# Learning to Select Features with Manifold Deep Unfolding PCA

arXiv: https://arxiv.org/abs/2610.19436 · HTML: https://mlsanity.com/paper/2610.19436/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 50 references that are in the map.
- First posted on arXiv 14 Oct 2026.

## Builds on (most cited first, 17 of 17)

- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Learning to Optimize: A Primer and A Benchmark](https://mlsanity.com/paper/2103.12828/) (2021)
- [Model-Based Deep Learning](https://mlsanity.com/paper/2012.08405/) (2020)
- [LLM-Select: Feature Selection with Large Language Models](https://mlsanity.com/paper/2407.02694/) (2024)
- [Deep Feature Selection using a Teacher-Student Network](https://mlsanity.com/paper/1903.07045/) (2019)
- [Orthogonal Directions Constrained Gradient Method: from non-linear equality constraints to Stiefel manifold](https://mlsanity.com/paper/2303.09261/) (2023)
- [Sparse PCA via l2,p-Norm Regularization for Unsupervised Feature Selection](https://mlsanity.com/paper/2012.14595/) (2020)
- [RPCANet++: Deep Interpretable Robust PCA for Sparse Object Segmentation](https://mlsanity.com/paper/2508.04190/) (2025)
- [Learning Feature Sparse Principal Components](https://mlsanity.com/paper/1904.10155/) (2019)
- [Bi-Sparse Unsupervised Feature Selection](https://mlsanity.com/paper/2412.16819/) (2024)
- [Spiking Meets Attention: Efficient Remote Sensing Image Super-Resolution with Attention Spiking Neural Networks](https://mlsanity.com/paper/2503.04223/) (2025)
- [Unsupervised Feature Selection via Nonnegative Orthogonal Constrained Regularized Minimization](https://mlsanity.com/paper/2403.16966/) (2024)
- [Comprehensive Review of Deep Unfolding Techniques for Next-Generation Wireless Communication Systems](https://mlsanity.com/paper/2502.05952/) (2025)
- [STAR-Net: An Interpretable Model-Aided Network for Remote Sensing Image Denoising](https://mlsanity.com/paper/2505.24327/) (2025)
- [Sparse Tensor CCA via Manifold Optimization for Multi-View Learning](https://mlsanity.com/paper/2504.02339/) (2025)
- [Causally-Aware Unsupervised Feature Selection Learning](https://mlsanity.com/paper/2410.12224/) (2024)
- [Robust Sparse Phase Retrieval: Statistical Guarantee, Optimality Theory and Convergent Algorithm](https://mlsanity.com/paper/2505.23273/) (2025)

## Abstract (arXiv)

Unsupervised feature selection (UFS) is of great significance in image processing and pattern recognition. Nevertheless, existing model-based methods often rely on manually tuned hyperparameters, while deep learning-based methods generally require massive training data. To address these issues, this paper proposes an efficient manifold deep unfolding feature selection network (MDUFS-Net). Technically, we first incorporate the ℓ2,0-norm into the classic principal component analysis (PCA) framework, then unfold the alternating direction method of multipliers (ADMM)-based iterative algorithm into an end-to-end trainable network, thereby enabling automatic parameter learning. Moreover, a manifold optimization strategy is developed to improve the numerical robustness. On this basis, we further extend MDUFS-Net into an enhanced variant called MDUFS-Net+ by introducing the ℓ0-norm for more discriminative feature representations. Extensive experiments validate that our proposed MDUFS-Net and MDUFS-Net+ outperform state-of-the-art methods in the UFS task, with promising performance in clustering. Our code is available at https://github.com/xianchaoxiu/MDUFS.