Polar Encoding: A Simple Baseline Approach for Classification With Missing Values

Abstract

We propose polar encoding, a representation of categorical and numerical [0, 1]-valued attributes with missing values to be used in a classification context. We argue that this is a good baseline approach, because it can be used with any classification algorithm, preserves missingness information, is very simple to apply, and offers good performance. In particular, unlike the existing missing-indicator approach, it does not require imputation, ensures that missing values are equidistant from nonmissing values, and lets decision tree algorithms choose how to split missing values, thereby, providing a practical realization of the missingness incorporated in attributes proposal. Furthermore, we show that categorical and [0, 1]-valued attributes can be viewed as special cases of a single attribute type, corresponding to the classical concept of barycentric coordinates, and that this offers a natural interpretation of polar encoding as a fuzzified form of one-hot encoding. With an experiment based on twenty real-life datasets with missing values, we show that, in terms of the resulting classification performance, polar encoding performs better than the state-of-the-art strategies multiple imputation by chained equations and multiple imputation with denoising autoencoders and - depending on the classifier - about as well or better than mean/mode imputation with missing-indicators.