Cluster analysis plays a very important role in data analysis. In these years, cluster ensemble, as a cluster analysis tool, has drawn much attention for its robustness, stability, and accuracy. Many efforts have been done to combine different initial clustering results into a single clustering solution with better performance. However, they neglect the structure information of the raw data in performing the cluster ensemble. In this paper, we propose a Structural Cluster Ensemble (SCE) algorithm for data partitioning formulated as a set-covering problem. In particular, we construct a Laplacian regularized objective function to capture the structure information among clusters. Moreover, considering the importance of the discriminative information underlying in the initial clustering results, we add a discriminative constraint into our proposed objective function. Finally, we verify the performance of the SCE algorithm on both synthetic and real data sets. The experimental results show the effectiveness of our proposed method SCE algorithm.
It is widely recognized that combining multiple classification or regression models typically provides superior results compared to using a single, well-tuned model. However, there are no well known approaches to combining multiple non-hierarchical clusterings. The idea of combining cluster labelings without accessing the original features leads us to a general knowledge reuse framework that we call cluster ensembles. Our contribution in this paper is to formally define the cluster ensemble problem as an optimization problem and to propose three effective and efficient combiners for solving it based on a hypergraph model. Results on synthetic as well as real data sets are given to show that cluster ensembles can (i) improve quality and robustness, and (ii) enable distributed clustering. A data set can be clustered in many ways depending on the clustering algorithm employed, parameter settings used and other factors. Can multiple clusterings be combined so that the final partitioning of data provides better clustering? The answer depends on the quality of clusterings to be combined as well as the properties of the fusion method. First, we introduce a unified representation for multiple clusterings and formulate the corresponding categorical clustering problem. As a result, we show that the consensus function is related to the classical intra-class variance criterion using the generalized mutual information definition. Second, we show the efficacy of combining partitions generated by weak clustering algorithms that use data projections and random data splits. A simple explanatory model is offered for the behavior of combinations of such weak clustering components. We analyze the combination accuracy as a function of parameters controlling the power and resolution of component partitions as well as the learning dynamics vs. the number of clusterings involved. Finally, some empirical studies compare the effectiveness of several consensus functions. Motivation: The microarray technology is increasingly being applied in biological and medical research to address a wide range of problems such as the classification of tumors. An important statistical question associatedwith tumor classification is the identification of new tumor classes using gene expression profiles. Essential aspects of this clustering problem include identifying accurate partitions of the tumor samples into clusters and assessing the confidence of cluster assignments for individual samples. Results: Two new resampling methods, inspired from bagging in prediction, are proposed to improve and assess the accuracy of a given clustering procedure. In these ensemble methods, a partitioning clustering procedure is applied to bootstrap learning sets and the resulting multiple partitions are combined by voting or the creation of a new dissimilarity matrix. As in prediction, the motivation behind bagging is to reduce variability in the partitioning results via averaging. The performances of the new and existing methods were compared using simulated data and gene expression data from two recently published cancer microarray studies. The bagged clustering procedures were in general at least as accurate and often substantially more accurate than a single application of the partitioning clustering procedure. A valuable by-product of bagged clustering are the cluster votes which can be used to assess the confidence of cluster assignments for individual observations. We present a novel optimization-based method for the combination of cluster ensembles for the class of problems with intracluster criteria, such as Minimum-Sum-of-Squares-Clustering (MSSC). We propose a simple and efficient algorithm-called EXAMCE-for this class of problems that is inspired from a Set-Partitioning formulation of the original clustering problem. We prove some theoretical properties of the solutions produced by our algorithm, and in particular that, under general assumptions, though the algorithm recombines solution fragments so as to find the solution of a Set-Covering relaxation of the original formulation, it is guaranteed to find better solutions than the ones in the ensemble. For the MSSC problem in particular, a prototype implementation of our algorithm found a new better solution than the previously best known for 21 of the test instances of the 40-instance TSPLIB benchmark data sets used in, and and found a worse-quality solution than the best known only five times. For other published benchmark data sets where the optimal MSSC solution is known, we match them. The algorithm is particularly effective when the number of clusters is large, in which case it is able to escape the local minima found by K-means type algorithms by recombining the solutions in a Set-Covering context. We also establish the stability of the algorithm with extensive computational experiments, by showing that multiple runs of EXAMCE for the same clustering problem instance produce high-quality solutions whose Adjusted Rand Index is consistently above 0.95. Finally, in experiments utilizing external criteria to compute the validity of clustering, EXAMCE is capable of producing high-quality results that are comparable in quality to those of the best known clustering algorithms.