Robust Unsupervised Feature Selection Algorithm Based on Fuzzy Anchor Graph

Unsupervised feature selection aims to characterize the cluster structure of original features and select the optimal subset without label guidance. However, existing methods overlook fuzzy information in the data, failing to model cluster structures between data effectively, and rely on squared error for data reconstruction, exacerbating noise impact. Therefore, a robust unsupervised feature selection algorithm based on fuzzy anchor graphs (FWFGFS) is proposed. To address the inaccuracies in neighbor assignments, a fuzzy anchor graph learning mechanism is designed. This mechanism models the association between nodes and clusters using fuzzy membership distributions, effectively capturing potential fuzzy neighborhood relationships between nodes and avoiding rigid assignments to specific clusters. This soft cluster assignment mechanism improves clustering accuracy and the robustness of the graph structure while maintaining low computational costs. Additionally, to mitigate the interference of noise in the feature selection process, an adaptive fuzzy weighting mechanism is presented. This mechanism assigns different weights to features based on their contribution to the error, thereby reducing errors caused by redundant features and noise. Orthogonal tri-factorization is applied to the low-dimensional representation matrix. This guarantees that each center represents only one class of features, resulting in more independent cluster centers. Experimental results on 12 public datasets show that FWFGFS improves the average clustering accuracy by 5.68% to 13.79% compared with the state-of-the-art methods.