Kernelized multi-view subspace clustering via auto-weighted graph learning

Multi-view subspace clustering has been an important and powerful tool for partitioning multi-view data, especially multi-view high-dimensional data. Despite great success, most of the existing multi-view subspace clustering methods still suffer from three limitations. First, they often recover the subspace structure in the original space, which can not guarantee the robustness when handling multi-view data with nonlinear structure. Second, these methods mostly regard subspace clustering and affinity matrix learning as two independent steps, which may not well discover the latent relationships among data samples. Third, many of them ignore the different importance of multiple views, whose performance may be badly affected by the low-quality views in multi-view data. To overcome these three limitations, this paper develops a novel subspace clustering method for multi-view data, termed Kernelized Multi-view Subspace Clustering via Auto-weighted Graph Learning (KMSC-AGL). Specifically, the proposed method implicitly maps the multi-view data from linear space into nonlinear space via kernel-induced functions, so as to exploit the nonlinear structure hidden in data. Furthermore, our method aims to enhance the clustering performance by learning a set of view-specific representations and their affinity matrix in a general framework. By integrating the view weighting strategy into this framework, our method can automatically assign the weights to different views, while learning an optimal affinity matrix that is well-adapted to the subsequent spectral clustering. Extensive experiments are conducted on a variety of multi-view data sets, which have demonstrated the superiority of the proposed method.

     

基于一致图学习的鲁棒多视图子空间聚类

针对多视图数据分析易受原始数据集噪声干扰,以及需要额外的步骤计算聚类结果的问题,提出一种基于一致图学习的鲁棒多视图子空间聚类（RMCGL）算法。首先,在各个视图下学习数据在子空间中的潜在鲁棒表示,并基于该表示得到各视图的相似度矩阵。随后,基于得到的多个相似度矩阵学习一个统一的相似度图。最后,通过对相似度图对应的拉普拉斯矩阵添加秩约束,确保得到的相似度图具有最优的聚类结构,并可直接得到最终的聚类结果。该过程在一个统一的优化框架中完成,能同时学习潜在鲁棒表示、相似度矩阵和一致图。RMCGL算法的聚类精度（ACC）在BBC、100leaves和MSRC数据集上比基于图的多视图聚类（GMC）算法分别提升了3.36个百分点、5.82个百分点和5.71个百分点。实验结果表明,该算法具有良好的聚类效果。     

Diversity and consistency embedding learning for multi-view subspace clustering

Applied Intelligence - With the emergence of multi-view data, many multi-view clustering methods have been developed due to the effectiveness of exploiting the complementary information of...     

Adaptive partial graph learning and fusion for incomplete multi-view clustering

Most of existing multi-view clustering methods assume that different feature views of data are fully observed. However, it is common that only portions of data features can be obtained in many practical applications. The presence of incomplete feature views hinders the performance of the conventional multi-view clustering methods to a large extent. Recently proposed incomplete multi-view clustering methods often focus on directly learning a common representation or a consensus affinity similarity graph from available feature views while ignore the valuable information hidden in the missing views. In this study, we present a novel incomplete multi-view clustering method via adaptive partial graph learning and fusion (APGLF), which can capture the local data structure of both within-view and cross-view. Specifically, we use the available data of each view to learn a corresponding view-specific partial graph, in which the within-view local structure can be well preserved. Then we design a cross-view graph fusion term to learn a consensus complete graph for different views, which can take advantage of the complementary information hidden in the view-specific partial graphs learned from incomplete views. In addition, a rank constraint is imposed on the graph Laplacian matrix of the fused graph to better recover the optimal cluster structure of original data. Therefore, APGLF integrates within-view partial graph learning, cross-view partial graph fusion and cluster structure recovering into a unified framework. Experiments on five incomplete multi-view data sets are conducted to validate the efficacy of APGLF when compared with eight state-of-the-art methods.     

