Geometry-Supported Residual Feature Selection: A Label-Blind Algorithm for Structural and Redundancy-Aware Feature Selection

Unsupervised feature selection is difficult when relevance must be inferred without labels, and redundancy, outliers, and sample-localized geometry can distort marginal criteria. This study presents Geometry-Supported Residual Feature Selection (GSR-FS), a fully label-blind algorithm and open-source Python library that represents each feature by its contribution to pairwise sample geometry. Structural relevance is quantified by Bhattacharyya affinity to the aggregate geometry of the remaining features, calibrated against within-feature permutations, and downweighted by an entropy-based Sample-Geometric Coverage term. A non-negative residual reconstruction criterion then penalizes candidates whose geometry is already represented by previously selected features. Automatic selection uses a feature-wise max-null permutation distribution, whereas fixed-cardinality selection follows the same greedy score without using target information. The released library additionally provides balanced pair subsampling, numerically equivalent residual solvers, source-integrity audits, publication guardrails, and diagnostic structural-group outputs. In a source-audited 30-dataset evidence panel, 29 datasets supported complete five-method comparisons. Mean balanced accuracy was 0.6031 for GSR-FS, compared with 0.6019 for SPEC, 0.5970 for MCFS, 0.5892 for MaxVariance, and 0.5810 for Laplacian Score. The Friedman test was not significant (p = 0.488), and no Holm-corrected pairwise comparison was significant. Additional robustness analyses showed that automatic GSR-FS achieved mean balanced accuracy of 0.6216 compared with 0.6069 for fixed-cardinality GSR-FS on the 30-dataset panel, without a significant paired difference (p = 0.1215). Further validation showed high-precision independent-null calibration at α = 0.05, with 25 of 500 datasets producing a non-empty subset (empirical rate of 0.050; exact 95% CI of 0.0326–0.0729). Controlled dependent-feature experiments showed that GSR-FS combined higher latent-group coverage with lower redundancy than Laplacian Score and MCFS in the examined structural-recovery scenarios, while a recent FGMRW-UFS comparator showed limited recovery under this specific criterion. An engineering stress test was completed successfully through 20,000 candidate features under explicitly capped pair and permutation budgets. Controlled nuisance simulations further confirmed that structurally coherent but target-independent variation can be selected, emphasizing that GSR-FS estimates internal structural relevance rather than guaranteed target-specific relevance. These results support GSR-FS as a reproducible, structurally motivated alternative rather than a statistically superior replacement.