Stratified Non-Negative Tensor Factorization

TL;DR

This paper extends Stratified Non-Negative Matrix Factorization to tensors, enabling better analysis of multi-modal data by preserving geometric structure and improving interpretability with lower memory use.

Contribution

The paper introduces a tensor extension of Stratified-NMF with a new multiplicative update rule and regularization, enhancing analysis of multi-modal data.

Findings

Stratified-NTF identifies interpretable topics effectively.

Lower memory requirements compared to Stratified-NMF.

Regularized version improves results on image data.

Abstract

Non-negative matrix factorization (NMF) and non-negative tensor factorization (NTF) decompose non-negative high-dimensional data into non-negative low-rank components. NMF and NTF methods are popular for their intrinsic interpretability and effectiveness on large-scale data. Recent work developed Stratified-NMF, which applies NMF to regimes where data may come from different sources (strata) with different underlying distributions, and seeks to recover both strata-dependent information and global topics shared across strata. Applying Stratified-NMF to multi-modal data requires flattening across modes, and therefore loses geometric structure contained implicitly within the tensor. To address this problem, we extend Stratified-NMF to the tensor setting by developing a multiplicative update rule and demonstrating the method on text and image data. We find that Stratified-NTF can identify interpretable topics with lower memory requirements than Stratified-NMF. We also introduce a regularized version of the method and demonstrate its effects on image data.