  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.
