# Bi-Sparse Unsupervised Feature Selection

arXiv: https://arxiv.org/abs/2412.16819 · HTML: https://mlsanity.com/paper/2412.16819/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 53 references that are in the map.
- First posted on arXiv 22 Dec 2024.

## Builds on (most cited first, 7 of 7)

- [Learning to Optimize: A Primer and A Benchmark](https://mlsanity.com/paper/2103.12828/) (2021)
- [Non-convex Optimization for Machine Learning](https://mlsanity.com/paper/1712.07897/) (2017)
- [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)
- [Fast Sparse PCA via Positive Semidefinite Projection for Unsupervised Feature Selection](https://mlsanity.com/paper/2309.06202/) (2023)
- [Revisiting Lq(0≤ q<1) Norm Regularized Optimization](https://mlsanity.com/paper/2306.14394/) (2023)
- [Unsupervised Feature Learning with Emergent Data-Driven Prototypicality](https://mlsanity.com/paper/2307.01421/) (2023)

## Built on by (most cited first, 6 of 6)

- [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)
- [GoPrune: Accelerated Structured Pruning with ℓ2,p-Norm Optimization](https://mlsanity.com/paper/2511.22120/) (2025)
- [Efficient Personalized Federated PCA with Manifold Optimization for IoT Anomaly Detection](https://mlsanity.com/paper/2602.12622/) (2026)
- [Heaviside Low-Rank Support Matrix Machine](https://mlsanity.com/paper/2603.00491/) (2026)
- [Learning to Select Features with Manifold Deep Unfolding PCA](https://mlsanity.com/paper/2610.19436/) (2026)

## Abstract (arXiv)

To deal with high-dimensional unlabeled datasets in many areas, principal component analysis (PCA) has become a rising technique for unsupervised feature selection (UFS). However, most existing PCA-based methods only consider the structure of datasets by embedding a single sparse regularization or constraint on the transformation matrix. In this paper, we introduce a novel bi-sparse method called BSUFS to improve the performance of UFS. The core idea of BSUFS is to incorporate ℓ2,p-norm and ℓq-norm into the classical PCA, which enables our method to select relevant features and filter out irrelevant noises, thereby obtaining discriminative features. Here, the parameters p and q are within the range of [0, 1). Therefore, BSUFS not only constructs a unified framework for bi-sparse optimization, but also includes some existing works as special cases. To solve the resulting non-convex model, we propose an efficient proximal alternating minimization (PAM) algorithm using Stiefel manifold optimization and sparse optimization techniques. In addition, the computational complexity analysis is presented. Extensive numerical experiments on synthetic and real-world datasets demonstrate the effectiveness of our proposed BSUFS. The results reveal the advantages of bi-sparse optimization in feature selection and show its potential for other fields in image processing. Our code is available at https://github.com/xianchaoxiu/BSUFS.