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The instance reduction is one of the data preprocessing methods and aims to remove noises and (or) redundant instances from the training set. In the instance reduction, one of the most representative techniques is the edition method which can remove harmful instances from the training set to improve the prediction accuracy of k nearest neighbor (KNN). Nevertheless, most of existing edition methods still have some drawbacks, such as the parameter dependency, high computational time and relatively low accuracy. To solve these problems, we present a new fast parameter-free edition method based on local sets with natural neighbors (ELS). In ELS, we define a new concept of local sets by introducing natural neighbors. ELS can use the local sets to keep more reasonable class boundaries and effectively filtering out noisy instances (including global outliers). The main advantages of ELS are that (a) it is parameter-free; (b) it can remove global outliers and noisy instances; (c) it is relatively fast. Experiments clearly verify that (a) ELS outperforms existing representative edition methods in improving the prediction accuracy of KNN; (b) ELS can improve the performance of the condensation method and hybrid method in terms of both accuracy and reduction; (c) ELS consumes relatively low running time.