$k$-POD: A Method for $k$-Means Clustering of Missing Data

TL;DR

The paper introduces $k$-POD, an extension of $k$-means clustering designed to handle missing data effectively without requiring data imputation or external information, even with high missingness.

Contribution

The novel $k$-POD method enables $k$-means clustering directly on incomplete data, addressing limitations of existing imputation-based approaches.

Findings

Works with unknown missingness mechanisms

Effective with high levels of missing data

Avoids costly data imputation

Abstract

The $k$-means algorithm is often used in clustering applications but its usage requires a complete data matrix. Missing data, however, is common in many applications. Mainstream approaches to clustering missing data reduce the missing data problem to a complete data formulation through either deletion or imputation but these solutions may incur significant costs. Our $k$-POD method presents a simple extension of $k$-means clustering for missing data that works even when the missingness mechanism is unknown, when external information is unavailable, and when there is significant missingness in the data.