基于子空间差异的投影聚类算法

针对传统K-means型软子空间聚类技术中子空间差异度量定义的困难问题,提出一种基于概率距离的子空间差异表示模型,以此为基础提出一种自适应的投影聚类算法。该方法首先基于子空间聚类理论提出一个描述各簇类所关联的软子空间之间的相异度公式;其次,将其与软子空间聚类相结合,定义了聚类目标优化函数,并根据局部搜索策略给出了聚类算法过程。在合成和实际数据集上进行了一系列实验,结果表明该算法引入子空间比较可以为簇类学习更优的软子空间;与现有主流子空间聚类算法相比,所提算法大幅度提升了聚类精度,适用于高维数据聚类分析。     

基于子空间聚类的高维数据可视分析方法综述

随着信息技术的飞速发展和大数据时代的来临,数据呈现出高维性、非线性等复杂特征。对于高维数据来说,在全维空间上往往很难找到反映分布模式的特征区域,而大多数传统聚类算法仅对低维数据具有良好的扩展性。因此,传统聚类算法在处理高维数据的时候,产生的聚类结果可能无法满足现阶段的需求。而子空间聚类算法搜索存在于高维数据子空间中的簇,将数据的原始特征空间分为不同的特征子集,减少不相关特征的影响,保留原数据中的主要特征。通过子空间聚类方法可以发现高维数据中不易展现的信息,并通过可视化技术展现数据属性和维度的内在结构,为高维数据可视分析提供了有效手段。总结了近年来基于子空间聚类的高维数据可视分析方法研究进展,从基于特征选择、基于子空间探索、基于子空间聚类的3种不同方法进行阐述,并对其交互分析方法和应用进行分析,同时对高维数据可视分析方法的未来发展趋势进行了展望。     

子空间聚类算法的研究新进展

高维数据聚类是聚类技术的难点和重点,子空间聚类是实现高维数据集聚类的有效途径,它是在高维数据空间中对传统聚类算法的一种扩展,其思想是将搜索局部化在相关维中进行.该文从不同的搜索策略即自顶向下策略和自底向上策略两个方面对子空间聚类算法的思想进行了介绍,对近几年提出的子空间聚类算法作了综述,从算法所需参数、算法对参数的敏感度、算法的可伸缩性以及算法发现聚类的形状等多个方面对典型的子空间聚类算法进行了比较分析,对子空间聚类算法面临的挑战和未来的发展趋势进行了讨论.     

基于稀疏子空间聚类的多层网络社团检测

现有的子空间聚类方法大多只适用于单层网络,或者仅对多层网络中每层的聚类结果简单地进行平均,未考虑每层网络中包含信息量不同的特点,致使聚类性能受限。针对该问题,提出一种面向多层网络的稀疏子空间聚类方法。将距离正则项和非负约束条件集成到稀疏子空间聚类框架中,从而在聚类时能够同时利用数据的全局信息和局部信息进行图学习。此外,通过引入稀疏约束使学习到的图具有更清晰的聚类结构,并设计迭代算法进行优化求解。在多个真实数据集上的实验结果表明,该方法能够挖掘网络不同层的互补信息,得到准确的一致性联合稀疏表示,有效提高社团聚类性能。     

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.

     

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.     

自适应的软子空间聚类算法

软子空间聚类是高维数据分析的一种重要手段.现有算法通常需要用户事先设置一些全局的关键参数,且没有考虑子空间的优化.提出了一个新的软子空间聚类优化目标函数,在最小化子空间簇类的簇内紧凑度的同时,最大化每个簇类所在的投影子空间.通过推导得到一种新的局部特征加权方式,以此为基础提出一种自适应的k-means型软子空间聚类算法.该算法在聚类过程中根据数据集及其划分的信息,动态地计算最优的算法参数.在实际应用和合成数据集上的实验结果表明,该算法大幅度提高了聚类精度和聚类结果的稳定性.     

