# Learning Feature Sparse Principal Components

arXiv: https://arxiv.org/abs/1904.10155 · HTML: https://mlsanity.com/paper/1904.10155/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Apr 2019.

## Built on by (most cited first, 8 of 8)

- [Bi-Sparse Unsupervised Feature Selection](https://mlsanity.com/paper/2412.16819/) (2024)
- [Semi-Supervised Sparse Gaussian Classification: Provable Benefits of Unlabeled Data](https://mlsanity.com/paper/2409.03335/) (2024)
- [Feature Grouping and Sparse Principal Component Analysis with Truncated Regularization](https://mlsanity.com/paper/2106.13685/) (2021)
- [Enhancing Unsupervised Feature Selection via Double Sparsity Constrained Optimization](https://mlsanity.com/paper/2501.00726/) (2025)
- [Analysis of Truncated Orthogonal Iteration for Sparse Eigenvector Problems](https://mlsanity.com/paper/2103.13523/) (2021)
- [Tuning-Free Structured Sparse PCA via Deep Unfolding Networks](https://mlsanity.com/paper/2502.20837/) (2025)
- [Bi-Level Unsupervised Feature Selection](https://mlsanity.com/paper/2505.20563/) (2025)
- [Learning to Select Features with Manifold Deep Unfolding PCA](https://mlsanity.com/paper/2610.19436/) (2026)

## Abstract (arXiv)

This paper presents new algorithms to solve the feature-sparsity constrained PCA problem (FSPCA), which performs feature selection and PCA simultaneously. Existing optimization methods for FSPCA require data distribution assumptions and are lack of global convergence guarantee. Though the general FSPCA problem is NP-hard, we show that, for a low-rank covariance, FSPCA can be solved globally (Algorithm 1). Then, we propose another strategy (Algorithm 2) to solve FSPCA for the general covariance by iteratively building a carefully designed proxy. We prove theoretical guarantees on approximation and convergence for the new algorithms. Experimental results show the promising performance of the new algorithms compared with the state-of-the-arts on both synthetic and real-world datasets.