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 introduce 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 to identify stable and informative features, and SFS-MWK++, a scalable variant based on subsampling. We support our approach with a theoretical guarantee under mild assumptions and extensive experiments showing that our methods consistently outperform existing alternatives. Our software can be found atthis https URL.

@article{zhang2025_2506.06114,
  title={ Scalable unsupervised feature selection via weight stability },
  author={ Xudong Zhang and Renato Cordeiro de Amorim },
  journal={arXiv preprint arXiv:2506.06114},
  year={ 2025 }
}