Three new instance selection methods based on local sets: A comparative study with several approaches from a bi-objective perspective

• We propose three selection strategies with different accuracy–reduction tradeoff.
• We assess them on 26 known databases with more than 1000 instances each one.
• The results are compared with those of 11 successful state-of-the-art methods.
• According to different criteria, the new methods are always among the top performers.

The local set is the largest hypersphere centered on an instance such that it does not contain instances from any other class. Due to its geometrical nature, this structure can be very helpful for distance-based classification, such as classification based on the nearest neighbor rule. This paper is focused on instance selection for nearest neighbor classification which, in short, aims to reduce the number of instances in the training set without affecting the classification accuracy. Three instance selection methods based on local sets, which follow different and complementary strategies, are proposed. In an experimental study involving 26 known databases, they are compared with 11 of the most successful state-of-the-art methods in standard and noisy environments. To evaluate their performances, two complementary approaches are applied, the Pareto dominance relation and the Technique for Order Preference by Similarity to Ideal Solution. The results achieved by the proposals reveal that they are among the most effective methods in this field.