Fast density-weighted low-rank approximation spectral clustering

While spectral clustering can produce high-quality clusterings on small data sets, computational cost makes it infeasible for large data sets. Affinity Propagation (AP) has a limitation that it is hard to determine the value of parameter ‘preference’ which can lead to an optimal clustering solution. These problems limit the scope of application of the two methods. In this paper, we develop a novel fast two-stage spectral clustering framework with local and global consistency. Under this framework, we propose a Fast density-Weighted low-rank Approximation Spectral Clustering (FWASC) algorithm to address the above issues. The proposed algorithm is a high-quality graph partitioning method, and simultaneously considers both the local and global structure information contained in the data sets. Specifically, we first present a new Fast Two-Stage AP (FTSAP) algorithm to coarsen the input sparse graph and produce a small number of final representative exemplars, which is a simple and efficient sampling scheme. Then we present a density-weighted low-rank approximation spectral clustering algorithm to operate those representative exemplars on the global underlying structure of data manifold. Experimental results show that our algorithm outperforms the state-of-the-art spectral clustering and original AP algorithms in terms of speed, memory usage, and quality.     

Semi-supervised graph clustering: a kernel approach

Semi-supervised clustering algorithms aim to improve clustering results using limited supervision. The supervision is generally given as pairwise constraints; such constraints are natural for graphs, yet most semi-supervised clustering algorithms are designed for data represented as vectors. In this paper, we unify vector-based and graph-based approaches. We first show that a recently-proposed objective function for semi-supervised clustering based on Hidden Markov Random Fields, with squared Euclidean distance and a certain class of constraint penalty functions, can be expressed as a special case of the weighted kernel k-means objective (Dhillon et al., in Proceedings of the 10th International Conference on Knowledge Discovery and Data Mining, 2004a). A recent theoretical connection between weighted kernel k-means and several graph clustering objectives enables us to perform semi-supervised clustering of data given either as vectors or as a graph. For graph data, this result leads to algorithms for optimizing several new semi-supervised graph clustering objectives. For vector data, the kernel approach also enables us to find clusters with non-linear boundaries in the input data space. Furthermore, we show that recent work on spectral learning (Kamvar et al., in Proceedings of the 17th International Joint Conference on Artificial Intelligence, 2003) may be viewed as a special case of our formulation. We empirically show that our algorithm is able to outperform current state-of-the-art semi-supervised algorithms on both vector-based and graph-based data sets.     

密度敏感的层次化聚类算法研究

以密度敏感距离作为相似性测度,结合近邻传播聚类算法和谱聚类算法,提出了一种密度敏感的层次化聚类算法。算法以密度敏感距离为相似度,多次应用近邻传播算法在数据集中选取一些“可能的类代表点”;用谱聚类算法将“可能的类代表点”再聚类得到“最终的类代表点”;每个数据点根据其类代表点的类标签信息找到自己的类标签。实验结果表明,该算法在处理时间、内存占用率和聚类错误率上都优于传统的近邻传播算法和谱聚类算法。     

Fast semi-supervised clustering with enhanced spectral embedding

In recent years, semi-supervised clustering (SSC) has aroused considerable interests from the machine learning and data mining communities. In this paper we propose a novel SSC approach with enhanced spectral embedding (ESE), which not only considers the geometric structure information contained in data sets, but also can make use of the given side information such as pairwise constraints. Specially, we first construct a symmetry-favored k-NN graph, which is highly robust to noise and outliers, and can reflect the underlying manifold structures of data sets. Then we learn the enhanced spectral embedding towards an ideal data representation as consistent with the given pairwise constraints as possible. Finally, by using the regularization of spectral embedding we formulate learning the new data representation as a semidefinite-quadratic-linear programming (SQLP) problem, which can be efficiently solved. Experimental results on a variety of synthetic and real-world data sets show that our ESE approach outperforms the state-of-the-art SSC algorithms in terms of speed and quality on both vector-based and graph-based clustering.     

Graph-based multimodal clustering for social multimedia

Real world datasets often consist of data expressed through multiple modalities. Clustering such datasets is in most cases a challenging task as the involved modalities are often heterogeneous. In this paper we propose a graph-based multimodal clustering approach. The proposed approach utilizes an example relevant clustering in order to learn a model of the “same cluster” relationship between a pair of items. This model is subsequently used in order to organize the items of the collection to be clustered in a graph, where the nodes represent the items and a link between a pair of nodes exists if the model predicted that the corresponding pair of items belong to the same cluster. Eventually, a graph clustering algorithm is applied on the graph in order to produce the final clustering. The proposed approach is applied on two problems that are typically treated using clustering techniques; in particular, it is applied on the problem of detecting social events and to the problem of discovering different landmark views in collections of social multimedia.     

