, numerous nonlinear approaches were proposed to extend successful subspace clustering approaches to data on a union of nonlinear m…
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…
Portland State University（波特兰州立大学）；University of Pennsylvania（宾夕法尼亚大学）；University of California, Berkeley（加州大学伯克利分校）；University of Michigan（密歇根大学）
Subspace clustering is the unsupervised grouping of points lying near a union of low-dimensional linear subspaces. Algorithms based directly on geometric properties of such data tend to either provide poor empirical performance, lack theoretical guarantees, or depend heavily on their initialization. We present a novel geometric approach to the subspace clustering problem that leverages ensembles of the K-subspaces (KSS) algorithm via the evidence accumulation clustering framework. Our algorithm, referred to as ensemble K-subspaces (EKSS), forms a co-association matrix whose (i,j)th entry is th…
Beijing University of Posts and Telecommunications（北京邮电大学）；University of California, Berkeley（加州大学伯克利分校）
State-of-the-art subspace clustering methods are based on self-expressive model, which represents each data point as a linear combination of other data points. By enforcing such representation to be sparse, sparse subspace clustering is guaranteed to produce a subspace-preserving data affinity where two points are connected only if they are from the same subspace. On the other hand, however, data points from the same subspace may not be well-connected, leading to the issue of over-segmentation. We introduce dropout to address the issue of over-segmentation, which is based on randomly dropping …
State-of-the-art algorithms for sparse subspace clustering perform spectral clustering on a similarity matrix typically obtained by representing each data point as a sparse combination of other points using either basis pursuit (BP) or orthogonal matching pursuit (OMP). BP-based methods are often prohibitive in practice while the performance of OMP-based schemes are unsatisfactory, especially in settings where data points are highly similar. In this paper, we propose a novel algorithm that exploits an accelerated variant of orthogonal least-squares to efficiently find the underlying subspaces.…
Beijing University of Posts and Telecommunications（北京邮电大学）；University of California, Berkeley（加州大学伯克利分校）；Shenzhen Research Institute of Big Data（深圳大数据研究院）；Peking University（北京大学）
Subspace clustering methods based on data self-expression have become very popular for learning from data that lie in a union of low-dimensional linear subspaces. However, the applicability of subspace clustering has been limited because practical visual data in raw form do not necessarily lie in such linear subspaces. On the other hand, while Convolutional Neural Network (ConvNet) has been demonstrated to be a powerful tool for extracting discriminative features from visual data, training such a ConvNet usually requires a large amount of labeled data, which are unavailable in subspace cluster…
Charles Sturt University（查尔斯特大学）；Western Sydney University（西悉尼大学）；The University of Sydney（悉尼大学）
In this paper we present Collaborative Low-Rank Subspace Clustering. Given multiple observations of a phenomenon we learn a unified representation matrix. This unified matrix incorporates the features from all the observations, thus increasing the discriminative power compared with learning the representation matrix on each observation separately. Experimental evaluation shows that our method outperforms subspace clustering on separate observations and the state of the art collaborative learning algorithm.
Discovering and clustering subspaces in high-dimensional data is a fundamental problem of machine learning with a wide range of applications in data mining, computer vision, and pattern recognition. Earlier methods divided the problem into two separate stages of finding the similarity matrix and finding clusters. Similar to some recent works, we integrate these two steps using a joint optimization approach. We make the following contributions: (i) we estimate the reliability of the cluster assignment for each point before assigning a point to a subspace. We group the data points into two group…
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…
This paper develops a novel iterative framework for subspace clustering in a learned discriminative feature domain. This framework consists of two modules of fuzzy sparse subspace clustering and discriminative transformation learning. In the first module, fuzzy latent labels containing discriminative information and latent representations capturing the subspace structure will be simultaneously evaluated in a feature domain. Then the linear transforming operator with respect to the feature domain will be successively updated in the second module with the advantages of more discrimination, subsp…
School of IoT Engineering, Jiangnan University（江南大学物联网工程学院）
Based on further studying the low-rank subspace clustering (LRSC) and L2-graph subspace clustering algorithms, we propose a F-graph subspace clustering algorithm with a symmetric constraint (FSSC), which constructs a new objective function with a symmetric constraint basing on F-norm, whose the most significant advantage is to obtain a closed-form solution of the coefficient matrix. Then, take the absolute value of each element of the coefficient matrix, and retain the k largest coefficients per column, set the other elements to 0, to get a new coefficient matrix. Finally, FSSC performs spectr…
Subspace clustering is an important problem in machine learning with many applications in computer vision and pattern recognition. Prior work has studied this problem using algebraic, iterative, statistical, low-rank and sparse representation techniques. While these methods have been applied to both linear and affine subspaces, theoretical results have only been established in the case of linear subspaces. For example, algebraic subspace clustering (ASC) is guaranteed to provide the correct clustering when the data points are in general position and the union of subspaces is transversal. In th…
