Original Article International Journal of Fuzzy Logic and Intelligent Systems Vol. 20, No. 2, June 2020, pp. 156-167 http://doi.org/10.5391/IJFIS.2020.20.2.156 ISSN(Print) 1598-2645 ISSN(Online) 2093-744X Automatic Determination of the Number of Clusters for Semi-Supervised Relational Fuzzy Clustering Norah Ibrahim Fantoukh ■ , Mohamed Maher Ben Ismail ■ , and Ouiem Bchir ■ Department of Computer Science, College of Computer and Information Sciences, King Saud University, Riyadh, Saudi Arabia Abstract Semi-supervised clustering relies on both labeled and unlabeled data to steer the clustering process towards optimal categorization and escape from local minima. In this paper, we pro- pose a novel fuzzy relational semi-supervised clustering algorithm based on an adaptive local distance measure (SSRF-CA). The proposed clustering algorithm utilizes side-information and formulates it as a set of constraints to supervise the learning task. These constraints are expressed using reward and penalty terms, which are integrated into a novel objective function. In particular, we formulate the clustering task as an optimization problem through the minimization of the proposed objective function. Solving this optimization problem provides the optimal values of different objective function parameters and yields the proposed semi- supervised clustering algorithm. Along with its ability to perform data clustering and learn the underlying dissimilarity measure between the data instances, our algorithm determines the optimal number of clusters in an unsupervised manner. Moreover, the proposed SSRF-CA is designed to handle relational data. This makes it appropriate for applications where only pairwise similarity (or dissimilarity) information between data instances is available. In this paper, we proved the ability of the proposed algorithm to learn the appropriate local distance measures and the optimal number of clusters while partitioning the data using various syn- thetic and real-world benchmark datasets that contain varying numbers of clusters with diverse shapes. The experimental results revealed that the proposed SSRF-CA accomplished the best performance among other state-of-the-art algorithms and confirmed the outperformance of our clustering approach. Keywords: Semi-supervised clustering, Relational data, Fuzzy clustering, Local distance measure learning, Optimal number of clusters Received: Feb. 16, 2020 Revised : May 10, 2020 Accepted: May 26, 2020 Correspondence to: Mohamed Maher Ben Ismail and Ouiem Bchir (maher.benismail@gmail.com, ouiem.bchir@gmail.com) ©The Korean Institute of Intelligent Systems cc This is an Open Access article dis- tributed under the terms of the Creative Commons Attribution Non-Commercial Li- cense (http://creativecommons.org/licenses/ by-nc/3.0/) which permits unrestricted non- commercial use, distribution, and reproduc- tion in any medium, provided the original work is properly cited. 1. Introduction Clustering is one of the most popular unsupervised learning techniques that are commonly used in data mining and pattern recognition fields [1, 2]. The resulting categories include sets of homogeneous patterns [1]. Accordingly, the distances between the data instances that belong to the same cluster exhibit high similarity to each other compared to those from other clusters. Clustering can be perceived as a data modeling technique that yields concise data summarization. Recently, clustering approaches have gained attention because they play a key | 156