On the Objective and Feature Weights of Minkowski Weighted k-Means

ArXi:2603.25958v1 Announce Type: new The Minkowski weighted k-means (mwk-means) algorithm extends classical k-means by incorporating feature weights and a Minkowski distance. Despite its empirical success, its theoretical properties remain insufficiently understood. We show that the mwk-means objective can be expressed as a power-mean aggregation of within-cluster dispersions, with the order determined by the Minkowski exponent p. This formulation reveals how p controls the transition between selective and uniform use of features.