Consistent auto-weighted multi-view subspace clustering

Pattern Analysis and Applications - Because the data in practical applications usually satisfy the assumption of mixing subspaces and contain multiple features, multi-view subspace clustering has...     

Coupled block diagonal regularization for multi-view subspace clustering

Data Mining and Knowledge Discovery - The object of multi-view subspace clustering is to uncover the latent low-dimensional structure by segmenting a collection of high-dimensional multi-source...     

Scalable multi-view clustering with graph filtering

Neural Computing and Applications - With the explosive growth of multi-source data, multi-view clustering has attracted great attention in recent years. Most existing multi-view methods operate in...     

Nonconvex low-rank and sparse tensor representation for multi-view subspace clustering

Applied Intelligence - Multi-view subspace clustering has attracted significant attention due to the popularity of multi-view datasets. The effectiveness of the existing multi-view clustering...     

结构图正则低秩子空间聚类

针对结构稀疏子空间聚类中不能很好地保证相似度矩阵连接性的问题,给出了一个新的统一优化模型。首先,引入了表示系数矩阵的子空间结构范数,增加了低秩表示来揭示高维数据的全局结构。其次,为了使相似度矩阵具有类内统一,类间稀疏的作用,还定义了分组效应来捕获数据的内部几何结构,提出了结构图正则低秩子空间聚类模型。最后使用自适应惩罚的线性化交替法（LADMAP）来得到最优解。实验结果表明,该模型不但可以捕获数据的全局结构,而且还可以捕获数据的内在几何结构,迫使相关数据紧密结合,不相关数据松散分离,从而使得相似度矩阵与分割矩阵变得更加一致。     

基于双重低秩分解的不完整多视图子空间学习

多视图数据在现实世界中应用广泛,各种视角和不同的传感器有助于更好的数据表示,然而,来自不同视图的数据具有较大的差异,尤其当多视图数据不完整时,可能导致训练效果较差甚至失败。为了解决该问题,本文提出了一个基于双重低秩分解的不完整多视图子空间学习算法。所提算法通过两方面来解决不完整多视图问题:一方面,基于双重低秩分解子空间框架,引入潜在因子来挖掘多视图数据中缺失的信息;另一方面,通过预先学习的多视图数据低维特征获得更好的鲁棒性,并以有监督的方式来指导双重低秩分解。实验结果证明,所提算法较之前的多视图子空间学习算法有明显优势;即使对于不完整的多视图数据,该算法也具有良好的分类性能。     

Semi-supervised multi-view binary learning for large-scale image clustering

Applied Intelligence - Large-scale image clustering has attracted sustained attention in machine learning. The traditional methods based on real value representation often suffer from the data...     

Robust deep multi-view subspace clustering networks with a correntropy-induced metric

Since multi-view subspace clustering combines the advantages of deep learning to capture the nonlinear nature of data, deep multi-view subspace clustering methods have demonstrated superior ability to shallow multi-view subspace clustering methods. Most existing methods assume that sample reconstruction errors incurred by noise conform to the prior distribution of the corresponding norm, allowing for simplification of the problem and focus on designing specific regularization on self-representation matrices to exploit consistent and diverse information among different views. However, the noise distributions in different views are always very complex, and in practice the noise distributions do not necessarily conform to this hypothesis. Furthermore, the commonly used diversity regularization based on value-awareness to enhance diversity among different view representations is not sufficiently accurate. To alleviate the above deficiencies, we propose novel robust deep multi-view subspace clustering networks with a correntropy-induced metric (RDMSCNet). (1) A correntropy-induced metric (CIM) is utilized to flexibly handle various complex noise distributions in a data-driven manner to improve the robustness of the model. (2) A position-aware diversity regularization based on the exclusivity definition is employed to enforce the diversity of the different view representations for modelling the consistency and diversity simultaneously. Extensive experiments show that RDMSCNet can deliver enhanced performance over state-of-the-art approaches.

