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

arXiv: https://arxiv.org/abs/2210.01905 · HTML: https://mlsanity.com/paper/2210.01905/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 91 references that are in the map.
- First posted on arXiv 4 Oct 2022.

## Builds on (most cited first, 7 of 7)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [On the consistency of supervised learning with missing values](https://mlsanity.com/paper/1902.06931/) (2019)
- [Benchmarking missing-values approaches for predictive models on health databases](https://mlsanity.com/paper/2202.10580/) (2022)
- [Trajectories, bifurcations and pseudotime in large clinical datasets: applications to myocardial infarction and diabetes data](https://mlsanity.com/paper/2007.03788/) (2020)
- [Prediction with Missing Data via Bayesian Additive Regression Trees](https://mlsanity.com/paper/1306.0618/) (2013)
- [Exoplanet Characterization using Conditional Invertible Neural Networks](https://mlsanity.com/paper/2202.00027/) (2022)
- [No imputation without representation](https://mlsanity.com/paper/2206.14254/) (2022)

## Abstract (arXiv)

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.