# Sparse PCA via l2,p-Norm Regularization for Unsupervised Feature Selection

arXiv: https://arxiv.org/abs/2012.14595 · HTML: https://mlsanity.com/paper/2012.14595/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Dec 2020.

## Built on by (most cited first, 13 of 13)

- [Bi-Sparse Unsupervised Feature Selection](https://mlsanity.com/paper/2412.16819/) (2024)
- [Fast Sparse PCA via Positive Semidefinite Projection for Unsupervised Feature Selection](https://mlsanity.com/paper/2309.06202/) (2023)
- [Orientation-Aware Sparse Tensor PCA for Efficient Unsupervised Feature Selection](https://mlsanity.com/paper/2407.16985/) (2024)
- [Enhancing Unsupervised Feature Selection via Double Sparsity Constrained Optimization](https://mlsanity.com/paper/2501.00726/) (2025)
- [Orthogonal Constrained Minimization with Tensor ℓ2,p Regularization for HSI Denoising and Destriping](https://mlsanity.com/paper/2407.03605/) (2024)
- [K-means Derived Unsupervised Feature Selection using Improved ADMM](https://mlsanity.com/paper/2411.15197/) (2024)
- [Tuning-Free Structured Sparse PCA via Deep Unfolding Networks](https://mlsanity.com/paper/2502.20837/) (2025)
- [Robust Unsupervised Fault Diagnosis For High-Dimensional Nonlinear Noisy Data](https://mlsanity.com/paper/2503.08916/) (2025)
- [Federated Structured Sparse PCA for Anomaly Detection in IoT Networks](https://mlsanity.com/paper/2503.23981/) (2025)
- [Robust Orthogonal NMF with Label Propagation for Image Clustering](https://mlsanity.com/paper/2504.21472/) (2025)
- [Bi-Level Unsupervised Feature Selection](https://mlsanity.com/paper/2505.20563/) (2025)
- [Generalized Geometry Block Proximal Linearized Method for Multiblock Nonconvex and Nonsmooth Optimization](https://mlsanity.com/paper/2609.39301/) (2026)
- [Learning to Select Features with Manifold Deep Unfolding PCA](https://mlsanity.com/paper/2610.19436/) (2026)

## Abstract (arXiv)

In the field of data mining, how to deal with high-dimensional data is an inevitable problem. Unsupervised feature selection has attracted more and more attention because it does not rely on labels. The performance of spectral-based unsupervised methods depends on the quality of constructed similarity matrix, which is used to depict the intrinsic structure of data. However, real-world data contain a large number of noise samples and features, making the similarity matrix constructed by original data cannot be completely reliable. Worse still, the size of similarity matrix expands rapidly as the number of samples increases, making the computational cost increase significantly. Inspired by principal component analysis, we propose a simple and efficient unsupervised feature selection method, by combining reconstruction error with l2,p-norm regularization. The projection matrix, which is used for feature selection, is learned by minimizing the reconstruction error under the sparse constraint. Then, we present an efficient optimization algorithm to solve the proposed unsupervised model, and analyse the convergence and computational complexity of the algorithm theoretically. Finally, extensive experiments on real-world data sets demonstrate the effectiveness of our proposed method.