     

On incremental and robust subspace learning

Principal Component Analysis (PCA) has been of great interest in computer vision and pattern recognition. In particular, incrementally learning a PCA model, which is computationally efficient for large-scale problems as well as adaptable to reflect the variable state of a dynamic system, is an attractive research topic with numerous applications such as adaptive background modelling and active object recognition. In addition, the conventional PCA, in the sense of least mean squared error minimisation, is susceptible to outlying measurements. To address these two important issues, we present a novel algorithm of incremental PCA, and then extend it to robust PCA. Compared with the previous studies on robust PCA, our algorithm is computationally more efficient. We demonstrate the performance of these algorithms with experimental results on dynamic background modelling and multi-view face modelling.     

Online multi-view subspace learning via group structure analysis for visual object tracking

In this paper, we focus on incrementally learning a robust multi-view subspace representation for visual object tracking. During the tracking process, due to the dynamic background variation and target appearance changing, it is challenging to learn an informative feature representation of tracking object, distinguished from the dynamic background. To this end, we propose a novel online multi-view subspace learning algorithm (OMEL) via group structure analysis, which consistently learns a low-dimensional representation shared across views with time changing. In particular, both group sparsity and group interval constraints are incorporated to preserve the group structure in the low-dimensional subspace, and our subspace learning model will be incrementally updated to prevent repetitive computation of previous data. We extensively evaluate our proposed OMEL on multiple benchmark video tracking sequences, by comparing with six related tracking algorithms. Experimental results show that OMEL is robust and effective to learn dynamic subspace representation for online object tracking problems. Moreover, several evaluation tests are additionally conducted to validate the efficacy of group structure assumption.     

Weighted and robust learning of subspace representations

A reliable system for visual learning and recognition should enable a selective treatment of individual parts of input data and should successfully deal with noise and occlusions. These requirements are not satisfactorily met when visual learning is approached by appearance-based modeling of objects and scenes using the traditional PCA approach. In this paper we extend standard PCA approach to overcome these shortcomings. We first present a weighted version of PCA, which, unlike the standard approach, considers individual pixels and images selectively, depending on the corresponding weights. Then we propose a robust PCA method for obtaining a consistent subspace representation in the presence of outlying pixels in the training images. The method is based on the EM algorithm for estimation of principal subspaces in the presence of missing data. We demonstrate the efficiency of the proposed methods in a number of experiments.     

基于近邻图改进的块对角子空间聚类算法

块对角表示（BDR）模型可以通过利用线性表示对数据有效地进行聚类,却无法很好地利用高维数据常见的非线性流形结构信息。针对这一问题,提出了基于近邻图改进的块对角子空间聚类（BDRNG）算法来通过近邻图来线性拟合高维数据的局部几何结构,并通过块对角约束来生成具有全局信息的块对角结构。BDRNG同时学习全局信息以及局部数据结构,从而获得更好的聚类表现。由于模型包含近邻图算子和非凸的块对角表示范数,BDRNG 采用了交替最小化来优化求解算法。实验结果如下：在噪声数据集上,BDRNG能够生成稳定的块对角结构系数矩阵,这说明了BDRNG对于噪声数据具有鲁棒性;在标准数据集上,BDRNG的聚类表现均优于BDR,尤其在人脸数据集上,相较于BDR,BDRNG的聚类准确度提高了8%。     

Adaptive subspace learning: an iterative approach for document clustering

The performance of clustering in document space can be influenced by the high dimension of the vectors, because there exists a great deal of redundant information in the high-dimensional vectors, which may make the similarity between vectors inaccurate. Hence, it is very considerable to derive a low-dimensional subspace that contains less redundant information, so that document vectors can be grouped more reasonably. In general, learning a subspace and clustering vectors are treated as two independent steps; in this case, we cannot estimate whether the subspace is appropriate for the method of clustering or vice versa. To overcome this drawback, this paper combines subspace learning and clustering into an iterative procedure named adaptive subspace learning (ASL). Firstly, the intracluster similarity and the intercluster separability of vectors can be increased via the initial cluster indicators in the step of subspace learning, and then affinity propagation is adopted to partition the vectors into a specific number of clusters, so as to update the cluster indicators and repeat subspace learning. In ASL, the obtained subspace can become more suitable for the clustering with the iterative optimization. The proposed method is evaluated using NG20, Classic3 and K1b datasets, and the results are shown to be superior to the conventional methods of document clustering.     

