Hierarchical and neural nonnegative tensor factorizations

Jamie Haddock
Harvey Mudd College

Nonnegative matrix factorization (NMF) has found many applications including topic modeling and document analysis. Hierarchical NMF (HNMF) variants are able to learn topics at various levels of granularity and illustrate their hierarchical relationship. Recently, nonnegative tensor factorization (NTF) methods have been applied in a similar fashion in order to handle data sets with complex, multi-modal structure. Hierarchical NTF (HNTF) methods have been proposed, however these methods do not naturally generalize their matrix-based counterparts. Furthermore, developing training methods that overcome devastating error propagation has been challenging. Here, we present recent works that provide new HNTF models which directly generalizes a HNMF model special case, and may be implemented in a neural network framework and trained via back propagation.

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