一种基于数据流的软子空间聚类算法

针对高维数据的聚类研究表明,样本在不同数据簇往往与某些特定的数据特征子集相对应.因此,子空间聚类技术越来越受到关注.然而,现有的软子空间聚类算法都是基于批处理技术的聚类算法,不能很好地应用于高维数据流或大规模数据的聚类研究中.为此,利用模糊可扩展聚类框架,与熵加权软子空间聚类算法相结合,提出了一种有效的熵加权流数据软子空间聚类算法——EWSSC(entropy-weighting streaming subspace clustering).该算法不仅保留了传统软子空间聚类算法的特性,而且利用了模糊可扩展聚类策略,将软子空间聚类算法应用于流数据的聚类分析中.实验结果表明,EWSSC 算法对于高维数据流可以得到与批处理软子空间聚类方法近似一致的实验结果.     

一种基于网格方法的高维数据流子空间聚类算法

基于对网格聚类方法的分析,结合由底向上的网格方法和自顶向下的网格方法,设计了一个能在线处理高维数据流的子空间聚类算法。通过利用由底向上网格方法对数据的压缩能力和自顶向下网格方法处理高维数据的能力,算法能基于对数据流的一次扫描,快速识别数据中位于不同子空间内的簇。理论分析以及在多个数据集上的实验表明算法具有较高的计算精度与计算效率。     

生成式不完整多视图数据聚类

基于自表示子空间聚类的多视图聚类引起越来越多的关注. 大多数现有算法假设每个样本的所有视图都可获得, 然而在实际应用中, 由于各种因素, 可能会导致某些视图缺失. 为了对视图不完整数据进行聚类, 本文提出了一种在统一框架下同时执行缺失视图补全和多视图子空间聚类的方法. 具体地, 缺失视图是由已观测视图数据约束的隐表示生成的. 此外, 多秩张量应用于挖掘不同视图之间的高阶相关性. 这样通过隐表示和高阶张量同时挖掘了不同视图以及所有样本(即使是不完整视图样本)之间的相关性. 本文使用增广拉格朗日交替方向最小化(AL-ADM)方法求解优化问题. 在真实数据集上的实验结果表明, 我们的方法优于最新的多视图聚类算法, 具有更好的聚类准确度和鲁棒性.     

Projective clustering by histograms

Recent research suggests that clustering for high-dimensional data should involve searching for "hidden" subspaces with lower dimensionalities, in which patterns can be observed when data objects are projected onto the subspaces. Discovering such interattribute correlations and location of the corresponding clusters is known as the projective clustering problem. We propose an efficient projective clustering technique by histogram construction (EPCH). The histograms help to generate "signatures", where a signature corresponds to some region in some subspace, and signatures with a large number of data objects are identified as the regions for subspace clusters. Hence, projected clusters and their corresponding subspaces can be uncovered. Compared to the best previous methods to our knowledge, this approach is more flexible in that less prior knowledge on the data set is required, and it is also much more efficient. Our experiments compare behaviors and performances of this approach and other projective clustering algorithms with different data characteristics. The results show that our technique is scalable to very large databases, and it is able to return accurate clustering results.     

稀疏子空间聚类综述

稀疏子空间聚类(Sparse subspace clustering, SSC)是一种基于谱聚类的数据聚类框架. 高维数据通常分布于若干个低维子空间的并上, 因此高维数据在适当字典下的表示具有稀疏性. 稀疏子空间聚类利用高维数据的稀疏表示系数构造相似度矩阵, 然后利用谱聚类方法得到数据的子空间聚类结果. 其核心是设计能够揭示高维数据真实子空间结构的表示模型, 使得到的表示系数及由此构造的相似度矩阵有助于精确的子空间聚类. 稀疏子空间聚类在机器学习、计算机视觉、图像处理和模式识别等领域已经得到了广泛的研究和应用, 但仍有很大的发展空间. 本文对已有稀疏子空间聚类方法的模型、算法和应用等方面进行详细阐述, 并分析存在的不足, 指出进一步研究的方向.     

