Feature selection seeks to identify optimal feature subsets from high-dimensional spaces for enhanced machine learning performance. Conventional approaches assume uniform feature relevance across all classes and employ global selection criteria, leading to suboptimal performance on complex real-world datasets where class distributions and feature relationships exhibit significant heterogeneity. We observe that in many practical scenarios, certain features demonstrate strong predictive power for specific classes while remaining irrelevant or even detrimental for others–a phenomenon we term class-specific feature relevance. To exploit this insight, we introduce Feature Selection with Class Self-Representation (FSCSR), a novel two-stage framework that first preserves global data structure to identify universally relevant features, then employs a self-representation mechanism to discover class-specific discriminative features within the globally selected subset. Extensive evaluation across twelve benchmark datasets demonstrates that FSCSR outperforms existing feature selection methods, achieving superior classification accuracy while maintaining computational efficiency. Our empirical analysis provides strong evidence supporting the hypothesis of class-specific feature relevance.