GAUFS: Genetic Algorithm for Unsupervised Feature Selection for clustering

Traditionally, Unsupervised Feature Selection (UFS) for clustering has been formulated as a ranking of features task under an assumed number of clusters. More recent UFS families can learn feature relevance without pre-specifying the number of clusters, but most do not infer it as part of the method, meaning that few proposals tackle the full problem of returning a feature subset and an estimated number of clusters. This work introduces GAUFS, a wrapper method based on a genetic algorithm (GA) that jointly identifies an informative feature subset and estimates the number of clusters from the data. Candidate solutions encode both the subset and the cluster count; Hierarchical clustering together with Silhouette index provide a deterministic internal fitness. An elitist hall-of-fame mechanism aggregates evidence across evolutionary search to derive feature weights, and an automatic stopping rule selects the subset size at which further features cease to improve a combined quality criterion, assigning the associated cluster estimate. In addition, two synthetic data generators are designed to test feature selection under controlled separability and axis-aligned projection ambiguity. Across 60 datasets (30 synthetic, 30 real), GAUFS attains near-perfect Adjusted Mutual Information (AMI) on synthetic benchmarks and outperforms eight established algorithms on real datasets, while returning both a concrete subset and an estimated cluster count. The findings indicate that coupling feature selection with the estimation of the number of clusters is critical for robust UFS in clustering. To enable fair comparison and strengthen reproducibility, the full implementation and the benchmark have been released publicly.