Cumulative voting consensus method for partitions with variable number of clusters

Over the past few years, there has been a renewed interest in the consensus clustering problem. Several new methods have been proposed for finding a consensus partition for a set of n data objects that optimally summarizes an ensemble. In this paper, we propose new consensus clustering algorithms with linear computational complexity in n. We consider clusterings generated with random number of clusters, which we describe by categorical random variables. We introduce the idea of cumulative voting as a solution for the problem of cluster label alignment, where, unlike the common one-to-one voting scheme, a probabilistic mapping is computed. We seek a first summary of the ensemble that minimizes the average squared distance between the mapped partitions and the optimal representation of the ensemble, where the selection criterion of the reference clustering is defined based on maximizing the information content as measured by the entropy. We describe cumulative vote weighting schemes and corresponding algorithms to compute an empirical probability distribution summarizing the ensemble. Given the arbitrary number of clusters of the input partitions, we formulate the problem of extracting the optimal consensus as that of finding a compressed summary of the estimated distribution that preserves maximum relevant information. An efficient solution is obtained using an agglomerative algorithm that minimizes the average generalized Jensen-Shannon divergence within the cluster. The empirical study demonstrates significant gains in accuracy and superior performance compared to several recent consensus clustering algorithms.     

Particle Swarm Clustering in clustering ensembles: Exploiting pruning and alignment free consensus

A clustering ensemble combines in a consensus function the partitions generated by a set of independent base clusterers. In this study both the employment of particle swarm clustering (PSC) and ensemble pruning (i.e., selective reduction of base partitions) using evolutionary techniques in the design of the consensus function is investigated. In the proposed ensemble, PSC plays two roles. First, it is used as a base clusterer. Second, it is employed in the consensus function; arguably the most challenging element of the ensemble. The proposed consensus function exploits a representation for the base partitions that makes cluster alignment unnecessary, allows for the combination of partitions with different number of clusters, and supports both disjoint and overlapping (fuzzy, probabilistic, and possibilistic) partitions. Results on both synthetic and real-world data sets show that the proposed ensemble can produce statistically significant better partitions, in terms of the validity indices used, than the best base partition available in the ensemble. In general, a small number of selected base partitions (below 20% of the total) yields the best results. Moreover, results produced by the proposed ensemble compare favorably to those of state-of-the-art clustering algorithms, and specially to swarm based clustering ensemble algorithms.     

基于投票机制的融合聚类算法

以一趟聚类算法作为划分数据的基本算法,讨论聚类融合问题.通过重复使用一趟聚类算法划分数据,并随机选择阈值和数据输入顺序,得到不同的聚类结果,将这些聚类结果映射为模式间的关联矩阵,在关联矩阵上使用投票机制获得最终的数据划分.在真实数据集和人造数据集上检验了提出的聚类融合算法,并与相关聚类算法进行了对比,实验结果表明,文中提出的算法是有效可行的.     

A novel member enhancement-based clustering ensemble algorithm

Clustering ensemble is a popular approach for identifying data clusters that combines the clustering results from multiple base clustering algorithms to produce more accurate and robust data clusters. However, the performance of clustering ensemble algorithms is highly dependent on the quality of clustering members. To address this problem, this paper proposes a member enhancement-based clustering ensemble (MECE) algorithm that selects the ensemble members by considering their distribution consistency. MECE has two main components, called heterocluster splitting and homocluster merging. The first component estimates two probability density functions (p.d.f.s) estimated on the sample points of an heterocluster and represents them using a Gaussian distribution and a Gaussian mixture model. If the random numbers generated by these two p.d.f.s have different probability distributions, the heterocluster is then split into smaller clusters. The second component merges the clusters that have high neighborhood densities into a homocluster, where the neighborhood density is measured using a novel evaluation criterion. In addition, a co-association matrix is presented, which serves as a summary for the ensemble of diverse clusters. A series of experiments were conducted to evaluate the feasibility and effectiveness of the proposed ensemble member generation algorithm. Results show that the proposed MECE algorithm can select high quality ensemble members and as a result yield the better clusterings than six state-of-the-art ensemble clustering algorithms, that is, cluster-based similarity partitioning algorithm (CSPA), meta-clustering algorithm (MCLA), hybrid bipartite graph formulation (HBGF), evidence accumulation clustering (EAC), locally weighted evidence accumulation (LWEA), and locally weighted graph partition (LWGP). Specifically, MECE algorithm has the nearly 23% higher average NMI, 27% higher average ARI, 15% higher average FMI, and 10% higher average purity than CSPA, MCLA, HBGF, EAC, LWEA, and LWGA algorithms. The experimental results demonstrate that MECE algorithm is a valid approach to deal with the clustering ensemble problems.     