改进线性邻近点传播在时间序列分类中的运用

线性邻近点传播(LNP)是一种非常有效的基于图的半监督分类方法,而类重叠与数据分布不平衡问题会使LNP构造图时由于选择的邻居不合理而影响分类性能。采用谱聚类来分析数据的分布,根据聚类结果对邻居选择时的距离度量进行调整,使得选择的邻居更合理。将基于谱聚类的LNP方法应用于时间序列分类,在UCR时间序列挖掘库的四个数据集上进行实验,结果表明该方法比LNP方法具有更高的分类准确率。     

基于MapReduce的分布式近邻传播聚类算法

随着信息技术迅速发展,数据规模急剧增长,大规模数据处理非常具有挑战性.许多并行算法已被提出,如基于MapReduce的分布式K平均聚类算法、分布式谱聚类算法等.近邻传播(affinity propagation,AP)聚类能克服K平均聚类算法的局限性,但是处理海量数据性能不高.为有效实现海量数据聚类,提出基于MapReduce的分布式近邻传播聚类算法——DisAP.该算法先将数据点随机划分为规模相近的子集,并行地用AP聚类算法稀疏化各子集,然后融合各子集稀疏化后的数据再次进行AP聚类,由此产生的聚类代表作为所有数据点的聚类中心.在人工合成数据、人脸图像数据、IRIS数据以及大规模数据集上的实验表明:DisAP算法对数据规模有很好的适应性,在保持AP聚类效果的同时可有效缩减聚类时间.     

一种基于极大熵的快速无监督线性降维方法

现实世界中高维数据无处不在,然而在高维数据中往往存在大量的冗余和噪声信息,这导致很多传统聚类算法在对高维数据聚类时不能获得很好的性能.实践中发现高维数据的类簇结构往往嵌入在较低维的子空间中.因而,降维成为挖掘高维数据类簇结构的关键技术.在众多降维方法中,基于图的降维方法是研究的热点.然而,大部分基于图的降维算法存在以下两个问题:(1)需要计算或者学习邻接图,计算复杂度高;(2)降维的过程中没有考虑降维后的用途.针对这两个问题,提出一种基于极大熵的快速无监督降维算法MEDR. MEDR算法融合线性投影和极大熵聚类模型,通过一种有效的迭代优化算法寻找高维数据嵌入在低维子空间的潜在最优类簇结构. MEDR算法不需事先输入邻接图,具有样本个数的线性时间复杂度.在真实数据集上的实验结果表明,与传统的降维方法相比, MEDR算法能够找到更好地将高维数据投影到低维子空间的投影矩阵,使投影后的数据有利于聚类.     

CMvSC:知识迁移下的深度一致性多视图谱聚类网络

谱聚类是聚类分析中极具代表性的方法之一,由于其对数据结构没有太多假设要求,受到了研究者们的广泛关注.但传统的谱聚类算法通常受到谱嵌入的可扩展性和泛化性的限制,即:无法应对大规模设置和复杂数据分布.为克服以上缺陷,旨在引入深度学习框架提升谱聚类的泛化能力与可扩展能力,同时,结合多视图学习挖掘数据样本的多样性特征,从而提出...     

Hyperspectral image classification using graph-based wavelet transform

ABSTRACT

Graph-based methods are developed to efficiently extract data information. In particular, these methods are adopted for high-dimensional data classification by exploiting information residing on weighted graphs. In this paper, we propose a new hyperspectral texture classifier based on graph-based wavelet transform. This recent graph transform allows extracting textural features from a constructed weighted graph using sparse representative pixels of hyperspectral image. Different measurements of spectral similarity between representative pixels are tested to decorrelate close pixels and improve the classification precision. To achieve the hyperspectral texture classification, Support Vector Machine is applied on spectral graph wavelet coefficients. Experimental results obtained by applying the proposed approach on Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) and Reflective Optics System Imaging Spectrometer (ROSIS) datasets provide good accuracy which could exceed 98.7%. Compared to other famous classification methods as conventional deep learning-based methods, the proposed method achieves better classification performance. Results have shown the effectiveness of the method in terms of robustness and accuracy.     

