A Generalized Hierarchical Nonnegative Tensor Decomposition

TL;DR

This paper introduces a new hierarchical nonnegative tensor factorization model that generalizes existing matrix-based methods, with a supervised extension and a training algorithm, demonstrating improved topic hierarchy elucidation.

Contribution

A novel HNTF model that directly generalizes hierarchical NMF, including a supervised version and a multiplicative updates training method.

Findings

Model more naturally illuminates topic hierarchy

Outperforms previous HNMF and HNTF methods

Provides a supervised extension for enhanced analysis

Abstract

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.