This paper proposes a unified framework for feature selection based on spectral graph theory, which can generate families of algorithms for both supervised and unsupervised learning. The framework is able to unify existing powerful algorithms such as ReliefF (supervised) and Laplacian Score (unsupervised) as special cases. The framework is based on the concept of graph structure and uses the spectrum of the graph induced from pairwise instance similarities to measure feature relevance. The paper introduces three feature ranking functions, which are derived from the properties of the graph's spectrum. These functions are used to rank features based on their consistency with the graph structure. The framework is evaluated on benchmark datasets, and the results show that the proposed algorithms outperform existing methods in terms of accuracy. The paper also discusses the connections between the proposed framework and existing algorithms, and shows that the framework can be extended to derive new algorithms. The study demonstrates the effectiveness of the framework in both supervised and unsupervised feature selection.This paper proposes a unified framework for feature selection based on spectral graph theory, which can generate families of algorithms for both supervised and unsupervised learning. The framework is able to unify existing powerful algorithms such as ReliefF (supervised) and Laplacian Score (unsupervised) as special cases. The framework is based on the concept of graph structure and uses the spectrum of the graph induced from pairwise instance similarities to measure feature relevance. The paper introduces three feature ranking functions, which are derived from the properties of the graph's spectrum. These functions are used to rank features based on their consistency with the graph structure. The framework is evaluated on benchmark datasets, and the results show that the proposed algorithms outperform existing methods in terms of accuracy. The paper also discusses the connections between the proposed framework and existing algorithms, and shows that the framework can be extended to derive new algorithms. The study demonstrates the effectiveness of the framework in both supervised and unsupervised feature selection.