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.

翻译：我们提出极坐标编码（polar encoding），这是一种用于分类场景中表示包含缺失值的类别属性和数值型$[0,1]$值属性的方法。我们认为该方法是一种优秀的基线方案，原因在于：它可以与任何分类算法兼容，保留缺失值信息，易于实现且性能良好。特别地，与现有的缺失指示器（missing-indicator）方法不同，它无需进行插补，确保缺失值与非缺失值保持等距，并允许决策树算法自主决定缺失值的分割方式，从而实现了“属性内嵌缺失信息”（MIA）方案的实际应用。此外，我们证明了类别属性和$[0,1]$值属性可被视为单一属性类型的特例，对应经典的重心坐标（barycentric coordinates）概念，这为极坐标编码提供了一种自然解释：将其视为独热编码（one-hot encoding）的模糊化形式。基于20个真实世界含缺失值数据集的实验表明，在分类性能方面，极坐标编码优于现有最优策略——链式方程多重插补（MICE）和去噪自编码器多重插补（MIDAS），且根据分类器的不同，其表现与均值/众数插补结合缺失指示器的方法相当或更优。