Exploring Scale-Measures of Data Sets

TL;DR

This paper investigates the properties of scale-measures in data sets, leveraging lattice theory and attribute exploration to enable efficient exploration and automatic scaling recommendations for data analysis.

Contribution

It introduces a novel exploration algorithm for scale-measures based on attribute exploration, advancing the understanding of their lattice structure and applications in data scaling.

Findings

The set of all scale-measures forms a lattice structure.

The proposed algorithm efficiently explores scale-measures.

Applications include semi-automatic data scaling and recommendations.

Abstract

Measurement is a fundamental building block of numerous scientific models and their creation. This is in particular true for data driven science. Due to the high complexity and size of modern data sets, the necessity for the development of understandable and efficient scaling methods is at hand. A profound theory for scaling data is scale-measures, as developed in the field of formal concept analysis. Recent developments indicate that the set of all scale-measures for a given data set constitutes a lattice and does hence allow efficient exploring algorithms. In this work we study the properties of said lattice and propose a novel scale-measure exploration algorithm that is based on the well-known and proven attribute exploration approach. Our results motivate multiple applications in scale recommendation, most prominently (semi-)automatic scaling.