Analyzing the elbow method in predicting the optimal number of clusters in Electronic Communications dataset

The aim of this article is to answer the question if elbow method giving us the best possible solution regarding the optimal number of clusters. Elbow method is one of the methodologies, which is often used in predicting the number of clusters. On the other side, it is always a question, how precise is a mathematical methodology in optimizing the number of clusters in comparison to qualitative methodologies. It is necessary to answer the question is elbow method giving us the best possible solution. It is crucial to answer what does it really mean in practical case, when analyzing the number of clusters in specific area in our case electronic communications development of different EU countries. The research is the combination of quantitative methodology and qualitative methodology. Elbow method itself is a quantitative methodology, which needs to be proved by qualitative method by analyzing and synthesis of the facts. In our case, we analyzed the sample of 32 different countries described by electronic communications development parameters and population density. The quantitative analyze was done in jupyter notebook environment by using the appropriate python code. It was proved by qualitative analyze using Rapidminer application (Alstair AI studio from 2024). K-means clustering was done by clustering the dataset into different number of clusters. By analyzing the results of clustering, we tried to prove the elbow method in this specific case by dividing the countries based on the electronic communications development parameters and population density. The result proved that in case of dataset of 32 samples, quantitative elbow method gave us satisfied result and separation in 3 clusters was optimal. It divided the countries in the most optimal way based on their specific characteristics regarding the electronic communications development parameters and population density.Elbow method is crucial and simple way to find optimal number of clusters, but all the quantitative methods need to be proved by qualitative method, where deep understanding of the research area is necessary.