Ensemble clustering using semidefinite programming with applications

In this paper, we study the ensemble clustering problem, where the input is in the form of multiple clustering solutions. The goal of ensemble clustering algorithms is to aggregate the solutions into one solution that maximizes the agreement in the input ensemble. We obtain several new results for this problem. Specifically, we show that the notion of agreement under such circumstances can be better captured using a 2D string encoding rather than a voting strategy, which is common among existing approaches. Our optimization proceeds by first constructing a non-linear objective function which is then transformed into a 0-1 Semidefinite program (SDP) using novel convexification techniques. This model can be subsequently relaxed to a polynomial time solvable SDP. In addition to the theoretical contributions, our experimental results on standard machine learning and synthetic datasets show that this approach leads to improvements not only in terms of the proposed agreement measure but also the existing agreement measures based on voting strategies. In addition, we identify several new application scenarios for this problem. These include combining multiple image segmentations and generating tissue maps from multiple-channel Diffusion Tensor brain images to identify the underlying structure of the brain.     

一种基于二部图谱划分的聚类集成方法

将二部图模型引入聚类集成问题中,使用二部图模型同时建模对象集和超边集,充分挖掘潜藏在对象之间的相似度信息和超边提供的属性信息.设计正则化谱聚类算法解决二部图划分问题,在低维嵌入空间运行K-means++算法划分对象集,获得最终的聚类结果.在多组基准数据集上进行实验,实验结果表明所提出方法不仅能获得优越的结果,而且具有较高的运行效率.     

基于互信息选择聚类集成的网络流量分类方法

针对互联网流量标注困难以及单个聚类器的泛化能力较弱,提出一种基于互信息(MI)理论的选择聚类集成方法,以提高流量分类的精度。首先计算不同初始簇个数K的K均值聚类结果与训练集中流量协议的真实分布之间的规范化互信息(NMI);然后基于NMI的值来选择用于聚类集成的K均值基聚类器的K值序列;最后采用二次互信息(QMI)的一致函数生成一致聚类结果,并使用一种半监督方法对聚类簇进行标注。通过实验比较了聚类集成方法与单个聚类算法在4个不同测试集上总体分类精度。实验结果表明,聚类集成方法的流量分类总体精度能达到90%。所提方法将聚类集成模型应用到网络流量分类中,提高了流量分类的精度和在不同数据集上的分类稳定性。     

Ensemble-based clustering of large probabilistic graphs using neighborhood and distance metric learning

Graphs are commonly used to express the communication of various data. Faced with uncertain data, we have probabilistic graphs. As a fundamental problem of such graphs, clustering has many applications in analyzing uncertain data. In this paper, we propose a novel method based on ensemble clustering for large probabilistic graphs. To generate ensemble clusters, we develop a set of probable possible worlds of the initial probabilistic graph. Then, we present a probabilistic co-association matrix as a consensus function to integrate base clustering results. It relies on co-occurrences of node pairs based on the probability of the corresponding common cluster graphs. Also, we apply two improvements in the steps before and after of ensembles generation. In the before step, we append neighborhood information based on node features to the initial graph to achieve a more accurate estimation of the probability between the nodes. In the after step, we use supervised metric learning-based Mahalanobis distance to automatically learn a metric from ensemble clusters. It aims to gain crucial features of the base clustering results. We evaluate our work using five real-world datasets and three clustering evaluation metrics, namely the Dunn index, Davies–Bouldin index, and Silhouette coefficient. The results show the impressive performance of clustering large probabilistic graphs.

     

Iterative shrinking method for clustering problems

Agglomerative clustering generates the partition hierarchically by a sequence of merge operations. We propose an alternative to the merge-based approach by removing the clusters iteratively one by one until the desired number of clusters is reached. We apply local optimization strategy by always removing the cluster that increases the distortion the least. Data structures and their update strategies are considered. The proposed algorithm is applied as a crossover method in a genetic algorithm, and compared against the best existing clustering algorithms. The proposed method provides best performance in terms of minimizing intra-cluster variance.     

Evolving clusters in gene-expression data

Clustering is a useful exploratory tool for gene-expression data. Although successful applications of clustering techniques have been reported in the literature, there is no method of choice in the gene-expression analysis community. Moreover, there are only a few works that deal with the problem of automatically estimating the number of clusters in bioinformatics datasets. Most clustering methods require the number k of clusters to be either specified in advance or selected a posteriori from a set of clustering solutions over a range of k. In both cases, the user has to select the number of clusters. This paper proposes improvements to a clustering genetic algorithm that is capable of automatically discovering an optimal number of clusters and its corresponding optimal partition based upon numeric criteria. The proposed improvements are mainly designed to enhance the efficiency of the original clustering genetic algorithm, resulting in two new clustering genetic algorithms and an evolutionary algorithm for clustering (EAC). The original clustering genetic algorithm and its modified versions are evaluated in several runs using six gene-expression datasets in which the right clusters are known a priori. The results illustrate that all the proposed algorithms perform well in gene-expression data, although statistical comparisons in terms of the computational efficiency of each algorithm point out that EAC outperforms the others. Statistical evidence also shows that EAC is able to outperform a traditional method based on multiple runs of k-means over a range of k.     

