Normalization in Proportional Feature Spaces

TL;DR

This paper explores normalization techniques for proportional and skewed features, introducing concepts, properties, and a modified similarity index, with preliminary experiments demonstrating their application in data analysis.

Contribution

It presents a duality relationship between uniform and proportional feature spaces and proposes new normalization methods based on non-centralized dispersion.

Findings

Duality relationship between feature spaces established

Normalization methods based on dispersion introduced

Modified Jaccard index incorporating normalization proposed

Abstract

The subject of features normalization plays an important central role in data representation, characterization, visualization, analysis, comparison, classification, and modeling, as it can substantially influence and be influenced by all of these activities and respective aspects. The selection of an appropriate normalization method needs to take into account the type and characteristics of the involved features, the methods to be used subsequently for the just mentioned data processing, as well as the specific questions being considered. After briefly considering how normalization constitutes one of the many interrelated parts typically involved in data analysis and modeling, the present work addressed the important issue of feature normalization from the perspective of uniform and proportional (right skewed) features and comparison operations. More general right skewed features are also considered in an approximated manner. Several concepts, properties, and results are described and discussed, including the description of a duality relationship between uniform and proportional feature spaces and respective comparisons, specifying conditions for consistency between comparisons in each of the two domains. Two normalization possibilities based on non-centralized dispersion of features are also presented, and also described is a modified version of the Jaccard similarity index which incorporates intrinsically normalization. Preliminary experiments are presented in order to illustrate the developed concepts and methods.