Scalable unsupervised feature selection via weight stability

Unsupervised feature selection is critical for improving clustering performance in high-dimensional data, where irrelevant features can obscure meaningful structure. In this work, we propose the Minkowski weighted $k$-means++, a novel initialisation strategy for the Minkowski Weighted $k$-means. Our initialisation selects centroids probabilistically using feature relevance estimates derived from the data itself. Building on this, we propose two new feature selection algorithms, FS-MWK++, which aggregates feature weights across a range of Minkowski exponents identifying stable and informative features, and SFS-MWK++, a scalable variant based on subsampling. We support our approach with a theoretical analysis, demonstrating that, under explicit assumptions on noise features and cluster structure, relevant features are assigned consistently higher weights than noise features across a range of Minkowski exponents. Our software can be found at https://github.com/xzhang4-ops1/FSMWK.