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The procedure of outliers detection in univariate circular data can be developed using clustering algorithm. In clustering, it is necessary to calculate the similarity measure in order to cluster the observations into their own group. The similarity measure in circular data can be determined by calculating circular distance between each point of angular observation. In this paper, clustering-based procedure for outlier detection in univariate circular biological data with different similarity distance measures will be developed and the performance will be investigated. Three different circular similarity distance measures are used for the outliers detection procedure using single-linkage clustering algorithm. However, there are two similarity measures namely Satari distance and Di distance that are found to have similarity in formula for univariate circular data. The aim of this study is to develop and demonstrate the effectiveness of proposed clustering-based procedure with different similarity distance measure in detecting outliers. Therefore, in this study the circular similarity distance of SL-Satari/Di and another similarity measure namely SL-Chang will be compared at certain cutting rule. It is found that clustering-based procedure using single-linkage algorithm with different similarity distances are applicable and promising approach for outlier detection in univariate circular data, particularly for biological data. The result also found that at a certain condition of data, the SL-Satari/Di distance seems to overperform the performance of SL-Chang distance.


Similarity measure Circular distance circular data Outliers Clustering algorithm

Article Details

Author Biographies

Nur Syahirah Zulkipli, 0000-0003-2354-8725

Centre for Mathematical Sciences, College of Computing and Applied Sciences, Universiti Malaysia Pahang, Malaysia

Siti Zanariah Satari, Centre for Mathematical Sciences, Universiti Malaysia Pahang, Malaysia

Centre for Mathematical Sciences, College of Computing and Applied Sciences, Universiti Malaysia Pahang, Malaysia

Wan Nur Syahidah Wan Yusoff, Centre for Mathematical Sciences, Universiti Malaysia Pahang, Malaysia

Centre for Mathematical Sciences, College of Computing and Applied Sciences, Universiti Malaysia Pahang, Malaysia

How to Cite
Zulkipli, N. S., Satari, S. Z., & Wan Yusoff, W. N. S. (2022). The Effect of Different Similarity Distance Measures in Detecting Outliers Using Single-Linkage Clustering Algorithm for Univariate Circular Biological Data. Pakistan Journal of Statistics and Operation Research, 18(3), 561-573.

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