Dimensional Analysis and Implicit Function: An Application to Textual Data

Abstract

The purpose of the research is to test the viability and usefulness of the dimensional analysis based on the Vaschy-Buckingham Π theorem and implicit function applied to textual data. The method uses hermeneuticalanalysis that allows identifying most frequent words, phrases, and the colocations of words, defining words as categories, and then, as fundamental and derived variables; collocation textual analysis also provides the word links that create a conceptual structure to building the dimensional matrixes and equations by the Vaschy-Buckingham Π theorem. The Gauss-Jordan method gives a solution to the matrixes. Besides, the implicit function theorem allows creating relationships among the Π numbers and solving them by partial derivatives, gaining insights about the relevance of variables and their relationships. As an example, the model applies to the financial summary report about Isodiol International Inc. Reports Profitable Q4 Financial Statements, delivered by EMIS. Results showed the following relevant categories:1)Company Financial Performance,2)Company,3)Continued,4)Global,5)Expand,6)Footprint,7)Diversification,8)Costs,9)Bioactive,10 )Acquisitions,11)CBD,12)Anticipate,13)Traction,14).Additional. They were classified as fundamental and derived variables. All of them were considered derived variables, while the fundamental variables were:1)Expand, 2)Footprint,3)Diversification,4)Costs,5)Bioactive,6)Acquisitions,7)CBD,8)Anticipate,9)Traction,10). The application of the Vaschy-Buckingham Π theoremresulted in four Πnumbers, rearranged into an implicit function where the dependent variable was Company Financial Performance. The solution by partial derivatives resulted in identifying the category “Company Financial Performance” as well as “Traction” and “Additional” as core categories in the financial report; however, the other categories are also relevant. Conclusions point out the relevance of the analysis to textual data as an interphase between qualitative and quantitative data and also in helping to find relevant variables.