稀疏条件下的重叠子空间聚类算法

现有子空间聚类算法不能很好地平衡子空间数据的稠密性和不同子空间数据稀疏性的关系,且无法处理数据的重叠问题。针对上述问题,提出一种稀疏条件下的重叠子空间聚类(OSCSC)算法。算法利用L1范数和Frobenius范数的混合范数表示方法建立子空间表示模型,并对L1范数正则项进行加权处理,提高不同子空间的稀疏性和同一子空间的稠密性;然后对划分好的子空间使用一种服从指数族分布的重叠概率模型进行二次校验,判断不同子空间数据的重叠情况,进一步提高聚类的准确率。在人造数据集和真实数据集上分别进行测试,实验结果表明,OSCSC算法能够获得良好的聚类结果。     

Evolutionary subspace clustering using variable genome length

Subspace clustering is a data-mining task that groups similar data objects and at the same time searches the subspaces where similarities appear. For this reason, subspace clustering is recognized as more general and complicated than standard clustering. In this article, we present ChameleoClust+, a bioinspired evolutionary subspace clustering algorithm that takes advantage of an evolvable genome structure to detect various numbers of clusters located in different subspaces. ChameleoClust+ incorporates several biolike features such as a variable genome length, both functional and nonfunctional elements, and mutation operators including large rearrangements. It was assessed and compared with the state-of-the-art methods on a reference benchmark using both real-world and synthetic data sets. Although other algorithms may need complex parameter settings, ChameleoClust+ needs to set only one subspace clustering ad hoc and intuitive parameter: the maximal number of clusters. The remaining parameters of ChameleoClust+ are related to the evolution strategy (eg, population size, mutation rate), and a single setting for all of them turned out to be effective for all the benchmark data sets. A sensitivity analysis has also been carried out to study the impact of each parameter on the subspace clustering quality.     

Mutual-manifold regularized robust fast latent LRR for subspace recovery and learning

In this paper, we propose a simple yet effective low-rank representation (LRR) and subspace recovery model called mutual-manifold regularized robust fast latent LRR. Our model improves the representation ability and robustness from twofold. Specifically, our model is built on the Frobenius norm-based fast latent LRR decomposing given data into a principal feature part, a salient feature part and a sparse error, but improves it clearly by designing mutual-manifold regularization to encode, preserve and propagate local information between coefficients and salient features. The mutual-manifold regularization is defined by using the coefficients as the adaptive reconstruction weights for salient features and constructing a Laplacian matrix over salient features for the coefficients. Thus, some important local topology structure information can be propagated between them, which can make the discovered subspace structures and features potentially more accurate for the data representations. Besides, our approach also considers to improve the robust properties of subspace recovery against noise and sparse errors in coefficients, which is realized by decomposing original coefficients matrix into an error-corrected part and a sparse error part fitting noise in coefficients, and the recovered coefficients are then used for robust subspace recovery. Experimental results on several public databases demonstrate that our method can outperform other related algorithms.

     

Density Conscious Subspace Clustering for High-Dimensional Data

Instead of finding clusters in the full feature space, subspace clustering is an emergent task which aims at detecting clusters embedded in subspaces. Most of previous works in the literature are density-based approaches, where a cluster is regarded as a high-density region in a subspace. However, the identification of dense regions in previous works lacks of considering a critical problem, called "the density divergence problem” in this paper, which refers to the phenomenon that the region densities vary in different subspace cardinalities. Without considering this problem, previous works utilize a density threshold to discover the dense regions in all subspaces, which incurs the serious loss of clustering accuracy (either recall or precision of the resulting clusters) in different subspace cardinalities. To tackle the density divergence problem, in this paper, we devise a novel subspace clustering model to discover the clusters based on the relative region densities in the subspaces, where the clusters are regarded as regions whose densities are relatively high as compared to the region densities in a subspace. Based on this idea, different density thresholds are adaptively determined to discover the clusters in different subspace cardinalities. Due to the infeasibility of applying previous techniques in this novel clustering model, we also devise an innovative algorithm, referred to as DENCOS (DENsity COnscious Subspace clustering), to adopt a divide-and-conquer scheme to efficiently discover clusters satisfying different density thresholds in different subspace cardinalities. As validated by our extensive experiments on various data sets, DENCOS can discover the clusters in all subspaces with high quality, and the efficiency of DENCOS outperformes previous works.     

