The emergence of high-dimensional data in various areas has brought new challenges to the ensemble clustering research. To deal with the curse of dimensionality, considerable efforts in ensemble clustering have been made by incorporating various subspace-based techniques. Besides the emphasis on subspaces, rather limited attention has been paid to the potential diversity in similarity dissimilarity metrics. It remains a surprisingly open problem in ensemble clustering how to create and aggregate a large number of diversified metrics, and furthermore, how to jointly exploit the multi-level diversity in the large number of metrics, subspaces, and clusters, in a unified framework. To tackle this problem, this paper proposes a novel multi-diversified ensemble clustering approach. In particular, we create a large number of diversified metrics by randomizing a scaled exponential similarity kernel, which are then coupled with random subspaces to form a large set of metric-subspace pairs. Based on the similarity matrices derived from these metric-subspace pairs, an ensemble of diversified base clusterings can thereby be constructed. Further, an entropy-based criterion is adopted to explore the cluster-wise diversity in ensembles, based on which the consensus function is therefore presented. Experimental results on twenty high-dimensional datasets have confirmed the superiority of our approach over the state-of-the-art.
The median partition based methods @cite_15 @cite_4 @cite_34 typically formulate the ensemble clustering problem into an optimization problem which aims to find the median partition such that the similarity between the base partitions (i.e., base clusterings) and the median partition is maximized. The median partition problem is NP-hard @cite_4 . To find an approximate solution, @cite_4 cast the median partition problem into a maximum likelihood problem and solved it by the EM algorithm. Franek and Jiang @cite_34 reduced the ensemble clustering problem to an Euclidean median problem and solved it by the Weiszfeld algorithm @cite_40 . @cite_15 formulated the ensemble clustering problem into a binary linear programming problem and obtained an approximate solution based on the factor graph model and the max-product belief propagation @cite_0 .
@cite_4 @cite_0 @cite_40 @cite_15 @cite_34
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Ensemble clustering is a recently evolving research direction in cluster analysis and has found several different application domains. In this work the complex ensemble clustering problem is reduced to the well-known Euclidean median problem by clustering embedding in vector spaces. The Euclidean median problem is solved by the Weiszfeld algorithm and an inverse transformation maps the Euclidean median back into the clustering domain. In the experiment study different evaluation strategies are considered. The proposed embedding strategy is compared to several state-of-art ensemble clustering algorithms and demonstrates superior performance. HighlightsThis paper presents a novel approach to solving the ensemble clustering problem.An embedding method successful for strings and graphs is adapted to clusterings.An extensive experiment study is presented.The proposed method is superior to several state-of-the-art related algorithms. 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 accumulation clustering (EAC) paradigm, the clustering ensemble is transformed into a pairwise co-association matrix, thus avoiding the label correspondence problem, which is intrinsic to other clustering ensemble schemes. In this paper, we propose a consensus clustering approach based on the EAC paradigm, which is not limited to crisp partitions and fully exploits the nature of the co-association matrix. Our solution determines probabilistic assignments of data points to clusters by minimizing a Bregman divergence between the observed co-association frequencies and the corresponding co-occurrence probabilities expressed as functions of the unknown assignments. We additionally propose an optimization algorithm to find a solution under any double-convex Bregman divergence. Experiments on both synthetic and real benchmark data show the effectiveness of the proposed approach. Clustering ensembles have emerged as a powerful method for improving both the robustness as well as the stability of unsupervised classification solutions. However, finding a consensus clustering from multiple partitions is a difficult problem that can be approached from graph-based, combinatorial, or statistical perspectives. This study extends previous research on clustering ensembles in several respects. First, we introduce a unified representation for multiple clusterings and formulate the corresponding categorical clustering problem. Second, we propose a probabilistic model of consensus using a finite mixture of multinomial distributions in a space of clusterings. A combined partition is found as a solution to the corresponding maximum-likelihood problem using the EM algorithm. Third, we define a new consensus function that is related to the classical intraclass variance criterion using the generalized mutual information definition. Finally, we demonstrate 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. Combination accuracy is analyzed as a function of several parameters that control the power and resolution of component partitions as well as the number of partitions. We also analyze clustering ensembles with incomplete information and the effect of missing cluster labels on the quality of overall consensus. Experimental results demonstrate the effectiveness of the proposed methods on several real-world data sets. Data clustering is an important task and has found applications in numerous real-world problems. Since no single clustering algorithm is able to identify all different types of cluster shapes and structures, ensemble clustering was proposed to combine different partitions of the same data generated by multiple clustering algorithms. The key idea of most ensemble clustering algorithms is to find a partition that is consistent with most of the available partitions of the input data. One problem with these algorithms is their inability to handle uncertain data pairs, i.e. data pairs for which about half of the partitions put them into the same cluster and the other half do the opposite. When the number of uncertain data pairs is large, they can mislead the ensemble clustering algorithm in generating the final partition. To overcome this limitation, we propose an ensemble clustering approach based on the technique of matrix completion. The proposed algorithm constructs a partially observed similarity matrix based on the data pairs whose cluster memberships are agreed upon by most of the clustering algorithms in the ensemble. It then deploys the matrix completion algorithm to complete the similarity matrix. The final data partition is computed by applying an efficient spectral clustering algorithm to the completed matrix. Our empirical studies with multiple real-world datasets show that the proposed algorithm performs significantly better than the state-of-the-art algorithms for ensemble clustering.