Australian National University（澳大利亚国立大学）；CVLab, EPFL（洛桑联邦理工学院计算机视觉实验室）；NICTA（澳大利亚国家信息与通信技术研究院）；ARC Centre of Excellence for Robotic Vision (ACRV)（澳大利亚研究理事会机器人视觉卓越中心）
The Shape Interaction Matrix (SIM) is one of the earliest approaches to performing subspace clustering (i.e., separating points drawn from a union of subspaces). In this paper, we revisit the SIM and reveal its connections to several recent subspace clustering methods. Our analysis lets us derive a simple, yet effective algorithm to robustify the SIM and make it applicable to realistic scenarios where the data is corrupted by noise. We justify our method by intuitive examples and the matrix perturbation theory. We then show how this approach can be extended to handle missing data, thus yieldin…
Nanjing University of Science and Technology（南京理工大学）；Brandeis University（布兰迪斯大学）；Adobe Research（Adobe研究院）；Northeastern University（东北大学）
This paper studies the large-scale subspace clustering (LSSC) problem with million data points. Many popular subspace clustering methods cannot directly handle the LSSC problem although they have been considered as state-of-the-art methods for small-scale data points. A basic reason is that these methods often choose all data points as a big dictionary to build huge coding models, which results in a high time and space complexity. In this paper, we develop a learnable subspace clustering paradigm to efficiently solve the LSSC problem. The key idea is to learn a parametric function to partition…
Mathematical Institute for Data Science（数据科学数学研究所）；Johns Hopkins University（约翰斯·霍普金斯大学）；University of California, Berkeley（加州大学伯克利分校）
Subspace clustering is an unsupervised clustering technique designed to cluster data that is supported on a union of linear subspaces, with each subspace defining a cluster with dimension lower than the ambient space. Many existing formulations for this problem are based on exploiting the self-expressive property of linear subspaces, where any point within a subspace can be represented as linear combination of other points within the subspace. To extend this approach to data supported on a union of non-linear manifolds, numerous studies have proposed learning an embedding of the original data …
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…
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 …
National University of Singapore（新加坡国立大学）；Pony AI（小马智行）
Subspace clustering has been extensively studied from the hypothesis-and-test, algebraic, and spectral clustering based perspectives. Most assume that only a single type/class of subspace is present. Generalizations to multiple types are non-trivial, plagued by challenges such as choice of types and numbers of models, sampling imbalance and parameter tuning. In this work, we formulate the multi-type subspace clustering problem as one of learning non-linear subspace filters via deep multi-layer perceptrons (mlps). The response to the learnt subspace filters serve as the feature embedding that i…
Beihang University（北京航空航天大学）；Griffith University（格里菲斯大学）；University of York, UK（英国约克大学）
Subspace clustering is a useful technique for many computer vision applications in which the intrinsic dimension of high-dimensional data is often smaller than the ambient dimension. Spectral clustering, as one of the main approaches to subspace clustering, often takes on a sparse representation or a low-rank representation to learn a block diagonal self-representation matrix for subspace generation. However, existing methods require solving a large scale convex optimization problem with a large set of data, with computational complexity reaches O(N^3) for N data points. Therefore, the efficie…
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 …
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…
City University of Hong Kong（香港城市大学）；Southeast University（东南大学）
Deep subspace clustering networks have attracted much attention in subspace clustering, in which an auto-encoder non-linearly maps the input data into a latent space, and a fully connected layer named self-expressiveness module is introduced to learn the affinity matrix via a typical regularization term (e.g., sparse or low-rank). However, the adopted regularization terms ignore the connectivity within each subspace, limiting their clustering performance. In addition, the adopted framework suffers from the coupling issue between the auto-encoder module and the self-expressiveness module, makin…
University of Electronic Science and Technology of China（电子科技大学）；Trusted Cloud Computing and Big Data Key Laboratory of Sichuan Province（四川省可信云计算与大数据重点实验室）
In recent years, multi-view subspace clustering has achieved impressive performance due to the exploitation of complementary imformation across multiple views. However, multi-view data can be very complicated and are not easy to cluster in real-world applications. Most existing methods operate on raw data and may not obtain the optimal solution. In this work, we propose a novel multi-view clustering method named smoothed multi-view subspace clustering (SMVSC) by employing a novel technique, i.e., graph filtering, to obtain a smooth representation for each view, in which similar data points hav…
University of Arizona（亚利桑那大学）；University of Texas at Arlington（德克萨斯大学阿灵顿分校）
This article explores subspace clustering algorithms using CUR decompositions, and examines the effect of various hyperparameters in these algorithms on clustering performance on two real-world benchmark datasets, the Hopkins155 motion segmentation dataset and the Yale face dataset. Extensive experiments are done for a variety of sampling methods and oversampling parameters for these datasets, and some guidelines for parameter choices are given for practical applications.
