Minkowski Metric, Feature Weighting and Anomalous Cluster Initialisation in K-Means Clustering

Abstract

This paper represents another step in overcoming a drawback of K-Means, its lack of defense against noisy features, using feature weights in the criterion. The Weighted K-Means method by Huang et al. (2008, 2004, 2005) [5–7] is extended to the corresponding Minkowski metric for measuring distances. Under Minkowski metric the feature weights become intuitively appealing feature rescaling factors in a conventional K-Means criterion. To see how this can be used in addressing another issue of K-Means, the initial setting, a method to initialize K-Means with anomalous clusters is adapted. The Minkowski metric based method is experimentally validated on datasets from the UCI Machine Learning Repository and generated sets of Gaussian clusters, both as they are and with additional uniform random noise features, and appears to be competitive in comparison with other K-Means based feature weighting algorithms.