A Generalization of Proximity Functions for K-Means

K-means is a widely used partitional clustering method. A large amount of effort has been made on finding better proximity (distance) functions for K-means. However, the common characteristics of proximity functions remain unknown. To this end, in this paper, we show that all proximity functions that fit K-means clustering can be generalized as K-means distance, which can be derived by a differentiable convex function. A general proof of sufficient and necessary conditions for K-means distance functions is also provided. In addition, we reveal that K-means has a general uniformization effect; that is, K-means tends to produce clusters with relatively balanced cluster sizes. This uniformization effect of K-means exists regardless of proximity functions. Finally, we have conducted extensive experiments on various real-world data sets, and the results show the evidence of the uniformization effect. Also, we observed that external clustering validation measures, such as Entropy and Var...

• Type: Conference
• Year: 2007
• Where: ICDM
• Authors: Junjie Wu, Hui Xiong, Jian Chen, Wenjun Zhou
• Keywords: Data Mining, ICDM 2007, K-means, K-means Distance, Proximity Functions