Fuzzy clustering as a new grouping technique to define the business size of SMEs through their financial information

Abstract

SMEs have a very important performance in any current economy because they contribute both to the generation of wealth and to the creation of jobs. In this article we analyze a sample of 12,658 Catalan SMEs and show the level of association that exists between some of their financial ratios to construct a synthetic measure that explains their business size. For the study of financial ratios, we used three data analysis techniques first, and to find the optimal number of clusters, we used the Two-Phase Clusters algorithm. Subsequently, and once the optimal number of groups was known, the most probable business size (cluster) for each company was calculated through a Fuzzy Clustering analysis. Finally, the optimal cluster, estimated for each company, was validated with a Probit model. The results allowed knowing that the size reported by each company is not necessarily equal to the synthetic measure proposed in this article. It is suggested to validate our results with an accounting analysis, other equally robust methodologies or algorithms, such as neural networks.