The impact of missing data imputation procedures on the data topology

Abstract

Non-responses in surveys, non-recorded data, limitations of measuring devices, time limitations, etc. usually result in data incompleteness. Since most statistical models and machine learning procedures are not designed for incomplete data, many different imputation procedures have been proposed so far. In this work, we review several most commonly used parametric and nonparametric missing data imputation procedures and compare their performance from different angles, including the impact on the underlying topological structure. The latter will be achieved by examining the relative change in persistency homology diagrams of true and imputed data sets. All imputation procedures are tested on many artificially generated data clouds with specific shapes, as well as on several real datasets.