# Cluster Analysis with K-Mean versus K-Medoid in Financial Performance Evaluation
###### Abstract  
Nowadays there is a large amount of information at our disposal, which is increasing day by day, and right now the question is not whether we have a method to process it, but which method is most effective, faster and best. When processing large databases, with different data, the formation of homogeneous groups is recommended. This paper presents the financial performance of Hungarian and Romanian food retail companies by using two well-known cluster analyzing methods (K-Mean and K-Medoid) based on ROS (Return on Sales), ROA (Return on Assets) and ROE (Return on Equity) financial ratios. The research is based on two complete databases, including the financial statements for five years of all retail food companies from one Hungarian and one Romanian county. The hypothesis of the research is: in the case of large databases with variable quantitative data, cluster analysis is necessary in order to obtain accurate results and the method chosen can bring different results. It is justified to think carefully about choosing a method depending on the available data and the research aim. The aim of this study is to highlight the differences between the results of these two grouping procedures. Using the two methods we reached different results, which means a different evaluation of financial performance. The results demonstrate that the method chosen for grouping may influence the assessment of the financial performance of companies: the K-Mean method produces a greater variety of groups and the range of results obtained after grouping is larger; whereas, the group distribution and the results obtained by the K-Medoid method are more balanced. d 20 June 202005  
algorithms and their applicability, characteristics and limitations. The most commonly used methods are K-Mean and K-Medoid algorithms [3]. The K-Mean method uses the group mean (centroid) for grouping the data. The limitation of this method is that very different, distinct values can distort the results. For the definition of reference points, the K-Medoid method uses some representative values (called medoids) instead of mean values [4]. The K-Medoid method is considered less sensitive to outliers in comparison with K-Mean clustering [5]. Prior to grouping the databases, identifying and eliminating the outliers is recommended for more accurate results. Due to the negative effects of the outliers on the results, it is necessary to eliminate them [6]. More ways to identify the outliers are recognized such as the distance-based method, density-based method and graph methods [7]. Hypotheses and Purpose of the PaperFrom the very beginning of the present research, in the phase of creating the database, but also further on, when the first calculations were made, many research questions appeared based on which the research hypotheses were formulated. The hypotheses of this research are:  
1. For large databases, any type of analysis (social, financial, economic, statistical, etc.) should start firstly with an examination of the variability of the data (how different or similar the elements in the database are). If the elements of the database differ greatly from each other, the formation of homogeneous groups is necessary for effective and correct analysis. 2. The selection and determination of the indicators or characteristics based on which the groups will be formed are very important, as they can influence the obtained results. These indicators or characteristics must reflect the aim of the research. 3. The method chosen for the formation of groups influences the obtained results. The different sizes and contents of groups may influence the results. Based on these assumptions, _the purpose of this paper_ is to perform a comparative analysis between the results of two well-known and frequently used clustering methods (K-Mean and K-Medoid) in the field of financial performance. The processing of databases with large and variable data is possible and recommended only with homogeneous group resolution, based on cluster analysis.