On Gower Similarity Coefficient and Missing Values

Abstract

The Gower similarity coefficient is a popular measure for comparing objects with possibly mixed-type attributes and missing values. One of its characteristics is that it calculates the coefficient value without considering attributes with missing values. In this article, we explore the properties of the coefficient in detail, including the consequences of omitting attributes with missing values. We also introduce strict lower and upper bounds on the actual similarity value on an attribute and strict lower and upper bounds on the actual value of the Gower similarity coefficient, derive a number of their properties and propose a new coefficient as a solution to the identified problem with the Gower similarity coefficient.