Missing values : processing with the Kohonen algorithm

TL;DR

This paper explores how the Kohonen algorithm can effectively handle datasets with missing values, offering an alternative to traditional imputation methods, and emphasizing its visualization advantages.

Contribution

It demonstrates that the Kohonen algorithm can process incomplete data directly without prior imputation, highlighting its practical benefits in real-world data analysis.

Findings

Kohonen algorithm handles missing data without prior imputation.

It preserves data structure and visualization quality.

Compared favorably to traditional methods like mean substitution.

Abstract

The processing of data which contain missing values is a complicated and always awkward problem, when the data come from real-world contexts. In applications, we are very often in front of observations for which all the values are not available, and this can occur for many reasons: typing errors, fields left unanswered in surveys, etc. Most of the statistical software (as SAS for example) simply suppresses incomplete observations. It has no practical consequence when the data are very numerous. But if the number of remaining data is too small, it can remove all significance to the results. To avoid suppressing data in that way, it is possible to replace a missing value with the mean value of the corresponding variable, but this approximation can be very bad when the variable has a large variance. So it is very worthwhile seeing that the Kohonen algorithm (as well as the Forgy algorithm) perfectly deals with data with missing values, without having to estimate them beforehand. We are particularly interested in the Kohonen algorithm for its visualization properties.