# Unsupervised Feature Selection with Adaptive Structure Learning

arXiv: https://arxiv.org/abs/1504.00736 · HTML: https://mlsanity.com/paper/1504.00736/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Apr 2015.

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

- [Local Sample-weighted Multiple Kernel Clustering with Consensus Discriminative Graph](https://mlsanity.com/paper/2207.02846/) (2022)
- [Nonnegative Matrix Factorization in Dimensionality Reduction: A Survey](https://mlsanity.com/paper/2405.03615/) (2024)
- [Fast Sparse PCA via Positive Semidefinite Projection for Unsupervised Feature Selection](https://mlsanity.com/paper/2309.06202/) (2023)
- [Compactness Score: A Fast Filter Method for Unsupervised Feature Selection](https://mlsanity.com/paper/2201.13194/) (2022)
- [A Novel Non-Invasive Estimation of Respiration Rate from Photoplethysmograph Signal Using Machine Learning Model](https://mlsanity.com/paper/2102.09483/) (2021)
- [Unsupervised Instance and Subnetwork Selection for Network Data](https://mlsanity.com/paper/2212.12771/) (2022)
- [Feature selection simultaneously preserving both class and cluster structures](https://mlsanity.com/paper/2307.03902/) (2023)
- [GOLFS: Feature Selection via Combining Both Global and Local Information for High Dimensional Clustering](https://mlsanity.com/paper/2507.10956/) (2025)

## Abstract (arXiv)

The problem of feature selection has raised considerable interests in the past decade. Traditional unsupervised methods select the features which can faithfully preserve the intrinsic structures of data, where the intrinsic structures are estimated using all the input features of data. However, the estimated intrinsic structures are unreliable/inaccurate when the redundant and noisy features are not removed. Therefore, we face a dilemma here: one need the true structures of data to identify the informative features, and one need the informative features to accurately estimate the true structures of data. To address this, we propose a unified learning framework which performs structure learning and feature selection simultaneously. The structures are adaptively learned from the results of feature selection, and the informative features are reselected to preserve the refined structures of data. By leveraging the interactions between these two essential tasks, we are able to capture accurate structures and select more informative features. Experimental results on many benchmark data sets demonstrate that the proposed method outperforms many state of the art unsupervised feature selection methods.