A Generalized Methodology for Data Analysis.

Area of Science:

• Data Science
• Statistical Analysis
• Machine Learning

Background:

• Traditional data analysis often assumes randomness or determinism, which may not hold true for complex, real-world datasets.
• Existing methods rely on a priori continuous probability density functions, limiting applicability in data-rich environments with unclear underlying phenomena.

Purpose of the Study:

• To propose a new functional approach for estimating data ensemble properties based on empirical observations of discrete data samples.
• To introduce Empirical Data Analysis (EDA) as a method that does not assume randomness, determinism, or independence of data.
• To develop computationally efficient nonparametric estimators for ensemble properties.

Main Methods:

• Developed a functional approach based on empirical observations and the relative proximity of discrete data points.
• Introduced nonparametric square centrality and typicality as key ensemble functions.
• Derived typicality directly from discrete data in a closed analytical form, enabling recursive calculation.
• Interpreted nonparametric estimators as a discrete form of information potential, akin to Parzen windows.

Main Results:

• EDA provides a method to estimate ensemble properties without assuming data randomness or determinism.
• The typicality measure is derived directly from discrete data, offering an alternative to traditional probability density functions.
• The recursive calculation of typicality ensures computational efficiency.
• Preliminary tests indicate good performance compared to traditional data analysis techniques.

Conclusions:

• Empirical Data Analysis (EDA) is a robust and efficient methodology suitable for data-rich environments where underlying phenomena are unclear.
• The nonparametric estimators and direct derivation of typicality offer significant advantages over traditional approaches.
• EDA's foundation in empirical observation makes it broadly applicable across various data analysis domains.