The impact of heterogeneous distance functions on missing data imputation and classification performance

This work performs an in-depth study of the impact of distance functions on K-Nearest Neighbours imputation of heterogeneous datasets. Missing data is generated at several percentages, on a large benchmark of 150 datasets (50 continuous, 50 categorical and 50 heterogeneous datasets) and data imputation is performed using different distance functions (HEOM, HEOM-R, HVDM, HVDM-R, HVDM-S, MDE and SIMDIST) and k values (1, 3, 5 and 7). The impact of distance functions on kNN imputation is then evaluated in terms of classification performance, through the analysis of a classifier learned from the imputed data, and in terms of imputation quality, where the quality of the reconstruction of the original values is assessed. By analysing the properties of heterogeneous distance functions over continuous and categorical datasets individually, we then study their behaviour over heterogeneous data. We discuss whether datasets with different natures may benefit from different distance functions and to what extent the component of a distance function that deals with missing values influences such choice. Our experiments show that missing data has a significant impact on distance computation and the obtained results provide guidelines on how to choose appropriate distance functions depending on data characteristics (continuous, categorical or heterogeneous datasets) and the objective of the study (classification or imputation tasks).