TY - CHAP

T1 - Empirical Approach

T2 - Introduction

AU - Angelov, Plamen Parvanov

AU - Gu, Xiaowei

N1 - Publisher Copyright:
© 2019, Springer Nature Switzerland AG.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

UR - http://www.research.lancs.ac.uk/portal/en/publications/empirical-approachintroduction(eff67c8d-5fa9-4042-bf23-d21c591591df).html

UR - http://www.scopus.com/inward/record.url?scp=85055330678&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-02384-3_4

DO - 10.1007/978-3-030-02384-3_4

M3 - Chapter

SN - 9783030023843

SN - 9783030023836

T3 - Studies in Computational Intelligence

SP - 103

EP - 133

BT - Empirical Approach to Machine Learning

PB - Springer Nature

ER -