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…
In this paper we present a new model and an algorithm for unsupervised clustering of 2-D data such as images. We assume that the data comes from a union of multilinear subspaces (UOMS) model, which is a specific structured case of the much studied union of subspaces (UOS) model. For segmentation under this model, we develop Multilinear Subspace Clustering (MSC) algorithm and evaluate its performance on the YaleB and Olivietti image data sets. We show that MSC is highly competitive with existing algorithms employing the UOS model in terms of clustering performance while enjoying improvement in …
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…
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 $\ell_1$, …
Beijing University of Technology（北京工业大学）；The University of Sydney（悉尼大学）
Low rank representation (LRR) has recently attracted great interest due to its pleasing efficacy in exploring low-dimensional sub- space structures embedded in data. One of its successful applications is subspace clustering, by which data are clustered according to the subspaces they belong to. In this paper, at a higher level, we intend to cluster subspaces into classes of subspaces. This is naturally described as a clustering problem on Grassmann manifold. The novelty of this paper is to generalize LRR on Euclidean space onto an LRR model on Grassmann manifold in a uniform kernelized LRR fra…
Nanjing University of Information Science and Technology（南京信息工程大学）；Soochow University（苏州大学）；Shanghai Jiao Tong University（上海交通大学）
Dimension reduction is widely regarded as an effective way for decreasing the computation, storage and communication loads of data-driven intelligent systems, leading to a growing demand for statistical methods that allow analysis (e.g., clustering) of compressed data. We therefore study in this paper a novel problem called compressive robust subspace clustering, which is to perform robust subspace clustering with the compressed data, and which is generated by projecting the original high-dimensional data onto a lower-dimensional subspace chosen at random. Given only the compressed data and se…
Australian National University（澳大利亚国立大学）；EPFL（洛桑联邦理工学院）；University of Adelaide（阿德莱德大学）
We present a novel deep neural network architecture for unsupervised subspace clustering. This architecture is built upon deep auto-encoders, which non-linearly map the input data into a latent space. Our key idea is to introduce a novel self-expressive layer between the encoder and the decoder to mimic the "self-expressiveness" property that has proven effective in traditional subspace clustering. Being differentiable, our new self-expressive layer provides a simple but effective way to learn pairwise affinities between all data points through a standard back-propagation procedure. Being nonl…
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…
In subspace clustering, a group of data points belonging to a union of subspaces are assigned membership to their respective subspaces. This paper presents a new approach dubbed Innovation Pursuit (iPursuit) to the problem of subspace clustering using a new geometrical idea whereby subspaces are identified based on their relative novelties. We present two frameworks in which the idea of innovation pursuit is used to distinguish the subspaces. Underlying the first framework is an iterative method that finds the subspaces consecutively by solving a series of simple linear optimization problems, …
Southern Illinois University（南伊利诺伊大学）；University of Hawaii at Hilo（夏威夷大学希洛分校）
Low-rank matrix is desired in many machine learning and computer vision problems. Most of the recent studies use the nuclear norm as a convex surrogate of the rank operator. However, all singular values are simply added together by the nuclear norm, and thus the rank may not be well approximated in practical problems. In this paper, we propose to use a log-determinant (LogDet) function as a smooth and closer, though non-convex, approximation to rank for obtaining a low-rank representation in subspace clustering. Augmented Lagrange multipliers strategy is applied to iteratively optimize the Log…
