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

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 \e{multiple imputation by chained equations} (MICE) and \e{multiple imputation with denoising autoencoders} (MIDAS) and -- depending on the classifier -- about as well or better than mean/mode imputation with missing-indicators.