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.
Clustering ensembles have emerged as a powerful method for improving both the robustness and 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. We offer a probabilistic model of consensus using a finite mixture of multinomial distributions in a space of clustering. A combined partition is found as a solution to the corresponding maximum likelihood problem using the GA algorithm. The excellent scalability of this algorithm and comprehensible underlying model are particularly important for clustering of large datasets. This study includes two sections, at the first, calculate correlation matrix. this matrix show correlation between samples and we found the best samples that can be in the center of clusters. In the other section a genetic algorithm is employed to produce the most stable partitions from an evolving ensemble (population) of clustering algorithms along with a special objective function. The objective function evaluates multiple partitions according to changes caused by data perturbations and prefers those clustering that are least susceptible to those perturbations. 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. 