A Generalized Hierarchical Nonnegative Tensor Decomposition
This work addresses hierarchical topic modeling for complex, multi-modal datasets, but it is incremental as it builds on existing hierarchical nonnegative factorization methods.
The authors tackled the problem of hierarchical topic modeling for multi-modal data by proposing a new hierarchical nonnegative tensor factorization (HNTF) model that generalizes a matrix-based counterpart and includes a supervised extension, with experimental results showing it more naturally illuminates topic hierarchies than previous methods.
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. Here, we propose a new HNTF model which directly generalizes a HNMF model special case, and provide a supervised extension. We also provide a multiplicative updates training method for this model. Our experimental results show that this model more naturally illuminates the topic hierarchy than previous HNMF and HNTF methods.