Sains Malaysiana
52(5)(2023):
1595-1606
http://doi.org/10.17576/jsm-2023-5205-20
Identifying Multiple Outliers in
Linear Functional Relationship Model Using a Robust Clustering Method
(Menentukan Data Terpencil Berganda bagi Model
Linear Hubungan Fungsian Menggunakan Kaedah Berkelompok yang Lebih Kukuh)
ADILAH ABDUL GHAPOR1,*, YONG
ZULINA ZUBAIRI2, SAYED MD. AL MAMUN3, SITI FATIMAH HASSAN4,
ELAYARAJA ARUCHUNAN5 & NURKHAIRANY AMYRA MOKHTAR6
1Department
of Decision Science, Faculty of Business and Economics, Universiti Malaya,
50603 Kuala Lumpur, Federal Territory, Malaysia
2Institute of
Advanced Studies, Universiti Malaya, 50603 Kuala Lumpur, Federal Territory,
Malaysia
3Department of
Statistics, University of Rajshahi, Bangladesh
4Centre for
Foundation Studies in Science, Universiti Malaya, Kuala Lumpur, Malaysia
5Institute
of Mathematical Sciences, Faculty of Science, Universiti Malaya, 50603 Kuala
Lumpur, Federal Territory, Malaysia
6Mathematical Sciences Studies, College of Computing,
Informatics and Media, Universiti Teknologi MARA, 85000 Segamat, Johor Darul
Takzim, Malaysia
Diserahkan:
12 Oktober 2022/Diterima: 10 Mei 2023
Abstract
Outliers are some observation points
outside the usual pattern of the other observations. It is essential to detect
outliers as anomalous observations can affect the inference made in the
analysis. In this study, we propose an efficient clustering procedure to
identify multiple outliers in the linear functional relationship model using
the single linkage algorithm with the Euclidean distance as the similarity
measure. A new robust cut-off point using the median and median absolute
deviation for the tree heights to classify the potential outliers are proposed
in this study. Experimental results from the simulation study suggest our
proposed method is able to identify the presence of multiple outliers with very
small probability of swamping and masking. Application in real data also shows
that the proposed clustering method for this linear functional relationship
model successfully detects the outliers, thus suggesting the method's
practicality in real-world problems.
Keywords: Clustering; linear; measurement
error; multiple outliers
Abstrak
Data terpencil merupakan
pemerhatian data yang berada di luar corak pemerhatian data yang lain.
Menentukan data terpencil adalah penting kerana pemerhatian yang luar biasa
boleh mempengaruhi inferens yang dibuat ke atas analisis tersebut. Dalam kajian
ini, kami mencadangkan kaedah berkelompok yang lebih kukuh untuk menentukan
data terpencil berganda bagi model linear hubungan fungsian (LFRM) menggunakan
satu hubungan algoritma dengan jarak Euclidean sebagai ukuran bersama. Satu
nilai potongan yang kukuh dicadangkan untuk mengumpulkan data terpencil
berganda dengan menggunakan median dan median sisihan mutlak bagi menentukan
ketinggian pokok tersebut. Keputusan uji kaji berdasarkan simulasi menunjukkan
kaedah yang dicadangkan berjaya mengesan data terpencil berganda di dalam
sesebuah set data dan menunjukkan prestasi yang bagus dengan nilai ‘masking’
dan ‘swamping’ yang rendah. Aplikasi pada data sebenar juga menunjukkan kaedah
berkelompok yang dicadangkan bagi model linear hubungan fungsian (LFRM) ini
berjaya menentukan data terpencil, justeru, dicadangkan penggunaan kaedah ini
dalam aplikasi pada data dunia yang sebenar.
Kata kunci: Berkelompok;
kesilapan pengukuran; linear; terpencil berganda
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*Pengarang untuk surat-menyurat; email:
adilahghapor@gmail.com
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