Weighted partition consensus via kernels

The combination of multiple clustering results (clustering ensemble) has emerged as an important procedure to improve the quality of clustering solutions. In this paper we propose a new cluster ensemble method based on kernel functions, which introduces the Partition Relevance Analysis step. This step has the goal of analyzing the set of partition in the cluster ensemble and extract valuable information that can improve the quality of the combination process. Besides, we propose a new similarity measure between partitions proving that it is a kernel function. A new consensus function is introduced using this similarity measure and based on the idea of finding the median partition. Related to this consensus function, some theoretical results that endorse the suitability of our methods are proven. Finally, we conduct a numerical experimentation to show the behavior of our method on several databases by making a comparison with simple clustering algorithms as well as to other cluster ensemble methods.     

Soft spectral clustering ensemble applied to image segmentation

An unsupervised learning algorithm, named soft spectral clustering ensemble (SSCE), is proposed in this paper. Until now many proposed ensemble algorithms cannot be used on image data, even images of a mere 256 × 256 pixels are too expensive in computational cost and storage. The proposed method is suitable for performing image segmentation and can, to some degree, solve some open problems of spectral clustering (SC). In this paper, a random scaling parameter and Nystr?m approximation are applied to generate the individual spectral clusters for ensemble learning. We slightly modify the standard SC algorithm to aquire a soft partition and then map it via a centralized logcontrast transform to relax the constraint of probability data, the sum of which is one. All mapped data are concatenated to form the new features for each instance. Principal component analysis (PCA) is used to reduce the dimension of the new features. The final aggregated result can be achieved by clustering dimension-reduced data. Experimental results, on UCI data and different image types, show that the proposed algorithm is more efficient compared with some existing consensus functions.     

Combining multiple clusterings using evidence accumulation

We explore the idea of evidence accumulation (EAC) for combining the results of multiple clusterings. First, a clustering ensemble - a set of object partitions, is produced. Given a data set (n objects or patterns in d dimensions), different ways of producing data partitions are: 1) applying different clustering algorithms and 2) applying the same clustering algorithm with different values of parameters or initializations. Further, combinations of different data representations (feature spaces) and clustering algorithms can also provide a multitude of significantly different data partitionings. We propose a simple framework for extracting a consistent clustering, given the various partitions in a clustering ensemble. According to the EAC concept, each partition is viewed as an independent evidence of data organization, individual data partitions being combined, based on a voting mechanism, to generate a new n /spl times/ n similarity matrix between the n patterns. The final data partition of the n patterns is obtained by applying a hierarchical agglomerative clustering algorithm on this matrix. We have developed a theoretical framework for the analysis of the proposed clustering combination strategy and its evaluation, based on the concept of mutual information between data partitions. Stability of the results is evaluated using bootstrapping techniques. A detailed discussion of an evidence accumulation-based clustering algorithm, using a split and merge strategy based on the k-means clustering algorithm, is presented. Experimental results of the proposed method on several synthetic and real data sets are compared with other combination strategies, and with individual clustering results produced by well-known clustering algorithms.     

Probabilistic consensus clustering using evidence accumulation

Machine Learning - Clustering ensemble methods produce a consensus partition of a set of data points by combining the results of a collection of base clustering algorithms. In the evidence...     

Effects of resampling method and adaptation on clustering ensemble efficacy

Clustering ensembles combine multiple partitions of data into a single clustering solution of better quality. Inspired by the success of supervised bagging and boosting algorithms, we propose non-adaptive and adaptive resampling schemes for the integration of multiple independent and dependent clusterings. We investigate the effectiveness of bagging techniques, comparing the efficacy of sampling with and without replacement, in conjunction with several consensus algorithms. In our adaptive approach, individual partitions in the ensemble are sequentially generated by clustering specially selected subsamples of the given dataset. The sampling probability for each data point dynamically depends on the consistency of its previous assignments in the ensemble. New subsamples are then drawn to increasingly focus on the problematic regions of the input feature space. A measure of data point clustering consistency is therefore defined to guide this adaptation. Experimental results show improved stability and accuracy for clustering structures obtained via bootstrapping, subsampling, and adaptive techniques. A meaningful consensus partition for an entire set of data points emerges from multiple clusterings of bootstraps and subsamples. Subsamples of small size can reduce computational cost and measurement complexity for many unsupervised data mining tasks with distributed sources of data. This empirical study also compares the performance of adaptive and non-adaptive clustering ensembles using different consensus functions on a number of datasets. By focusing attention on the data points with the least consistent clustering assignments, whether one can better approximate the inter-cluster boundaries or can at least create diversity in boundaries and this results in improving clustering accuracy and convergence speed as a function of the number of partitions in the ensemble. The comparison of adaptive and non-adaptive approaches is a new avenue for research, and this study helps to pave the way for the useful application of distributed data mining methods.     

