A New Weighted k-Nearest Neighbor Algorithm Based on Newton's Gravitational Force

The kNN algorithm has three main advantages that make it appealing to the community: it is easy to understand, it regularly offers competitive performance and its structure can be easily tuning to adapting to the needs of researchers to achieve better results. One of the variations is weighting the instances based on their distance. In this paper we propose a weighting based on the Newton’s gravitational force, so that a mass (or relevance) has to be assigned to each instance. We evaluated this idea in the kNN context over 13 benchmark data sets used for binary and multi-class classification experiments. Results in \(\mathrm {F}_1\) score, statistically validated, suggest that our proposal outperforms the original version of kNN and is statistically competitive with the distance weighted kNN version as well.

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