Gower's similarity coefficients with automatic weight selection

TL;DR

This paper introduces an automatic weight selection method for Gower's similarity coefficients, improving dissimilarity measurement in mixed-type variables for nearest-neighbor methods, with demonstrated benefits in classification and missing data imputation.

Contribution

It proposes a new weighting scheme for Gower's dissimilarity that minimizes correlation differences, enhancing variable contribution balance in mixed-type data.

Findings

Improved classification accuracy in simulations.

Enhanced missing value imputation performance.

Effective handling of mixed variable types.

Abstract

Nearest-neighbor methods have become popular in statistics and play a key role in statistical learning. Important decisions in nearest-neighbor methods concern the variables to use (when many potential candidates exist) and how to measure the dissimilarity between units. The first decision depends on the scope of the application while second depends mainly on the type of variables. Unfortunately, relatively few options permit to handle mixed-type variables, a situation frequently encountered in practical applications. The most popular dissimilarity for mixed-type variables is derived as the complement to one of the Gower's similarity coefficient. It is appealing because ranges between 0 and 1, being an average of the scaled dissimilarities calculated variable by variable, handles missing values and allows for a user-defined weighting scheme when averaging dissimilarities. The discussion on the weighting schemes is sometimes misleading since it often ignores that the unweighted "standard" setting hides an unbalanced contribution of the single variables to the overall dissimilarity. We address this drawback following the recent idea of introducing a weighting scheme that minimizes the differences in the correlation between each contributing dissimilarity and the resulting weighted Gower's dissimilarity. In particular, this note proposes different approaches for measuring the correlation depending on the type of variables. The performances of the proposed approaches are evaluated in simulation studies related to classification and imputation of missing values.