New clustering approach for symbolic polygonal data: application to the clustering of entrepreneurial regimes

TL;DR

This paper introduces a novel polygonal symbolic data clustering method that overcomes limitations of traditional approaches, enabling richer data representation and improved analysis of entrepreneurial regimes, demonstrated on GEM data.

Contribution

The paper presents a new polygonal cluster analysis approach for symbolic data, with theoretical justification and application to entrepreneurial regimes using GEM data.

Findings

Developed a dynamic clustering algorithm for polygonal symbolic data.

Constructed typologies of countries based on entrepreneurial responses.

Proved main theorems validating the clustering method.

Abstract

Entrepreneurial regimes are topic, receiving ever more research attention. Existing studies on entrepreneurial regimes mainly use common methods from multivariate analysis and some type of institutional related analysis. In our analysis, the entrepreneurial regimes is analyzed by applying a novel polygonal symbolic data cluster analysis approach. Considering the diversity of data structures in Symbolic Data Analysis (SDA), interval-valued data is the most popular. Yet, this approach requires assuming equidistribution hypothesis. We use a novel polygonal cluster analysis approach to address this limitation with additional advantages: to store more information, to significantly reduce large data sets preserving the classical variability through polygon radius, and to open new possibilities in symbolic data analysis. We construct a dynamic cluster analysis algorithm for this type of data with proving main theorems and lemmata to justify its usage. In the empirical part we use dataset of Global Entrepreneurship Monitor (GEM) for year 2015 to construct typologies of countries based on responses to main entrepreneurial questions. The article presents a novel approach to clustering in statistical theory (with novel type of variables never accounted for) and application to a pressing issue in entrepreneurship with novel results.