Merging K-Means Solutions for Clustering

• Activity Number: 649 - Advances in Finite Mixture Modeling and Model-Based Clustering
• Type: Topic Contributed
• Date/Time: Thursday, August 3, 2017 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Semhar Michael* and Volodymyr Melnykov
• Companies: South Dakota State University and The University of Alabama
• Keywords: K-means ; finite mixture models ; merging ; BIC ; pairwise overlap

Abstract

Existing clustering methods range from simple but very restrictive to complex but more flexible. The K-means algorithm is one of the most popular clustering procedures due to its computational speed and intuitive construction. Unfortunately, the application of K-means in its traditional form based on Euclidean distances is limited to cases with spherical clusters of approximately the same size. At the same time, it is a common practice among researchers to use the algorithm without checking underlying assumptions. As a result, obtained solutions are often meaningless or misleading. We propose merging solutions obtained by K-means to produce meaningful groupings. The notion of pairwise overlap is used to measure the closeness of groups in the K-means solution. A novel display called overlap map is proposed to decide on the optimal number of clusters. The ideas are illustrated on challenging examples and applied to the problem of color quantization with good results.