As a classic NP-hard problem in machine learning and computational geometry, the k-means problem aims to partition the given dataset into k clusters according to the minimal squared Euclidean distance. Different from k-means problem and most of its variants, fuzzy k-means problem belongs to the soft clustering problem, where each given data point has relationship to every center point. Compared to fuzzy k-means problem, fuzzy k-means problem with penalties allows that some data points need not be clustered instead of being paid penalties. In this paper, we propose an O(αk ln k)- approximation algorithm based on seeding algorithm for fuzzy k-means problem with penalties, where α involves the ratio of the maximal penalty value to the minimal one. Furthermore, we implement numerical experiments to show the effectiveness of our algorithm.
Wen-Zhao Liu, Min Li
. An Approximation Algorithm Based on Seeding Algorithm for Fuzzy k-Means Problem with Penalties[J]. Journal of the Operations Research Society of China, 2024
, 12(2)
: 387
-409
.
DOI: 10.1007/s40305-022-00399-4
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