  Motivated by the problem of identifying potential hierarchical population
structure on modern survey data containing a wide range of complex data types,
we introduce population-based hierarchical non-negative matrix factorization
(PHNMF). PHNMF is a variant of hierarchical non-negative matrix factorization
based on feature similarity. As such, it enables an automatic and interpretable
approach for identifying and understanding hierarchical structure in a data
matrix constructed from a wide range of data types. Our numerical experiments
on synthetic and real survey data demonstrate that PHNMF can recover latent
hierarchical population structure in complex data with high accuracy. Moreover,
the recovered subpopulation structure is meaningful and can be useful for
improving downstream inference.
