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

TL;DR

Polar encoding offers a simple, effective baseline for handling missing data in classification tasks, preserving missingness information without imputation and performing competitively with advanced methods.

Contribution

The paper introduces polar encoding as a universal, easy-to-apply method that naturally incorporates missingness and unifies categorical and numerical attributes under a barycentric coordinate framework.

Findings

Outperforms MICE and MIDAS in classification accuracy on real datasets.

Does not require imputation, simplifying the data preprocessing pipeline.

Compatible with any classification algorithm, including decision trees.

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 non-missing values, and lets decision tree algorithms choose how to split missing values, thereby providing a practical realisation of the "missingness incorporated in attributes" (MIA) 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" (MICE) and "multiple imputation with denoising autoencoders" (MIDAS) and -- depending on the classifier -- about as well or better than mean/mode imputation with missing-indicators.