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.

翻译：线性回归分析侧重于依据特定回归变量的数值来预测数值型回归目标值。在此背景下，k-最近邻（k-NN）是一种常见的非参数回归算法，与文献中的其他算法相比，其性能表现高效。本研究通过利用所引入的一种算术方法的潜力，提出对k-NN算法的优化，该方法能为涉及任意数量实变量的线性方程提供解。具体而言，采用算术方法算法（AMA）来评估所引入算术方法的效率，同时提出算术方法回归（AMR）算法作为利用AMA潜力对k-NN的优化。该算法根据引入的最优推断决策规则，与其他回归算法进行了比较，并在某些公开可用的真实世界数据源上进行了评估。结果令人鼓舞，因为所提出的AMR算法与其他算法性能相当，且在大多数情况下其性能优于k-NN。输出结果表明，所引入的AMR是对k-NN的一种优化。