  Non-negative matrix factorization (NMF) is an important technique for
obtaining low dimensional representations of datasets. However, classical NMF
does not take into account data that is collected at different times or in
different locations, which may exhibit heterogeneity. We resolve this problem
by solving a modified NMF objective, Stratified-NMF, that simultaneously learns
strata-dependent statistics and a shared topics matrix. We develop
multiplicative update rules for this novel objective and prove convergence of
the objective. Then, we experiment on synthetic data to demonstrate the
efficiency and accuracy of the method. Lastly, we apply our method to three
real world datasets and empirically investigate their learned features.
