This paper presents a unified framework for spectral feature selection, which integrates both supervised and unsupervised learning approaches. The framework leverages spectral graph theory to measure feature relevance based on the structure of the graph induced from pairwise instance similarities. By designing different similarity matrices and ranking functions, the framework can generate families of algorithms for both types of feature selection. The authors demonstrate that powerful algorithms like ReliefF (supervised) and Laplacian Score (unsupervised) are special cases of the proposed framework. Experiments on benchmark datasets show that the proposed framework outperforms or matches the performance of existing algorithms, highlighting its effectiveness and generality. The framework provides a comprehensive approach to feature selection, enabling joint study and derivation of new algorithms.This paper presents a unified framework for spectral feature selection, which integrates both supervised and unsupervised learning approaches. The framework leverages spectral graph theory to measure feature relevance based on the structure of the graph induced from pairwise instance similarities. By designing different similarity matrices and ranking functions, the framework can generate families of algorithms for both types of feature selection. The authors demonstrate that powerful algorithms like ReliefF (supervised) and Laplacian Score (unsupervised) are special cases of the proposed framework. Experiments on benchmark datasets show that the proposed framework outperforms or matches the performance of existing algorithms, highlighting its effectiveness and generality. The framework provides a comprehensive approach to feature selection, enabling joint study and derivation of new algorithms.