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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - A Generalized Methodology for Data Analysis
AU - Angelov, Plamen Parvanov
AU - Gu, Xiaowei
AU - Principe, Jose
N1 - ©2017 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
PY - 2018/10
Y1 - 2018/10
N2 - Based on a critical analysis of data analytics and its foundations, we propose a functional approach to estimate data ensemble properties, which is based entirely on the empirical observations of discrete data samples and the relative proximity of these points in the data space and hence named empirical data analysis (EDA). The ensemble functions include the nonparametric square centrality (a measure of closeness used in graph theory) and typicality (an empirically derived quantity which resembles probability). A distinctive feature of the proposed new functional approach to data analysis is that it does not assume randomness or determinism of the empirically observed data, nor independence. The typicality is derived from the discrete data directly in contrast to the traditional approach, where a continuous probability density function is assumed a priori. The typicality is expressed in a closed analytical form that can be calculated recursively and, thus, is computationally very efficient. The proposed nonparametric estimators of the ensemble properties of the data can also be interpreted as a discrete form of the information potential (known from the information theoretic learning theory as well as the Parzen windows). Therefore, EDA is very suitable for the current move to a data-rich environment, where the understanding of the underlying phenomena behind the available vast amounts of data is often not clear. We also present an extension of EDA for inference. The areas of applications of the new methodology of the EDA are wide because it concerns the very foundation of data analysis. Preliminary tests show its good performance in comparison to traditional techniques.
AB - Based on a critical analysis of data analytics and its foundations, we propose a functional approach to estimate data ensemble properties, which is based entirely on the empirical observations of discrete data samples and the relative proximity of these points in the data space and hence named empirical data analysis (EDA). The ensemble functions include the nonparametric square centrality (a measure of closeness used in graph theory) and typicality (an empirically derived quantity which resembles probability). A distinctive feature of the proposed new functional approach to data analysis is that it does not assume randomness or determinism of the empirically observed data, nor independence. The typicality is derived from the discrete data directly in contrast to the traditional approach, where a continuous probability density function is assumed a priori. The typicality is expressed in a closed analytical form that can be calculated recursively and, thus, is computationally very efficient. The proposed nonparametric estimators of the ensemble properties of the data can also be interpreted as a discrete form of the information potential (known from the information theoretic learning theory as well as the Parzen windows). Therefore, EDA is very suitable for the current move to a data-rich environment, where the understanding of the underlying phenomena behind the available vast amounts of data is often not clear. We also present an extension of EDA for inference. The areas of applications of the new methodology of the EDA are wide because it concerns the very foundation of data analysis. Preliminary tests show its good performance in comparison to traditional techniques.
KW - Data mining and analysis
KW - machine learning
KW - pattern recognition
KW - probability
KW - statistics
KW - CENTRALITY
U2 - 10.1109/TCYB.2017.2753880
DO - 10.1109/TCYB.2017.2753880
M3 - Journal article
VL - 48
SP - 2981
EP - 2993
JO - IEEE Transactions on Cybernetics
JF - IEEE Transactions on Cybernetics
SN - 2168-2267
IS - 10
ER -