A tutorial review on heterogeneity measurement: Theory and applications

Understanding heterogeneity in datasets poses a critical challenge in data science, with substantial implications across various fields, including ecology, medical sciences, social sciences, and sensor measurements. Heterogeneity results from diverse data sources, formats, and collection methods, making its accurate quantification essential for interpreting complex systems. This review offers a comprehensive overview of established techniques for quantifying heterogeneity, including Shannon entropy, q-logarithmic entropy, R’enyi entropy, the Leinster–Cobbold diversity index, Rao’s quadratic diversity index, and the Simpson diversity index. A mathematical discussion of these techniques is provided along with a comparative analysis to highlight the properties and applications of each technique. Furthermore, a detailed discussion addresses the application and significance of these approaches in quantifying heterogeneity across various data types, including numerical, imaging, and categorical data. Finally, the review discusses the existing challenges in the field of data heterogeneity and provides insights into its future perspectives. This work can serve as a comprehensive reference for researchers who focus on the measurement and analysis of data heterogeneity in broad domains of science and engineering.