A comparative study on imputation methods for clustering with missing data

Abstract

Managing missing data by data imputation always challenges the subsequent data analysis process.  Especially when a small amount of important data cannot be eliminated. In General, missing data can be imputed by filling its central value, such as the mean or mode value, although such methods might be unsuitable for every dataset with various distributions. Therefore, machine learning approaches to predict missing values are an interesting option. In this research, the impact of five missing data imputation methods was experimented with by clustering data with three missing rate levels. Two simulated 2D datasets and one real-world bank customer dataset were used in this work. Five missing data imputation methods, including Mean/Mode, K-Nearest Neighbors (KNN), Multivariate Imputation by Chained Equations (MICE), KNN, MICE Random Forest, and MICE Bayesian Ridge methods, were compared. After imputation, the data were clustered by both Hierarchical Clustering and Density-based Spatial Clustering of Applications with Noise (DBSCAN) Clustering approaches with various parameter setups for comparison. The experimental results show that KNN, MICE KNN, and MICE Random Forest imputation methods usually perform well, and consistently yield high values of Adjusted Rand Index (ARI), Normalized Mutual Information (NMI), Fowlkes-Mallows Index (FMI), and Purity regardless of data missing rate level. In addition, each clustering method may be suitable for each dataset differently.  Therefore, using both an appropriate clustering approach and an imputation method to fill up data in this study, rather than traditional mean and mode imputation techniques, can expressively enhance clustering performance values ranging from 0.81 to nearly 1.