Empirical Approach: Introduction

In this chapter, we will describe the fundamentals of the proposed new “empirical” approach as a systematic methodology with its nonparametric quantities derived entirely from the actual data with no subjective and/or problem-specific assumptions made. It has a potential to be a powerful extension of (and/or alternative to) the traditional probability theory, statistical learning and computational intelligence methods. The nonparametric quantities of the proposed new empirical approach include: (1) the cumulative proximity; (2) the eccentricity, and the standardized eccentricity; (3) the data density, and (4) the typicality. They can be recursively updated on a sample-by-sample basis, and they have unimodal and multimodal, discrete and continuous forms/versions. The nonparametric quantities are based on ensemble properties of the data and not limited by prior restrictive assumptions. The discrete version of the typicality resembles the unimodal probability density function, but is in a discrete form. The discrete multimodal typicality resembles the probability mass function.