This paper introduces the hypergraph embedded entropy approach for gene selection (HEEGS), an innovative unsupervised algorithm designed to enhance clustering performance in high-dimensional biological data. HEEGS achieves this by preserving local structure through the integration of cluster indicators and entropy measures, enabling efficient data processing and the identification of distinct, biologically meaningful clusters. Unlike conventional methods that rely on the Laplacian matrix for pattern similarity, HEEGS uses the hyper-Laplacian, which provides a more robust similarity measure by capturing higher-order relationships among data points. Comparative experiments on twelve datasets and five state-of-the-art unsupervised algorithms demonstrate that HEEGS consistently outperforms its counterparts, achieving higher normalized mutual information (NMI) scores and clustering accuracy in nearly all cases. Statistical validation using the Nemenyi post hoc test further confirms that the performance improvements achieved by HEEGS are statistically significant. These results highlight HEEGS’s potential for critical applications such as biomarker discovery and disease classification.