A Novel and Efficient Data Point Neighborhood Construction Algorithm based on Apollonius Circle

TL;DR

This paper introduces a new data neighborhood construction algorithm based on Apollonius circles, which improves geometric pattern detection and local similarity assessment without relying on fixed parameters.

Contribution

The proposed algorithm leverages Apollonius circles for precise neighborhood detection, offering a geometric approach that outperforms traditional methods like k-NN and epsilon-neighborhood.

Findings

Higher accuracy in neighborhood detection compared to traditional methods

Effective geometric pattern recognition among data points

No need for prior parameter setting

Abstract

Neighborhood construction models are important in finding connection among the data points, which helps demonstrate interrelations among the information. Hence, employing a new approach to find neighborhood among the data points is a challenging issue. The methods, suggested so far, are not useful for simultaneous analysis of distances and precise examination of the geometric position of the data as well as their geometric relationships. Moreover, most of the suggested algorithms depend on regulating parameters including number of neighborhoods and limitations in fixed regions. The purpose of the proposed algorithm is to detect and offer an applied geometric pattern among the data through data mining. Precise geometric patterns are examined according to the relationships among the data in neighborhood space. These patterns can reveal the behavioural discipline and similarity across the data. It is assumed that there is no prior information about the data sets at hand. The aim of the present research study is to locate the precise neighborhood using Apollonius circle, which can help us identify the neighborhood state of data points. High efficiency of Apollonius structure in assessing local similarities among the observations has opened a new field of the science of geometry in data mining. In order to assess the proposed algorithm, its precision is compared with the state-of-the-art and well-known (k-Nearest Neighbor and epsilon-neighborhood) algorithms.