Evolutionary K-Means with pair-wise constraints

Abstract

K-Means users usually have to decide on the number of clusters and the initial state by themselves. Evolutionary K-Means (EKM), a hybrid algorithm of K-Means and genetic algorithm, solves the problem by choosing the two parameters automatically through partition evolution; however, the final partition obtained often doesn't meet users' expectations. As a solution to this problem, we suggest using background knowledge for enhancing clustering quality and propose a semi-supervised approach that incorporates instance level constraints into the objective function of EKM. Firstly, we define Constrained Silhouette Index (CS) for data instances, which decreases the silhouette index of the instance having violated constraints. Then, we present two weighted approaches to extend the influence of constraints beyond the level of instance for evaluating the quality of a cluster or a partition. To evaluate the performance of CS in guiding EKM algorithms, we combine the two types of CS with F-EAC algorithm, and get two constrained EKM algorithms, which are named as CEAC1 and CEAC2, respectively. Experimental results on two artificial datasets and eight UCI datasets suggest a few constraints are often powerful enough to improve the accuracy of labelling instances and choosing K, and more constraints may improve the performance even more.