# An arithmetic method algorithm optimizing k-nearest neighbors compared to regression algorithms and evaluated on real world data sources

## TL;DR

This paper introduces an optimized k-NN regression algorithm using an arithmetic method, showing it performs as well or better than traditional methods on real-world data.

## Contribution

A novel Arithmetic Method Regression (AMR) algorithm is proposed as an optimized version of k-NN.

## Key findings

- The AMR algorithm performs comparably to or better than other regression algorithms on real-world data.
- AMR outperforms the traditional k-NN in most cases.
- The introduced arithmetic method enhances the efficiency of the k-NN algorithm.

## Abstract

Linear regression analysis focuses on predicting a numeric regressand value based on certain regressor values. In this context, k-Nearest Neighbors (k-NN) is a common non-parametric regression algorithm, which achieves efficient performance when compared with other algorithms in literature. In this research effort an optimization of the k-NN algorithm is proposed by exploiting the potentiality of an introduced arithmetic method, which can provide solutions for linear equations involving an arbitrary number of real variables. Specifically, an Arithmetic Method Algorithm (AMA) is adopted to assess the efficiency of the introduced arithmetic method, while an Arithmetic Method Regression (AMR) algorithm is proposed as an optimization of k-NN adopting the potentiality of AMA. Such algorithm is compared with other regression algorithms, according to an introduced optimal inference decision rule, and evaluated on certain real world data sources, which are publicly available. Results are promising since the proposed AMR algorithm has comparable performance with the other algorithms, while in most cases it achieves better performance than the k-NN. The output results indicate that introduced AMR is an optimization of k-NN.

The online version contains supplementary material available at 10.1038/s41598-025-33966-9.