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Neighborhood construction models are important in finding connection amongthe data points, which helps demonstrate interrelations among the information.Hence, employing a new approach to find neighborhood among the data points is achallenging issue. The methods, suggested so far, are not useful forsimultaneous analysis of distances and precise examination of the geometricposition of the data as well as their geometric relationships. Moreover, mostof the suggested algorithms depend on regulating parameters including number ofneighborhoods and limitations in fixed regions. The purpose of the proposedalgorithm is to detect and offer an applied geometric pattern among the datathrough data mining. Precise geometric patterns are examined according to therelationships among the data in neighborhood space. These patterns can revealthe behavioural discipline and similarity across the data. It is assumed thatthere is no prior information about the data sets at hand. The aim of thepresent research study is to locate the precise neighborhood using Apolloniuscircle, which can help us identify the neighborhood state of data points. Highefficiency of Apollonius structure in assessing local similarities among theobservations 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 thestate-of-the-art and well-known (k-Nearest Neighbor and epsilon-neighborhood)algorithms.

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