Overlapping coefficient in network-based semi-supervised clustering

Network-based Semi-Supervised Clustering (NeSSC) is a semi-supervised approach for clustering in the presence of an outcome variable. It uses a classification or regression model on resampled versions of the original data to produce a proximity matrix that indicates the magnitude of the similarity between pairs of observations measured with respect to the outcome. This matrix is transformed into a complex network on which a community detection algorithm is applied to search for underlying community structures which is a partition of the instances into highly homogeneous clusters to be evaluated in terms of the outcome. In this paper, we focus on the case the outcome variable to be used in NeSSC is numeric and propose an alternative selection criterion of the optimal partition based on a measure of overlapping between density curves as well as a penalization criterion which takes accounts for the number of clusters in a candidate partition. Next, we consider the performance of the proposed method for some artificial datasets and for 20 different real datasets and compare NeSSC with the other three popular methods of semi-supervised clustering with a numeric outcome. Results show that NeSSC with the overlapping criterion works particularly well when a reduced number of clusters are scattered localized.