Adaptive edge weighting for graph-based learning algorithms

Graph-based learning algorithms including label propagation and spectral clustering are known as the effective state-of-the-art algorithms for a variety of tasks in machine learning applications. Given input data, i.e. feature vectors, graph-based methods typically proceed with the following three steps: (1) generating graph edges, (2) estimating edge weights and (3) running a graph based algorithm. The first and second steps are difficult, especially when there are only a few (or no) labeled instances, while they are important because the performance of graph-based methods heavily depends on the quality of the input graph. For the second step of the three-step procedure, we propose a new method, which optimizes edge weights through a local linear reconstruction error minimization under a constraint that edges are parameterized by a similarity function of node pairs. As a result our generated graph can capture the manifold structure of the input data, where each edge represents similarity of each node pair. To further justify this approach, we also provide analytical considerations for our formulation such as an interpretation as a cross-validation of a propagation model in the feature space, and an error analysis based on a low dimensional manifold model. Experimental results demonstrated the effectiveness of our adaptive edge weighting strategy both in synthetic and real datasets.     

A density-adaptive affinity propagation clustering algorithm based on spectral dimension reduction

As a novel clustering method, affinity propagation (AP) clustering can identify high-quality cluster centers by passing messages between data points. But its ultimate cluster number is affected by a user-defined parameter called self-confidence. When aiming at a given number of clusters due to prior knowledge, AP has to be launched many times until an appropriate setting of self-confidence is found. K-AP algorithm overcomes this disadvantage by introducing a constraint in the process of message passing to exploit the immediate results of K clusters. The key to K-AP clustering is constructing a suitable similarity matrix, which can truly reflect the intrinsic structure of the dataset. In this paper, a density-adaptive similarity measure is designed to describe the relations between data points more reasonably. Meanwhile, in order to solve the difficulties faced by K-AP algorithm in high-dimensional data sets, we use the dimension reduction method based on spectral graph theory to map the original data points to a low-dimensional eigenspace and propose a density-adaptive AP clustering algorithm based on spectral dimension reduction. Experiments show that the proposed algorithm can effectively deal with the clustering problem of datasets with complex structure and multiple scales, avoiding the singularity problem caused by the high-dimensional eigenvectors. Its clustering performance is better than AP clustering algorithm and K-AP algorithm.     

基于相似图投影学习的多视图聚类

随着数据来源方式的多样化发展,多视图聚类成为研究热点。大多数算法过于专注利用图结构寻求一致表示,却忽视了如何学习图结构本身;此外,一些方法通常基于固定视图进行算法优化。为了解决这些问题,提出了一种基于相似图投影学习的多视图聚类算法(multi-view clustering based on similarity graph projection learning, MCSGP),通过利用投影图有效地融合了全局结构信息和局部潜在信息到一个共识图中,而不仅是追求每个视图与共识图的一致性。通过在共识图矩阵的图拉普拉斯矩阵上施加秩约束,该算法能够自然地将数据点划分到所需数量的簇中。在两个人工数据集和七个真实数据集的实验中,MCSGP算法在人工数据集上的聚类效果表现出色,同时在涉及21个指标的真实数据集中,有17个指标达到了最优水平,从而充分证明了该算法的优越性能。     

基于共享最近邻的密度自适应邻域谱聚类算法

在谱聚类算法没有先验信息的情况下,对于具有复杂形状和不同密度变化的数据集很难构建合适的相似图,且基于欧氏距离的高斯核函数的相似性度量忽略了全局一致性。针对该问题,提出一种基于共享最近邻的密度自适应邻域谱聚类算法（SC-DANSN）。通过一种无参数的密度自适应邻域构建方法构建无向图,将共享最近邻作为衡量样本之间的相似性度量进而消除参数对构建相似图的影响,体现全局和局部的一致性。实验结果表明,SC-DANSN算法相比K-means算法和基于K最近邻的谱聚类算法（SC-KNN）具有更高的聚类精度,同时相比SC-KNN算法对参数的选取敏感性更低。     

A novel graph-based clustering method using noise cutting

Recently, many methods have appeared in the field of cluster analysis. Most existing clustering algorithms have considerable limitations in dealing with local and nonlinear data patterns. Algorithms based on graphs provide good results for this problem. However, some widely used graph-based clustering methods, such as spectral clustering algorithms, are sensitive to noise and outliers. In this paper, a cut-point clustering algorithm (CutPC) based on a natural neighbor graph is proposed. The CutPC method performs noise cutting when a cut-point value is above the critical value. Normally, the method can automatically identify clusters with arbitrary shapes and detect outliers without any prior knowledge or preparatory parameter settings. The user can also adjust a coefficient to adapt clustering solutions for particular problems better. Experimental results on various synthetic and real-world datasets demonstrate the obvious superiority of CutPC compared with k-means, DBSCAN, DPC, SC, and DCore.     

