This chapter introduces the concept of local feature selection (LFS) as a contrast to traditional methods. Unlike existing LFS algorithms, which use distance-like objective functions, we propose a region purity-based LFS (RP-LFS) (Zhou et al. in IEEE Trans Evol Comput (2022), [1]) that incorporates a novel objective function, region purity, for multi-objective optimization. RP-LFS partitions the sample space into local regions and obtains a feature subset for each region, resulting in improved classification accuracy. To solve the RP-LFS problem, we propose an improved non-dominated sorting genetic algorithm III, which includes a network-inspired crossover operator and a quick bit mutation. We also develop a regional feature sharing strategy to preserve effective features between different local models. Experimental studies on 11 UCI datasets and nine high-dimensional datasets confirm the effectiveness of RP-LFS. Compared to state-of-the-art feature selection and LFS algorithms, RP-LFS achieves competitive classification accuracy while reducing the feature subset size.