An efficient $k$-means-type algorithm for clustering datasets with incomplete records

TL;DR

This paper introduces an efficient $k$-means-type algorithm, called $k_m$-means, designed to cluster datasets with incomplete records without needing imputation or discarding data, demonstrated through simulations and real MRI data.

Contribution

The paper presents $k_m$-means, a novel extension of $k$-means that handles missing data directly, along with initialization and model selection strategies.

Findings

$k_m$-means effectively clusters incomplete datasets.

The method performs well across various missing data patterns.

Application to MRI data shows practical utility.

Abstract

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.