# A Generalized Hierarchical Nonnegative Tensor Decomposition

arXiv: https://arxiv.org/abs/2109.14820 · HTML: https://mlsanity.com/paper/2109.14820/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 26 references that are in the map.
- First posted on arXiv 30 Sep 2021.

## Builds on (most cited first, 3 of 3)

- [A deep matrix factorization method for learning attribute representations](https://mlsanity.com/paper/1509.03248/) (2015)
- [Compositional Hierarchical Tensor Factorization: Representing Hierarchical Intrinsic and Extrinsic Causal Factors](https://mlsanity.com/paper/1911.04180/) (2019)
- [Supervised Deep Sparse Coding Networks](https://mlsanity.com/paper/1701.08349/) (2017)

## Built on by (most cited first, 3 of 3)

- [What is the Relationship between Tensor Factorizations and Circuits (and How Can We Exploit it)?](https://mlsanity.com/paper/2409.07953/) (2024)
- [Causal Deep Learning](https://mlsanity.com/paper/2301.00314/) (2023)
- [Trustworthy Domain-Specific AI for Structured Knowledge Retrieval and Reasoning](https://mlsanity.com/paper/2610.08894/) (2026)

## Abstract (arXiv)

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.