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 pair-wise co-occurrence based methods @cite_17 @cite_27 @cite_13 typically construct a co-association matrix by considering the frequency that two data samples occur in the same cluster among the multiple base clusterings. The co-association matrix is then used as the similarity matrix for the data samples, upon which some clustering algorithms can thereby be performed to obtain the final clustering result. Fred and Jain @cite_17 first introduced the concept of the co-association matrix and proposed the evidence accumulation clustering (EAC) method, which applied a hierarchical agglomerative clustering algorithm @cite_25 on the co-association matrix to build the consensus clustering. To extend the EAC method, @cite_27 took the cluster sizes into consideration and proposed the probability accumulation method. @cite_13 dealt with the uncertain entries in the co-association matrix by first labeling them as unobserved, and then recovering the unobserved entries by the matrix completion technique. @cite_23 proved that the spectral clustering of the co-association matrix is equivalent to a weighted version of @math -means, and proposed the spectral ensemble clustering (SEC) method to effectively and efficiently obtain the consensus result.
@cite_27 @cite_23 @cite_13 @cite_25 @cite_17
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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. Since a large number of clustering algorithms exist, aggregating different clustered partitions into a single consolidated one to obtain better results has become an important problem. In Fred and Jain's evidence accumulation algorithm, they construct a co-association matrix on original partition labels, and then apply minimum spanning tree to this matrix for the combined clustering. In this paper, we will propose a novel clustering aggregation scheme, probability accumulation. In this algorithm, the construction of correlation matrices takes the cluster sizes of original clusterings into consideration. An alternate improved algorithm with additional pre- and post-processing is also proposed. Experimental results on both synthetic and real data-sets show that the proposed algorithms perform better than evidence accumulation, as well as some other methods. As a promising way for heterogeneous data analytics, consensus clustering has attracted increasing attention in recent decades. Among various excellent solutions, the co-association matrix based methods form a landmark, which redefines consensus clustering as a graph partition problem. Nevertheless, the relatively high time and space complexities preclude it from wide real-life applications. We, therefore, propose Spectral Ensemble Clustering (SEC) to leverage the advantages of co-association matrix in information integration but run more efficiently. We disclose the theoretical equivalence between SEC and weighted K-means clustering, which dramatically reduces the algorithmic complexity. We also derive the latent consensus function of SEC, which to our best knowledge is the first to bridge co-association matrix based methods to the methods with explicit global objective functions. Further, we prove in theory that SEC holds the robustness, generalizability, and convergence properties. We finally extend SEC to meet the challenge arising from incomplete basic partitions, based on which a row-segmentation scheme for big data clustering is proposed. Experiments on various real-world data sets in both ensemble and multi-view clustering scenarios demonstrate the superiority of SEC to some state-of-the-art methods. In particular, SEC seems to be a promising candidate for big data clustering. Many stability measures, such as Normalized Mutual Information NMI, have been proposed to validate a set of partitionings. It is highly possible that a set of partitionings may contain one or more high quality clusters but is still adjudged a bad cluster by a stability measure, and as a result, is completely neglected. Inspired by evaluation approaches measuring the efficacy of a set of partitionings, researchers have tried to define new measures for evaluating a cluster. Thus far, the measures defined for assessing a cluster are mostly based on the well-known NMI measure. The drawback of this commonly used approach is discussed in this paper, after which a new asymmetric criterion, called the Alizadeh--Parvin--Moshki--Minaei criterion APMM, is proposed to assess the association between a cluster and a set of partitionings. We show that the APMM criterion overcomes the deficiency in the conventional NMI measure. We also propose a clustering ensemble framework that incorporates the APMM's capabilities in order to find the best performing clusters. The framework uses Average APMM AAPMM as a fitness measure to select a number of clusters instead of using all of the results. Any cluster that satisfies a predefined threshold of the mentioned measure is selected to participate in an elite ensemble. To combine the chosen clusters, a co-association matrix-based consensus function by which the set of resultant partitionings are obtained is used. Because Evidence Accumulation Clustering EAC can not derive the co-association matrix from a subset of clusters appropriately, a new EAC-based method, called Extended EAC EEAC, is employed to construct the co-association matrix from the chosen subset of clusters. Empirical studies show that our proposed approach outperforms other cluster ensemble approaches.