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VPOS: Faster, More Accurate Feature Selection via Orthogonal Deflation

Baran Koseoglu, Berrin Yanikoglu· July 28, 2026 View original

Summary

Variance-Preserving Orthogonal Selection (VPOS) is a new greedy unsupervised feature selection framework that operates in the weighted PCA loading space. It achieves superior reconstruction MSE and significantly faster performance than graph-based methods by orthogonally deflating chosen features' variance directions.

Researchers have introduced Variance-Preserving Orthogonal Selection (VPOS), a novel greedy framework for unsupervised feature selection. This method operates within the weighted Principal Component Analysis (PCA) loading space, offering a distinct approach to identifying the most informative features. A key innovation of VPOS is its use of orthogonal deflation: after each feature is selected, its variance direction is projected out via null-space deflation. This mechanism ensures that subsequent selections are compelled to cover orthogonal segments of the covariance structure, thereby promoting diversity and comprehensiveness in the chosen feature subset. Each step in VPOS provably reduces the loading matrix rank by one, and its greedy objective function is linked to monotone submodular maximization, providing a theoretical foundation for its effectiveness. The framework includes a reproducible rule for selecting its single hyperparameter, `d`, by minimizing reconstruction Mean Squared Error (MSE) through a sensitivity sweep. Evaluations across eight benchmark datasets demonstrate VPOS's superior performance. It consistently achieves the lowest reconstruction MSE on all benchmarks while operating significantly faster, showing a 10-140x speed improvement compared to graph-based methods at scale. A comparison against PCA without deflation, at matched `d` values, confirms that the deflation mechanism is the primary driver of VPOS's enhanced performance, reducing MSE by 10-73%.

Why it matters

For data scientists and machine learning engineers, VPOS offers a faster and more accurate method for unsupervised feature selection, leading to more efficient model training, reduced dimensionality, and potentially better model performance.

How to implement this in your domain

  1. 1Integrate VPOS into your data preprocessing pipelines for unsupervised feature selection tasks.
  2. 2Benchmark VPOS against existing feature selection methods on your datasets to assess performance gains.
  3. 3Apply VPOS to reduce the dimensionality of high-dimensional data before training machine learning models.
  4. 4Explore the use of VPOS in scenarios where interpretability of selected features is important due to its connection to PCA.

Who benefits

Data ScienceMachine LearningFinancial ServicesHealthcareE-commerce

Key takeaways

  • VPOS is a new greedy unsupervised feature selection method.
  • It uses orthogonal deflation in PCA loading space for efficient selection.
  • VPOS achieves lower reconstruction MSE and is significantly faster than alternatives.
  • It offers a principled way to select diverse and informative features.

Original post by Baran Koseoglu, Berrin Yanikoglu

"arXiv:2607.23198v1 Announce Type: new 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…"

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Originally posted by Baran Koseoglu, Berrin Yanikoglu on X · view source

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