Variance-Preserving Orthogonal Selection (VPOS): Greedy Feature Selection via Orthogonal Deflation in PCA Loading Space
Mirrored from arXiv — Machine Learning for archival readability. Support the source by reading on the original site.
Computer Science > Machine Learning
Title:Variance-Preserving Orthogonal Selection (VPOS): Greedy Feature Selection via Orthogonal Deflation in PCA Loading Space
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%.
| Comments: | 23 pages |
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2607.23198 [cs.LG] |
| (or arXiv:2607.23198v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2607.23198
arXiv-issued DOI via DataCite (pending registration)
|
Access Paper:
- View PDF
- HTML (experimental)
- TeX Source
References & Citations
Bookmark
Bibliographic and Citation Tools
Code, Data and Media Associated with this Article
Demos
Recommenders and Search Tools
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
More from arXiv — Machine Learning
-
LoKiFormer: Locality-aware Attention with Decoupled Knowledge Memory for Efficient Large Language Model Pretraining
Aug 14
-
Which Site, and When: A Free-Satellite-Data Test of Himalayan Glacial Lake Bursts, Landslides, and Ice Floods
Aug 14
-
MARCH: Scaling Recurrent Memory with Content-Routed State Anchors
Aug 14
-
Multi-AUV Ad-hoc network-based Target Tracking: A Value Gradient Guidance Multi-Agent Diffusion Reinforcement Learning Approach
Aug 14
Discussion (0)
Sign in to join the discussion. Free account, 30 seconds — email code or GitHub.
Sign in →No comments yet. Sign in and be the first to say something.