A Generalized Methodology for Data Analysis

By Plamen Parvanov Angelov, Xiaowei Gu, José Carlos Príncipe. 2018

71 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Statistical and Nonlinear Physics

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Citations in the corpus

Towards Explainable Deep Neural Networks (xDNN) (2019, background): “It is based on prototypes and the data density [13] as well as typicality - an empirically derived pdf [14].”
Deep rule-based classifier with human-level performance and characteristics (2018, methodology): “Because of the prototype-based nature, the DRB classifier is free from prior assumptions about the type of distribution as well as the random or deterministic nature of data [6], the requirements of setting ad hoc model structure, handcrafting membership functions, etc.”
Novelty Detection and Learning from Extremely Weak Supervision (2019, background): “Finally, it also has a statistical nature and offers an empirical form of the pdf [13].”