Variance-Preserving Orthogonal Selection (VPOS): Greedy Feature Selection via Orthogonal Deflation in PCA Loading Space

2026-07-25

AI Summary

This work addresses the challenge of preserving data variance while avoiding redundancy in unsupervised feature selection by proposing a greedy selection method grounded in a weighted PCA loading space. The approach incorporates a null-space ablation mechanism that, after each selection step, removes the variance direction of already-selected features, thereby enforcing subsequent selections to cover orthogonal subspaces within the covariance structure. The method establishes a theoretical connection to monotone submodular maximization and introduces a reproducible hyperparameter selection criterion based on sensitivity scanning of reconstruction mean squared error (MSE). Experimental results across eight benchmark datasets demonstrate that the proposed method consistently achieves the lowest reconstruction MSE, offers speedups of 10–140× over graph-based baselines, and reduces MSE by 10%–73% compared to standard PCA without ablation at equivalent dimensions.

Abstract

We propose Variance-Preserving Orthogonal Selection (VPOS), a greedy framework for unsupervised feature selection that operates in the weighted PCA loading space. After each selection, VPOS projects out the chosen feature's variance direction via null-space deflation, forcing subsequent selections to cover orthogonal parts of the covariance structure. Each step provably reduces the loading matrix rank by one, and the greedy objective connects to monotone submodular maximization. The single hyperparameter $d$ is selected via a reproducible rule: the value minimising reconstruction MSE in a sensitivity sweep. On eight benchmarks, VPOS achieves the lowest reconstruction MSE on all eight while running 10-140x faster than graph-based methods at scale. Comparing against PCA (no deflation) at matched $d$ confirms deflation as the primary driver, reducing MSE by 10-73%.

Problem

• unsupervised feature selection
• variance preservation
• orthogonal deflation
• PCA loading space
• covariance structure

Innovation

• Variance-Preserving Orthogonal Selection
• orthogonal deflation
• PCA loading space
• greedy feature selection
• submodular maximization