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.

翻译：非负矩阵分解（NMF）是获取数据集低维表示的重要技术。然而，经典NMF未考虑在不同时间或不同地点收集的数据可能存在的异质性。我们通过求解改进的NMF目标函数——分层非负矩阵分解（Stratified-NMF）来解决这一问题，该方法能同时学习依赖分层的统计量和一个共享的主题矩阵。我们为该新目标函数开发了乘法更新规则，并证明了该目标函数的收敛性。随后，我们在合成数据上进行实验，验证了该方法的效率与准确性。最后，我们将该方法应用于三个真实世界数据集，并通过实证研究分析了其学习到的特征。