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

2026-01-07

Scientific Reports

AI Summary

This work proposes a novel Arithmetic Method Regression (AMR) algorithm to address the limitations of traditional k-nearest neighbors (k-NN) regression, which suffers from efficiency and accuracy bottlenecks in high-dimensional or complex data and lacks an efficient mechanism for solving linear systems. AMR uniquely integrates the Arithmetic Method for solving general linear equations (AMA) into the k-NN framework and incorporates an optimal inference decision rule to achieve structured optimization in nonparametric regression. Experimental results on multiple real-world datasets demonstrate that AMR consistently outperforms standard k-NN across most scenarios and achieves performance comparable to or even surpassing that of state-of-the-art regression algorithms, highlighting its potential as an effective enhancement to the k-NN paradigm.

Technology Category

• Machine Learning: Kernel Methods
• Data Mining & Knowledge Management: Data Compression
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

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.

Problem

• k-Nearest Neighbors
• regression algorithms
• algorithm optimization
• real world data
• non-parametric regression

Innovation

• Arithmetic Method Algorithm
• k-Nearest Neighbors optimization
• Arithmetic Method Regression
• non-parametric regression
• optimal inference decision rule