Careful seeding for the k-medoids algorithm with incremental k++ cluster construction

The k-medoids algorithm is a popular variant of the k-means algorithm and widely used in pattern recognition and machine learning. A main drawback of the k-medoids algorithm is that it can be trapped in local optima. An improved k-medoids algorithm (INCKM) was recently proposed to overcome this drawback, based on constructing a candidate medoids subset with a parameter choosing procedure, but it may fail when dealing with imbalanced datasets. In this paper, we propose a novel incremental k-medoids algorithm (INCKPP) which dynamically increases the number of clusters from 2 to k through a nonparametric and stochastic k-means++ search procedure. Our algorithm can overcome the parameter selection problem in the improved k-medoids algorithm, improve the clustering performance, and deal with imbalanced datasets very well. But our algorithm has a weakness in computation efficiency. To address this issue, we propose a fast INCKPP algorithm (called INCKPP$_{sample}$) which preserves the computational efficiency of the simple and fast k-medoids algorithm with an improved clustering performance. The proposed algorithm is compared with three state-of-the-art algorithms: the improved k-medoids algorithm (INCKM), the simple and fast k-medoids algorithm (FKM) and the k-means++ algorithm (KPP). Extensive experiments on both synthetic and real world datasets including imbalanced datasets illustrate the effectiveness of the proposed algorithm.