Optimizing the Division of Study Class Groups Using the Partitioning Around Medoids (PAM) Method

− Optimization is a step to solve a problem to get more profitable results. Profitable based on the point of view used or the desired needs. The optimization value can be profitable in the maximum position or profitable in the minimum position. A problem can be solved in different ways, to produce the best solution. The best conditions can be viewed from many things, including tolerance, methods, and problems. Many theories have been developed to solve optimization problems. This optimization problem is often discussed because it is very close to human life. In this case, optimization can be interpreted as the process of achieving the most optimal results by adjusting input, selecting equipment, mathematical processes, and testing. Thereby in this paper, the Partitioning Around Medoids (PAM) method has succeeded in optimizing class grouping by calculating the closest distance between the achievement and intelligence of each student.


INTRODUCTION
Class is another form of set or grouping. Each class is filled with a variety of different variables. In the formation of a class ideally, class members can be grouped based on uniformity of achievement [1]. This uniformity of achievement can affect the teaching process more effectively and efficiently. The level of intelligence of students is very influential in the achievement of material in the classroom [2]. Because students with above-average intelligence will prefer a fast learning process and material that is always increasing. Whereas students with lower levels of intelligence would prefer a slower and more repetitive learning process [3]. With this difference, the learning process will experience inequality [4].
The correct teaching process can also improve the quality of learning. This class grouping needs to be done because there are differences in variations between the abilities and skills of each student [5], [6]. Schools often classify students using a random method, ignoring student achievement and intelligence levels [7]. The right method in group formation is to use the cluster method. The cluster method can group students mathematically and can reduce the boundaries between students and other students. Based on this explanation, it is necessary to research grouping student classes using the PAM cluster technique.
The PAM algorithm is better than other algorithms because it uses the entire dataset to find the best potential. This algorithm is classified as an algorithm with high computational complexity because it always calculates the distance between datasets[8] [9]. The PAM method is also proven to be stronger than the k-means method in clustering because k-means has a weakness in handling noise and outliners [10], [11].

Clustering
Clustering is a method of analyzing data, which is often included as a data mining method. The purpose of clustering is to group data with the same characteristics into the same area and data with different characteristics to another region [12]. Various methods can be used to measure the similarity value between objects being compared, one of which is the Euclidean Distance [13]. (1)

Optimization
Optimization aims to be able to solve a certain problem so that the most favorable conditions are obtained from a certain point of view [14]. Optimization is a process related to input adjustment, characteristic selection, mathematical process, and testing [15].

Partitioning Around Medoids (PAM)
K-Medoid or also known as Partitioning Around Medoids (PAM) is a classic partition clustering technique that groups data sets from ni objects into k groups known as a priori. The cluster formation process begins by randomly assigning k objects from the dataset as medoids [9].
Step of PAM algorithm: a. Initialize k cluster centers (number of clusters) b. Allocate each data (object) to the nearest cluster using the Euclidian Distance measurement equation c. Randomly select objects in each cluster as candidates for the new medoid. d. Calculate the distance of each object in each cluster with the new medoid candidate. e. Calculate the total deviation (S) by calculating the value of the new total distance -the old total distance. If S <0, then swap objects with cluster data to form a set of k new objects as medoids. f. Repeat steps 3 to 5 until there is no change in medoid, so that you get the cluster and the members of each cluster.

RESULT AND DISCUSSION
The initial stage is to prepare a dataset. In this study using data on school X with the average school score and the average exam score shown in table 1. The average school score was obtained from the diploma, while the average exam score was obtained at the time of school entrance selection. The data used are as many as 40 data, which will be grouped into two clusters. The data grouping is used in the following stages: Initialization of the cluster center as much as 2 clusters from the sample data. For selection, each medoid was selected randomly. Assume P5 and P17 as initial medoids P5(85, 80), P17(89, 73).

CONCLUSION
The results of this study indicate that in the second iteration, the PAM method has succeeded in grouping data into 2 clusters. This happens because the cluster members do not change anymore and the value S is greater than zero. Dataset of 40 participants who have passed, they can be grouped into 2 clusters using the PAM method. The first cluster is formed with members P2, P4, P5, P6, P10, P11, P12, P13, P14, P16, P18, P20, P21, P22, P23, P26, P28, P33, P35, P36, P38, and P40. The second cluster (C2) are P1, P3, P7, P8, P9, P15, P17, P19, P24, P26, P27, P29, P30, P31, P32, P34, P37, and P39. The K-medoid method or the PAM method succeeded in grouping 40 students into two clusters. In Figure 3, it is clear that the difference between cluster 1 and cluster 2. Calculating the distance and iteration on the k-medoids successfully classifies the data. The cluster method is very important to implement because with the PAM method students with the same level of intelligence will be grouped into one group. This clustering process can support the teaching and learning process to be better so that the learning process can be more effective and efficient. It is hoped that this research can be used as a reference for schools that want to divide students into several parts based on the scores obtained at school with the scores obtained at the time of selection.