Problems of Information Technology (2022), vol. 13, no. 2, 3-15 3 AN ADAPTIVE  -MEDIANS CLUSTERING ALGORITHM Adil M. Bagirov 1,a , Sona Taheri 2,a,b , Burak Ordin 3,c a School of Engineering, Information Technology and Physical Sciences, Federation University Australia, Ballarat, Australia b School of Mathematical Sciences, RMIT University, Melbourne, Australia c Department of Mathematics, Faculty of Science, Ege University, Izmir, Turkey 1 a.bagirov@federation.edu.au; 2 sona.taheri@rmit.edu.au; 3 burak.ordin@ege.edu.tr 1 0000-0003-2075-1699; 2 0000-0003-1779-4567; 3 0000-0001-7897-3265 1. Introduction Clustering deals with the problem of organizing a collection of objects into clusters based on their similarity. It has a wide range of applications in many fields (Bagirov, Karmitsa, & Taheri, 2020; Castellanos, Cigarran, & Garcia- Serrano, 2017; Dai et al., 2019; Jain, 2010). The similarity measure is a fundamental notion in cluster analysis. In data sets with only numeric attributes this measure can be defined using different norms. Clustering problems with the similarity measure defined using the squared Euclidean norm have been studied in far more detailed than those with similarity measures based on other norms (Bagirov, Karmitsa & Taheri, 2020; Bai et al., 2013; Karmitsa, Bagirov & Taheri, 2017; Karmitsa, Bagirov & Taheri, 2018; Lai & Huang, 2010; Xavier & Xavier, 2011). Clustering algorithms with the similarity measure defined using the  1 -norm are more robust to outliers than those with the squared Euclidean norm (Zhang et al., 2012). These algorithms are more preferable in high dimensional data (Aggarwal, Hinneburg, & Keim, 2001). They produce the highest identification and the best verification rates in the speaker recognition systems (Hanilci & Ertas, 2011). To the best of our knowledge, the paper (Carmichael & Sneath, 1969) is the first where the clustering problem with the  1 -norm is considered. The -medians algorithm was developed in (Spath, 1976). The ISODATA algorithm with the  1 -norm was introduced in 13 (2) 2022 Available online at www.jpit.az A R T I C L E I N F O http://doi.org/10.25045/jpit.v13.i2.01 Article history: Received 14 March 2022 Received in revised form 27 May 2022 Accepted 17 June 2022 Keywords: Cluster analysis -medians algorithm Adaptive clustering A B S T R A C T A new version of the -medians algorithm, the adaptive k-medians algorithm, is introduced to solve clustering problems with the similarity measure defined using the  1 -norm. The proposed algorithm first calculates the center of the whole data set as its median. To solve the -clustering problem (>1), we formulate the auxiliary clustering problem to generate a set of starting points for the -th cluster center. Then, the -medians algorithm is applied starting from the previous ( − 1) cluster centers and each point from the set of starting points to solve the -clustering problem. A solution with the least value of the clustering function is accepted as the solution to the -clustering problem. We evaluate the performance of the adaptive -medians algorithm and compare it with other concurrent clustering algorithms using 8 real-world data sets.