基于自步学习的鲁棒多样性多视角聚类

目的 大数据环境下的多视角聚类是一个非常有价值且极具挑战性的问题。现有的适合大规模多视角数据聚类的方法虽然在一定程度上能够克服由于目标函数非凸性导致的局部最小值,但是缺乏对异常点鲁棒性的考虑,且在样本选择过程中忽略了视角多样性。针对以上问题,提出一种基于自步学习的鲁棒多样性多视角聚类模型（RD-MSPL）。方法 1）通过在目标函数中引入结构稀疏范数L_2,1来建模异常点;2）通过在自步正则项中对样本权值矩阵施加反结构稀疏约束来增加在多个视角下所选择样本的多样性。结果 在Extended Yale B、Notting-Hill、COIL-20和Scene15公开数据集上的实验结果表明：1）在4个数据集上,所提出的RD-MSPL均优于现有的2个最相关多视角聚类方法。与鲁棒多视角聚类方法（RMKMC）相比,聚类准确率分别提升4.9%,4.8%,3.3%和1.3%;与MSPL相比,准确率分别提升7.9%,4.2%,7.1%和6.5%。2）通过自对比实验,证实了所提模型考虑鲁棒性和样本多样性的有效性;3）与单视角以及多个视角简单拼接的实验对比表明,RD-MSPL能够更有效地探索视角之间关联关系。结论 本文提出一种基于自步学习的鲁棒多样性多视角聚类模型,并针对该模型设计了一种高效求解算法。所提方法能够有效克服异常点对聚类性能的影响,在聚类过程中逐步加入不同视角下的多样性样本,在避免局部最小值的同时,能更好地获取不同视角的互补信息。实验结果表明,本文方法优于现有的相关方法。     

Distance metric learning guided adaptive subspace semi-supervised clustering

Most existing semi-supervised clustering algorithms are not designed for handling high-dimensional data. On the other hand, semi-supervised dimensionality reduction methods may not necessarily improve the clustering performance, due to the fact that the inherent relationship between subspace selection and clustering is ignored. In order to mitigate the above problems, we present a semi-supervised clustering algorithm using adaptive distance metric learning (SCADM) which performs semi-supervised clustering and distance metric learning simultaneously. SCADM applies the clustering results to learn a distance metric and then projects the data onto a low-dimensional space where the separability of the data is maximized. Experimental results on real-world data sets show that the proposed method can effectively deal with high-dimensional data and provides an appealing clustering performance.     

Locality-constrained nonnegative robust shape interaction subspace clustering and its applications

In this paper, we present a locality-constrained nonnegative robust shape interaction (LNRSI) subspace clustering method. LNRSI integrates the local manifold structure of data into the robust shape interaction (RSI) in a unified formulation, which guarantees the locality and the low-rank property of the optimal affinity graph. Compared with traditional low-rank representation (LRR) learning method, LNRSI can not only pursuit the global structure of data space by low-rank regularization, but also keep the locality manifold, which leads to a sparse and low-rank affinity graph. Due to the clear block-diagonal effect of the affinity graph, LNRSI is robust to noise and occlusions, and achieves a higher rate of correct clustering. The theoretical analysis of the clustering effect is also discussed. An efficient solution based on linearized alternating direction method with adaptive penalty (LADMAP) is built for our method. Finally, we evaluate the performance of LNRSI on both synthetic data and real computer vision tasks, i.e., motion segmentation and handwritten digit clustering. The experimental results show that our LNRSI outperforms several state-of-the-art algorithms.