Abstract
The global k-means algorithm is an incremental approach to clustering that dynamically adds one cluster center at a time through a deterministic global search procedure from suitable initial positions, and employs k-means to minimize the sum of the intra-cluster variances. However the global k-means algorithm sometimes results singleton clusters and the initial positions sometimes are bad, after a bad initialization, poor local optimal can be easily obtained by k-means algorithm. In this paper, we modified the global k-means algorithm to eliminate the singleton clusters at first, and then we apply MinMax k-means clustering error method to global k-means algorithm to overcome the effect of bad initialization, proposed the global Minmax k-means algorithm. The proposed clustering method is tested on some popular data sets and compared to the k-means algorithm, the global k-means algorithm and the MinMax k-means algorithm. The experiment results show our proposed algorithm outperforms other algorithms mentioned in the paper.
Highlights
Clustering is one of classic problems in pattern recognition, image processing, machine learning and statistics (Xu and Wunsch 2005; Jain 2010; Berkhin 2006)
We find that the Esum of modified global k-means is more lower than that of global k-means
12, first, we find that the global Minmax k-means algorithm attains better Emax than k-means algorithm and global algorithm, and in most of cases it better than the MinMax k-means algorithm, sometimes equal to the MinMax k-means algorithm
Summary
Clustering is one of classic problems in pattern recognition, image processing, machine learning and statistics (Xu and Wunsch 2005; Jain 2010; Berkhin 2006). A fuzzy clustering version is available (Zang et al 2014) All of these are incremental approaches that start from one cluster and at each step a new cluster is deterministically added to the solution according to an appropriate criterion. Using this method can learn the number of data clusters (Kalogeratos and Likas 2012). The global k-means algorithm is deterministic and often performs well, but sometimes the new cluster center may be a outlier, it may arise that some of the clusters just have single point, the result is awful Another way to avoid the choice of initial starting conditions
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