A bad partition in an ensemble will be removed by a cluster ensemble selection framework from the final ensemble. It is the main idea in cluster ensemble selection to remove these partitions (bad partitions) from the selected ensemble. But still, it is likely that one of them contains some reliable clusters. Therefore, it may be reasonable to apply the selection phase on cluster level. To do this, a cluster evaluation metric is needed. Some of these metrics have been recently introduced; each of them has its limitations. The weak points of each method have been addressed in the paper. Subsequently, a new metric for cluster assessment has been introduced. The new measure is named Balanced Normalized Mutual Information (BNMI) criterion. It balances the deficiency of the traditional NMI-based criteria. Additionally, an innovative cluster ensemble approach has been proposed. To create the consensus partition considering the elected clusters, a set of different aggregation-functions (called also consensus-functions) have been utilized: the ones which are based upon the co-association matrix (CAM), the ones which are based on hyper graph partitioning algorithms, and the ones which are based upon intermediate space. The experimental study indicates that the state-of-the-art cluster ensemble methods are outperformed by the proposed cluster ensemble approach.
GRACE: A Graph-Based Cluster Ensemble Approach for Single-Cell RNA-Seq Data Clustering
