Imputation methods for high-dimensional mixed-type datasets by nearest neighbors

In modern biomedical research, the data often contain a large number of variables of mixed data types (continuous, multi-categorical, or binary) but on some variables observations are missing. Imputation is a common solution when the downstream analyses require a complete data matrix. Several imputation methods are available that work under specific distributional assumptions. We propose an improvement over the popular non-parametric nearest neighbor imputation method which requires no particular assumptions. The proposed method makes practical and effective use of the information on the association among the variables. In particular, we propose a weighted version of the L_q distance for mixed-type data, which uses the information from a subset of important variables only. The performance of the proposed method is investigated using a variety of simulated and real data from different areas of application. The results show that the proposed methods yield smaller imputation error and better performance when compared to other approaches. It is also shown that the proposed imputation method works efficiently even when the number of samples is smaller than the number of variables.