# Bi-Level Unsupervised Feature Selection

arXiv: https://arxiv.org/abs/2505.20563 · HTML: https://mlsanity.com/paper/2505.20563/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 53 references that are in the map.
- First posted on arXiv 26 May 2025.

## Builds on (most cited first, 4 of 4)

- [Investigating Bi-Level Optimization for Learning and Vision from a Unified Perspective: A Survey and Beyond](https://mlsanity.com/paper/2101.11517/) (2021)
- [Sparse PCA via l2,p-Norm Regularization for Unsupervised Feature Selection](https://mlsanity.com/paper/2012.14595/) (2020)
- [Learning Feature Sparse Principal Components](https://mlsanity.com/paper/1904.10155/) (2019)
- [Unsupervised Feature Selection via Nonnegative Orthogonal Constrained Regularized Minimization](https://mlsanity.com/paper/2403.16966/) (2024)

## Abstract (arXiv)

Unsupervised feature selection (UFS) is an important task in data engineering. However, most UFS methods construct models from a single perspective and often fail to simultaneously evaluate feature importance and preserve their inherent data structure, thus limiting their performance. To address this challenge, we propose a novel bi-level unsupervised feature selection (BLUFS) method, including a clustering level and a feature level. Specifically, at the clustering level, spectral clustering is used to generate pseudo-labels for representing the data structure, while a continuous linear regression model is developed to learn the projection matrix. At the feature level, the ℓ2,0-norm constraint is imposed on the projection matrix for more effectively selecting features. To the best of our knowledge, this is the first work to combine a bi-level framework with the ℓ2,0-norm. To solve the proposed bi-level model, we design an efficient proximal alternating minimization (PAM) algorithm, whose subproblems either have explicit solutions or can be computed by fast solvers. Furthermore, we establish the convergence result and computational complexity. Finally, extensive experiments on two synthetic datasets and eight real datasets demonstrate the superiority of BLUFS in clustering and classification tasks.