Graph optimization for dimensionality reduction with sparsity constraints

Graph-based dimensionality reduction (DR) methods play an increasingly important role in many machine learning and pattern recognition applications. In this paper, we propose a novel graph-based learning scheme to conduct Graph Optimization for Dimensionality Reduction with Sparsity Constraints (GODRSC). Different from most of graph-based DR methods where graphs are generally constructed in advance, GODRSC aims to simultaneously seek a graph and a projection matrix preserving such a graph in one unified framework, resulting in an automatically updated graph. Moreover, by applying an l₁ regularizer, a sparse graph is achieved, which models the “locality” structure of data and contains natural discriminating information. Finally, extensive experiments on several publicly available UCI and face databases verify the feasibility and effectiveness of the proposed method.     

基于黎曼流形的多视角谱聚类算法

现有的多视角谱聚类算法大多只线性结合了各视角的基拉普拉斯矩阵,未考虑不同视角数据的差异性对最优拉普拉斯矩阵的影响,存在聚类性能受限的问题。提出一种基于黎曼几何均值与高阶拉普拉斯矩阵的谱聚类算法(RMMSC),挖掘多视角数据中的高阶连接信息与流形信息,提高最优拉普拉斯矩阵对各视角的信息利用率。按一定的权重线性结合数据单一视角的各阶拉普拉斯矩阵,得到每个视角的基拉普拉斯矩阵,通过低阶与高阶连接信息的结合使用,充分体现多视角数据集的全局结构。在此基础上,计算各视角基拉普拉斯矩阵的黎曼几何均值,将其作为最优拉普拉斯矩阵输入谱聚类算法,得到聚类结果。相比于传统矩阵算数均值的计算,基于黎曼流形的黎曼几何均值能够更好地恢复互补层数据的流形信息。实验结果表明,RMMSC在多组标准数据集上聚类效果优于ONMSC、MLAN、AMGL等算法。其中,在Flower17数据集上,精确度较基准算法ONMSC提高了2.14%,纯度提高了1.7%,且收敛性较好。     

免疫克隆选择图划分方法

为了解决谱聚类方法中大规模的相似性矩阵的存储和特征分解困难的问题,利用权核K-均值算法的目标函数和图谱划分准则的等价性,将图谱划分准则作为免疫克隆选择优化算法的亲和度函数,提出一种利用免疫克隆选择优化算法求解图谱划分问题的新方法——免疫克隆选择图划分方法。该方法在免疫克隆选择操作的过程中引入了一个个体修正算子,使得个体以更快的速度向更优的个体进化。此外,在新方法中还引入了流形距离测度来构造相似性矩阵,使得新算法可以有效处理具有复杂结构的数据。采用人工数据集、USPS手写体数字识别和UMIST人脸识别的仿真实验验证了新方法的有效性和鲁棒性。     

Kernel clustering using a hybrid memetic algorithm

This paper proposes a novel kernel clustering algorithm using a hybrid memetic algorithm for clustering complex, unlabeled, and linearly non-separable datasets. The kernel function can transform nonlinear data into a high dimensional feature space. It increases the probability of the linear separability of the patterns within the transformed space and simplifies the associated data structure. According to the distribution of various datasets, three local learning operators are designed; meanwhile double mutation operators incorporated into local learning operators to further enhance the ability of global exploration and overcome premature convergence effectively. The performance comparisons of the proposed method with k-means, kernel k-means, global kernel k-means and spectral clustering algorithms on artificial datasets and UCI datasets indicate that the proposed clustering algorithm outperforms the compared algorithms.     

Incremental K-clique clustering in dynamic social networks

Clustering entities into dense parts is an important issue in social network analysis. Real social networks usually evolve over time and it remains a problem to efficiently cluster dynamic social networks. In this paper, a dynamic social network is modeled as an initial graph with an infinite change stream, called change stream model, which naturally eliminates the parameter setting problem of snapshot graph model. Based on the change stream model, the incremental version of a well known k-clique clustering problem is studied and incremental k-clique clustering algorithms are proposed based on local DFS (depth first search) forest updating technique. It is theoretically proved that the proposed algorithms outperform corresponding static ones and incremental spectral clustering algorithm in terms of time complexity. The practical performances of our algorithms are extensively evaluated and compared with the baseline algorithms on ENRON and DBLP datasets. Experimental results show that incremental k-clique clustering algorithms are much more efficient than corresponding static ones, and have no accumulating errors that incremental spectral clustering algorithm has and can capture the evolving details of the clusters that snapshot graph model based algorithms miss.