Representing missing values through polar encoding

We propose polar encoding, a representation of categorical and numerical $[0,1]$-valued attributes with missing values that preserves the information encoded in the distribution of the missing values. Unlike the existing missing-indicator approach, this does not require imputation. We support our proposal with three different arguments. Firstly, polar encoding ensures that missing values become equidistant from all non-missing values by mapping the latter onto the unit circle. Secondly, polar encoding lets decision trees choose how missing values should be split, providing a practical realisation of the missingness incorporated in attributes (MIA) proposal. And lastly, polar encoding corresponds to the normalised representation of categorical and $[0,1]$-valued attributes when viewed as barycentric attributes, a new concept based on traditional barycentric coordinates. In particular, we show that barycentric attributes are fuzzified categorical attributes, that their normalised representation generalises one-hot encoding, and that the polar encoding of $[0, 1]$-valued attributes is analogous to the one-hot encoding of binary attributes. With an experiment based on twenty real-life datasets with missing values, we show that polar encoding performs about as well or better than the missing-indicator approach in terms of the resulting classification performance.