Unbiased mixed variables distance

TL;DR

This paper introduces a new class of unbiased distance measures for mixed variables that ensure each variable's contribution is unaffected by its type or measurement scale, improving fairness in data analysis.

Contribution

It provides a formal framework and general formulation for constructing unbiased distances in mixed variable settings, addressing biases present in existing methods.

Findings

Proposes a formal concept of bias in mixed variable distances.

Develops a general formulation for unbiased mixed variable distances.

Addresses limitations of existing biased distance measures.

Abstract

Defining a distance in a mixed setting requires the quantification of observed differences of variables of different types and of variables that are measured on different scales. There exist several proposals for mixed variable distances, however, such distances tend to be biased towards specific variable types and measurement units. That is, the variable types and scales influence the contribution of individual variables to the overall distance. In this paper, we define unbiased mixed variable distances for which the contributions of individual variables to the overall distance are not influenced by measurement types or scales. We define the relevant concepts to quantify such biases and we provide a general formulation that can be used to construct unbiased mixed variable distances.