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 GHAPOR^1,*, 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

Received: 12 October 2022/Accepted: 10 May 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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^*Corresponding author; email: adilahghapor@gmail.com