# Enhancing Unsupervised Feature Selection via Double Sparsity Constrained Optimization

arXiv: https://arxiv.org/abs/2501.00726 · HTML: https://mlsanity.com/paper/2501.00726/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 39 references that are in the map.
- First posted on arXiv 1 Jan 2025.

## Builds on (most cited first, 9 of 9)

- [Deep Feature Selection using a Teacher-Student Network](https://mlsanity.com/paper/1903.07045/) (2019)
- [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)
- [A Convex Sparse PCA for Feature Analysis](https://mlsanity.com/paper/1411.6233/) (2014)
- [Deep Unsupervised Learning for Joint Antenna Selection and Hybrid Beamforming](https://mlsanity.com/paper/2106.03127/) (2021)
- [Fast Sparse PCA via Positive Semidefinite Projection for Unsupervised Feature Selection](https://mlsanity.com/paper/2309.06202/) (2023)
- [Computing One-bit Compressive Sensing via Double-Sparsity Constrained Optimization](https://mlsanity.com/paper/2101.03599/) (2021)
- [Fused Lasso for Feature Selection using Structural Information](https://mlsanity.com/paper/1902.09947/) (2019)
- [Gradient Projection Newton Algorithm for Sparse Collaborative Learning Using Synthetic and Real Datasets of Applications](https://mlsanity.com/paper/2108.06605/) (2021)

## Built on by (most cited first, 1 of 1)

- [Variance-Preserving Orthogonal Selection (VPOS): Greedy Feature Selection via Orthogonal Deflation in PCA Loading Space](https://mlsanity.com/paper/2607.23198/) (2026)

## Abstract (arXiv)

Unsupervised feature selection (UFS) is widely applied in machine learning and pattern recognition. However, most of the existing methods only consider a single sparsity, which makes it difficult to select valuable and discriminative feature subsets from the original high-dimensional feature set. In this paper, we propose a new UFS method called DSCOFS via embedding double sparsity constrained optimization into the classical principal component analysis (PCA) framework. Double sparsity refers to using ℓ2,0-norm and ℓ0-norm to simultaneously constrain variables, by adding the sparsity of different types, to achieve the purpose of improving the accuracy of identifying differential features. The core is that ℓ2,0-norm can remove irrelevant and redundant features, while ℓ0-norm can filter out irregular noisy features, thereby complementing ℓ2,0-norm to improve discrimination. An effective proximal alternating minimization method is proposed to solve the resulting nonconvex nonsmooth model. Theoretically, we rigorously prove that the sequence generated by our method globally converges to a stationary point. Numerical experiments on three synthetic datasets and eight real-world datasets demonstrate the effectiveness, stability, and convergence of the proposed method. In particular, the average clustering accuracy (ACC) and normalized mutual information (NMI) are improved by at least 3.34% and 3.02%, respectively, compared with the state-of-the-art methods. More importantly, two common statistical tests and a new feature similarity metric verify the advantages of double sparsity. All results suggest that our proposed DSCOFS provides a new perspective for feature selection.