Missing Value Imputation in Cluster Analysis

Introduction
The problem of missing values is unavoidable in clinical research. In literature, missing value has been investigated by extensive methods. One of the most attractive methods for handling missing data is multiple imputation (MI). However, applying MI method within the framework of clustering involves several difficulties and limitations.
Objective
Many classical clustering algorithms cannot deal with missing values, therefore, in this study, we proposed a new procedure for applying multiple imputation and variable reduction when the main goal is cluster analysis on the dataset contains missing values. The important part of this new procedure is to combine the clustering for each imputed dataset to produce the best result of the subject clustering in terms of classification. Therefore, we propose a clustering combination algorithm with a novel framework.
Method
The proposed procedure starts by applying a multiple imputation technique, then uses factor analysis of mixed data (FAMD) for reducing the complexity of high-dimensional data. In the clustering step, several methods (k-means, hierarchical and model-based) are used for clustering imputed datasets. In the final merging step, we propose to use indices which have been developed to determine the optimal number of clusters to offer the best permutation of clustering for assigning the subject to the cluster. The derived results are compared with previous methods (majority vote and fuzzy k-means). The main difficulty in this procedure is that the cluster analysis involves many technical decisions, therefore, various algorithms are defined and compared.
Results
Simulation studies are conducted to illustrate the usefulness of our methodology against commonly used alternative models. Also, the practicality is examined by analyzing chronic obstructive pulmonary disease (COPD) that are taken from the Pneumology Department of the University hospital of Liege, which aimed to identify clinical phenotypes among adults suffering from COPD.
Conclusions
In conclusion, our proposed procedure is very practical and flexible to allow the user to compare several methods in clustering and merging step.