We investigate here the behavior of the standard k-means clustering algorithm and several alternatives to it: the k-harmonic means algorithm due to Zhang and colleagues, fuzzy k-means, Gaussian expectation-maximization, and two new variants of k-harmonic means. Our aim is to find which aspects of these algorithms contribute to finding good clusterings, as opposed to converging to a low-quality local optimum. We describe each algorithm in a unified framework that introduces separate cluster membership and data weight functions. We then show that the algorithms do behave very differently from each other on simple low-dimensional synthetic datasets, and that the k-harmonic means method is superior. Having a soft membership function is essential for finding high-quality clusterings, but having a non-constant data weight function is useful also.
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