### Journals Information

Mathematics and Statistics Vol. 10(5), pp. 895 - 908
DOI: 10.13189/ms.2022.100501
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## The Initialization of Flexible K-Medoids Partitioning Method Using a Combination of Deviation and Sum of Variable Values

Kariyam 1,2,*, Abdurakhman 1, Subanar 2, Herni Utami 1
1 Department of Mathematics, Faculty of Mathematics and Natural Sciences, Gadjah Mada University, Indonesia
2 Department of Statistics, Faculty of Mathematics and Natural Sciences, Universitas Islam Indonesia, Indonesia

ABSTRACT

This research proposed a new algorithm for clustering datasets using the Flexible K-Medoids Partitioning Method. The procedure is divided into two phases, selecting the initial medoids and determining the partitioned dataset. The initial medoids are selected based on the block representation of a combination of the sum and deviation of the variable values. The relative positions of the objects will be separated when the sum of the values of the p variables is different even though these objects have the same variance. The objects are selected flexibly from each block as the initial medoids to construct the initial groups. This process ensures that any identical objects will be in the same group. The candidate of final medoids is determined randomly by selecting objects from each initial group. Then, the final medoids were identified based on the combination of objects that produces the minimum value of the total deviation within the cluster. The proposed method overcomes the empty group that may arise in a simple and fast k-medoids algorithm. In addition, it overcomes identical objects in the different groups that may occur in the initialization of the simple k-medoids algorithm. Furthermore, the artificial data and six real datasets, namely iris, ionosphere, soybean small, primary tumor, heart disease case 1 and zoo were used to evaluate this method, and the results were compared with other algorithms based on the initial and final groups' performance. The experiment results showed that the proposed method ensures that no initial groups are empty. For real datasets, the adjusted Rand index and clustering accuracy of the final groups of the new algorithm outperforms the other methods.

KEYWORDS
Clustering, Flexible K-Medoids, Initialization, Deviation

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Kariyam , Abdurakhman , Subanar , Herni Utami , "The Initialization of Flexible K-Medoids Partitioning Method Using a Combination of Deviation and Sum of Variable Values," Mathematics and Statistics, Vol. 10, No. 5, pp. 895 - 908, 2022. DOI: 10.13189/ms.2022.100501.

(b). APA Format:
Kariyam , Abdurakhman , Subanar , Herni Utami (2022). The Initialization of Flexible K-Medoids Partitioning Method Using a Combination of Deviation and Sum of Variable Values. Mathematics and Statistics, 10(5), 895 - 908. DOI: 10.13189/ms.2022.100501.