A novel and efficient data point neighborhood construction algorithm based on Apollonius circle

Abstract

Keywords: Apollonius circle, geometric patterns, neighborhood construction

Improving neighborhood construction with Apollonius region algorithm based on density for clustering

“…We will show the results of the experiments on NCARD algorithm and will indicate enhancement of its accuracy in clustering and locating outlier data in comparison with other algorithms. Neighborhood construction algorithm was compared with εneighborhood, KNN (Jarvis & Patric 1973, Lu & Fu 1978, Qin et al, 2018, Tao et al, 2006, NCAR (Pourbahrami et al, 2018), and NC (İnkaya et al, 2015). After normalizing the data, performance of NCARD algorithm on real and artificial data are presented.…”

“…In the present paper, we analyzed the complexity of NCARD algorithm and compared it against several famous algorithms on neighborhood construction the results of which are shown in Table 3. As the table indicates, the proposed method is less complex than other geometric methods such as DPC-PCA (Du et al, 2016), DPC-KNN (Rodriguez & Laio, 2014), NCAR (Pourbahrami et al, 2018) and NC (İnkaya et al, 2015). The experiments are coded in MATLAB software on a 4 Due Intel Core, 3 GHz CPU and 4 GHz of RAM.…”

“…NCARD algorithm uses density and the decision region among the data points to determine neighborhood and explores the direct/indirect relationship among the data points using Apollonius circle. The goal is enhancing the accuracy of NCAR algorithm (Pourbahrami et al, 2018) in order to obtain different forms of clustering inside Apollonius circles by defining Apollonius region and density among the points. In case new clusters are formed inside the obtained circles (as a result of neighborhood with NCARD algorithm) we will try to explore them.…”

“…The first step in our algorithm is extracting the original neighborhood groups with Apollonius circle which is included in NCAR algorithm (Pourbahrami et al, 2018). This step includes three parts the first of which involves detecting target points (T).…”

“…The complexity of our algorithm is of O (n2) type; later we can use principal components analysis methods to reduce its complexity so that it would be applicable to very large data. NC (İnkaya et al, 2015) DPC-PCA (Du et al, 2016) DPC-KNN (Rodriguez & Laio, 2014) NCAR (Pourbahrami et al, 2018)…”