An efficient $k$-means-type algorithm for clustering datasets with incomplete records
This addresses a practical issue for data analysts and researchers dealing with incomplete datasets, but it is incremental as it extends an existing method rather than introducing a new paradigm.
The paper tackled the problem of clustering datasets with incomplete records, which standard k-means cannot handle, by developing an efficient k-means-type algorithm called k_m-means that works with missing data and includes initialization and group estimation methods, demonstrating efficacy in simulations and a functional MRI application.
The $k$-means algorithm is arguably the most popular nonparametric clustering method but cannot generally be applied to datasets with incomplete records. The usual practice then is to either impute missing values under an assumed missing-completely-at-random mechanism or to ignore the incomplete records, and apply the algorithm on the resulting dataset. We develop an efficient version of the $k$-means algorithm that allows for clustering in the presence of incomplete records. Our extension is called $k_m$-means and reduces to the $k$-means algorithm when all records are complete. We also provide initialization strategies for our algorithm and methods to estimate the number of groups in the dataset. Illustrations and simulations demonstrate the efficacy of our approach in a variety of settings and patterns of missing data. Our methods are also applied to the analysis of activation images obtained from a functional Magnetic Resonance Imaging experiment.