Clustering for malware classification

In this research, we apply clustering techniques to the malware classification problem. We compute clusters using the well-known K-means and Expectation Maximization algorithms, with the underlying scores based on Hidden Markov Models. We compare the results obtained from these two clustering approaches and we carefully consider the interplay between the dimension (i.e., number of models used for clustering), and the number of clusters, with respect to the accuracy of the clustering.     

Clusterer ensemble

Ensemble methods that train multiple learners and then combine their predictions have been shown to be very effective in supervised learning. This paper explores ensemble methods for unsupervised learning. Here, an ensemble comprises multiple clusterers, each of which is trained by k-means algorithm with different initial points. The clusters discovered by different clusterers are aligned, i.e. similar clusters are assigned with the same label, by counting their overlapped data items. Then, four methods are developed to combine the aligned clusterers. Experiments show that clustering performance could be significantly improved by ensemble methods, where utilizing mutual information to select a subset of clusterers for weighted voting is a nice choice. Since the proposed methods work by analyzing the clustering results instead of the internal mechanisms of the component clusterers, they are applicable to diverse kinds of clustering algorithms.     

A review: accuracy optimization in clustering ensembles using genetic algorithms

The clustering ensemble has emerged as a prominent method for improving robustness, stability, and accuracy of unsupervised classification solutions. It combines multiple partitions generated by different clustering algorithms into a single clustering solution. Genetic algorithms are known as methods with high ability to solve optimization problems including clustering. To date, significant progress has been contributed to find consensus clustering that will yield better results than existing clustering. This paper presents a survey of genetic algorithms designed for clustering ensembles. It begins with the introduction of clustering ensembles and clustering ensemble algorithms. Subsequently, this paper describes a number of suggested genetic-guided clustering ensemble algorithms, in particular the genotypes, fitness functions, and genetic operations. Next, clustering accuracies among the genetic-guided clustering ensemble algorithms is compared. This paper concludes that using genetic algorithms in clustering ensemble improves the clustering accuracy and addresses open questions subject to future research.     

To improve the quality of cluster ensembles by selecting a subset of base clusters

Conventional clustering ensemble algorithms employ a set of primary results; each result includes a set of clusters which are emerged from data. Given a large number of available clusters, one is faced with the following questions: (a) can we obtain the same quality of results with a smaller number of clusters instead of full ensemble? (b) If so, which subset of clusters is more efficient to be used in the ensemble? In this paper, these two questions are going to be answered. We explore a clustering ensemble approach combined with a cluster stability criterion as well as a dataset simplicity criterion to discover the finest subset of base clusters for each kind of datasets. Also, a novel method is proposed in order to accumulate the selected clusters and to extract final partitioning. Although it is expected that by reducing the size of ensemble the performance decreases, our experimental results show that our selecting mechanism generally lead to superior results.     

A new hybrid method based on partitioning-based DBSCAN and ant clustering

Clustering problem is an unsupervised learning problem. It is a procedure that partition data objects into matching clusters. The data objects in the same cluster are quite similar to each other and dissimilar in the other clusters. Density-based clustering algorithms find clusters based on density of data points in a region. DBSCAN algorithm is one of the density-based clustering algorithms. It can discover clusters with arbitrary shapes and only requires two input parameters. DBSCAN has been proved to be very effective for analyzing large and complex spatial databases. However, DBSCAN needs large volume of memory support and often has difficulties with high-dimensional data and clusters of very different densities. So, partitioning-based DBSCAN algorithm (PDBSCAN) was proposed to solve these problems. But PDBSCAN will get poor result when the density of data is non-uniform. Meanwhile, to some extent, DBSCAN and PDBSCAN are both sensitive to the initial parameters. In this paper, we propose a new hybrid algorithm based on PDBSCAN. We use modified ant clustering algorithm (ACA) and design a new partitioning algorithm based on ‘point density’ (PD) in data preprocessing phase. We name the new hybrid algorithm PACA-DBSCAN. The performance of PACA-DBSCAN is compared with DBSCAN and PDBSCAN on five data sets. Experimental results indicate the superiority of PACA-DBSCAN algorithm.