Sains Malaysiana 50(6)(2021): 1787-1798

http://doi.org/10.17576/jsm-2021-5006-24

Comparative Study of Clustering-Based Outliers Detection Methods in Circular-Circular Regression Model

(Kajian Perbandingan Kaedah Penetapan Titik Terpencil Berasaskan Kelompok dalam Model Pendaftaran Lingkaran)

SITI ZANARIAH SATARI¹*, NUR FARAIDAH MUHAMMAD D¹*, YONG ZULINA ZUBAIRI² & ABDUL GHAPOR HUSSIN³

¹Centre for Mathematical Sciences College of Computing & Applied Sciences, Universiti Malaysia Pahang, 26300 Kuantan, Pahang Darul Makmur, Malaysia

²Centre for Foundation Studies in Sciences, University of Malaya, 50603 Kuala Lumpur, Federal Territory, Malaysia

³Faculty of Defence Sciences and Technology, National Defence University of Malaysia, Sungai Besi Camp, 57000 Kuala Lumpur, Federal Territory, Malaysia

Received: 7 May 2019/Accepted: 14 October 2020

ABSTRACT

This paper is a comparative study of several algorithms for detecting multiple outliers in circular-circular regression model based on the clustering algorithms. Three measures of similarity based on the circular distance were used to obtain a cluster tree using the agglomerative hierarchical methods. A stopping rule for the cluster tree based on the mean direction and circular standard deviation of the tree height was used as the cutoff point and classifier to the cluster group that exceeded the stopping rule as potential outliers. The performances of the algorithms have been demonstrated using the simulation studies that consider several outlier scenarios with a certain degree of contamination. Application to real data using wind data and a simulated data set are given for illustrative purposes. Thus, it has been found that Satari’s algorithm (S-SL algorithm) performs well for any values of sample size n and error concentration parameter. The algorithms are good in identifying outliers which are not limited to one or few outliers only, but the presence of multiple outliers at one time.

Keywords: Circular distance; circular-circular regression model; clustering; outliers; stopping rule

ABSTRAK

Kertas ini membincangkan kajian perbandingan beberapa algoritma yang mengesan titik terpencil berganda dalam model regresi bulatan berdasarkan algoritma berkelompok. Tiga ukuran persamaan berasaskan jarak bulatan telah digunakan bagi mendapatkan pokok kelompok menggunakan algoritma aglomeratif hierarki. Satu nilai potongan untuk pokok kelompok berdasarkan min terarah dan sisihan piawai bulatan bagi ketinggian pokok tersebut telah digunakan bagi mengkelaskan kumpulan kelompok yang melebihi titik potongan ini sebagai titik terpencil. Prestasi algoritma ini telah diuji dalam kajian simulasi yang mengambil kira beberapa senario titik terpencil dengan tahap berbeza. Untuk tujuan illustrasi, satu aplikasi data sebenar menggunakan data angin dan satu set data simulasi telah diberikan. Kami mendapati algoritma Satari (Algoritma S-SL) adalah baik untuk sebarang nilai saiz sampel dan parameter menumpu. Algoritma tersebut adalah baik dalam mengenal pasti titik terpencil atau berganda pada satu masa.

Kata kunci: Algoritma berkelompok; jarak bulatan; model regresi bulatan; nilai potongan; titik terpencil

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*Corresponding author; email: zanariah@ump.edu.my