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.
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.