Sohrab Azimpour | Searcharxiv

arXiv2018

NCARD: Improving Neighborhood Construction by Apollonius Region Algorithm based on Density

Due to the increased rate of information in the present era, local identification of similar and related data points by using neighborhood construction algorithms is highly significant for processing information in various sciences. Geometric methods are especially useful for their accuracy in locating highly similar neighborhood points using efficient geometric structures. Geometric methods should be examined for each individual point in neighborhood data set so that similar groups would be formed. Those algorithms are not highly accurate for high dimension of data. Due to the important challenges in data point analysis, we have used geometric method in which the Apollonius circle is used to achieve high local accuracy with high dimension data. In this paper, we propose a neighborhood construction algorithm, namely Neighborhood Construction by Apollonius Region Density (NCARD). In this study, the neighbors of data points are determined using not only the geometric structures, but also the density information. Apollonius circle, one of the state-of-the-art proximity geometry methods, Apollonius circle, is used for this purpose. For efficient clustering, our algorithm works better with high dimension of data than the previous methods; it is also able to identify the local outlier data. We have no prior information about the data in the proposed algorithm. Moreover, after locating similar data points with Apollonius circle, we will extract density and relationship among the points, and a unique and accurate neighborhood is created in this way. The proposed algorithm is more accurate than the state-of-the-art and well-known algorithms up to almost 8-13% in real and artificial data sets.

cs.CG↗

arXiv2018

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

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.

cs.CG↗