A popular algorithm for finding clusters in unlabeled data optimizes the k-means clustering model. This algorithm converges quickly but is sensitive to initialization. Two ways to overcome this drawback are fuzzification and harmonic means. We show that k-harmonic means is a special case of reformulated fuzzy k-means. The main focus of this paper is on partially supervised clustering. Partially supervised clustering finds clusters in data sets that contain both unlabeled and labeled data. We review partially supervised k-means, partially supervised fuzzy k-means, and introduce a partially supervised extension of k-harmonic means. Experiments with four benchmark data sets indicate that partially supervised k-harmonic means inherits the advantages of its completely unsupervised variant: It is significantly less sensitive to initialization than partially supervised k-means.
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