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We introduce a new method based on nonnegative matrix factorization, NeuralNMF, for detecting latent hierarchical structure in data. Datasets withhierarchical structure arise in a wide variety of fields, such as documentclassification, image processing, and bioinformatics. Neural NMF recursivelyapplies NMF in layers to discover overarching topics encompassing thelower-level features. We derive a backpropagation optimization scheme thatallows us to frame hierarchical NMF as a neural network. We test Neural NMF ona synthetic hierarchical dataset, the 20 Newsgroups dataset, and the MyLymeDatasymptoms dataset. Numerical results demonstrate that Neural NMF outperformsother hierarchical NMF methods on these data sets and offers better learnedhierarchical structure and interpretability of topics.

Neural Nonnegative Matrix Factorization for Hierarchical Multilayer Topic Modeling