k-means型软子空间聚类算法

软子空间聚类是聚类研究领域的一个重要分支和研究热点。高维空间聚类以数据分布稀疏和"维度效应"现象等问题而成为难点。在分析现有软子空间聚类算法不足的基础上,引入子空间差异的概念;在此基础上,结合簇内紧凑度的信息来设计新的目标优化函数;提出了一种新的k-means型软子空间聚类算法,该算法在聚类过程中无需设置额外的参数。理论分析与实验结果表明,相对于其他的软子空间算法,该算法具有更好的聚类精度。     

A Generalized Fuzzy Clustering Regularization Model With Optimality Tests and Model Complexity Analysis

In this paper, we propose a generalized fuzzy clustering regularization (GFCR) model and then study its theoretical properties. GFCR unifies several fuzzy clustering algorithms, such as fuzzy c-means (FCM), maximum entropy clustering (MEC), fuzzy clustering based on Fermi-Dirac entropy, and fuzzy bidirectional associative clustering network, etc. The proposed GFCR becomes an alternative model of the generalized FCM (GFCM) that was recently proposed by Yu and Yang. To advance theoretical study, we have the following three considerations. 1) We give an optimality test to monitor if GFCR converges to a local minimum. 2) We relate the GFCR optimality tests to Occam's razor principle, and then analyze the model complexity for fuzzy clustering algorithms. 3) We offer a general theoretical method to evaluate the performance of fuzzy clustering algorithms. Finally, some numerical experiments are used to demonstrate the validity of our theoretical results and complexity analysis.     

An affine subspace clustering algorithm based on ridge regression

Recent subspace clustering algorithms, which use sparse or low-rank representations, conduct clustering by considering the errors and noises into their objective functions. Then, the similarity matrix is solved via alternating direction method of multipliers. However, these approaches are subject to the restriction that the characteristic of errors and outliers in sample points should be known as the prior information. Furthermore, these algorithms are time-consuming during the iterative process. Motivated by this observation, this paper proposes a new subspace clustering algorithm: an affine subspace clustering algorithm based on ridge regression. The method introduces ridge regression as objective function which applies affine criteria into subspace clustering. An analytic solution to the problem has been determined for the coefficient matrix. Experimental results obtained on face datasets demonstrate that the proposed method not only improves the accuracy of the clustering results, but also enhances the robustness. Furthermore, the proposed method reduces the computational complexity.     

图正则化非负矩阵分解的异质网社区发现

挖掘数据网络中有价值的、具有稳定性的社区,对网络信息的获取、推荐及网络的演化预测具有重要的价值。针对现有异质网络聚类方法难以在同一维度有效整合网络中异质信息的问题,提出了一种基于图正则化非负矩阵分解的异质网络聚类方法。通过加入图正则项,将中心类型子空间和属性类型子空间的内部连接关系作为约束项,引入到非负矩阵分解模型中,从而找到高维数据在低维空间的紧致嵌入,成功消除了异质节点之间的部分噪声,同时,对反映不同子网络共有潜在结构的共识矩阵进行优化,有效整合异质信息,并且在降维过程中较大限度地保留了异质信息的完整性,提高了异质网络聚类方法的精度,在真实世界数据集上的实验结果也验证了该方法的有效性。