# Rank-R FNN: A Tensor-Based Learning Model for High-Order Data Classification

arXiv: https://arxiv.org/abs/2104.05048 · HTML: https://mlsanity.com/paper/2104.05048/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 38 references that are in the map.
- First posted on arXiv 11 Apr 2021.

## Builds on (most cited first, 14 of 14)

- [Tensor Fusion Network for Multimodal Sentiment Analysis](https://mlsanity.com/paper/1707.07250/) (2017)
- [Tensorizing Neural Networks](https://mlsanity.com/paper/1509.06569/) (2015)
- [Speeding-up Convolutional Neural Networks Using Fine-tuned CP-Decomposition](https://mlsanity.com/paper/1412.6553/) (2014)
- [On the Expressive Power of Deep Learning: A Tensor Analysis](https://mlsanity.com/paper/1509.05009/) (2015)
- [Ultimate tensorization: compressing convolutional and FC layers alike](https://mlsanity.com/paper/1611.03214/) (2016)
- [Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives](https://mlsanity.com/paper/1708.09165/) (2017)
- [Tensor Regression Networks](https://mlsanity.com/paper/1707.08308/) (2017)
- [Expressive power of recurrent neural networks](https://mlsanity.com/paper/1711.00811/) (2017)
- [Multilinear tensor regression for longitudinal relational data](https://mlsanity.com/paper/1412.0048/) (2014)
- [Tucker Tensor Regression and Neuroimaging Analysis](https://mlsanity.com/paper/1304.5637/) (2013)
- [Linked Component Analysis from Matrices to High Order Tensors: Applications to Biomedical Data](https://mlsanity.com/paper/1508.07416/) (2015)
- [Tensor-Based Classifiers for Hyperspectral Data Analysis](https://mlsanity.com/paper/1709.08164/) (2017)
- [Common Mode Patterns for Supervised Tensor Subspace Learning](https://mlsanity.com/paper/1902.02075/) (2019)
- [Tensor-based Nonlinear Classifier for High-Order Data Analysis](https://mlsanity.com/paper/1802.05981/) (2018)

## Built on by (most cited first, 6 of 6)

- [Towards trustworthy Energy Disaggregation: A review of challenges, methods and perspectives for Non-Intrusive Load Monitoring](https://mlsanity.com/paper/2207.02009/) (2022)
- [AffRankNet+: Ranking Affect Using Privileged Information](https://mlsanity.com/paper/2108.05598/) (2021)
- [Enhancing Plant Disease Detection: A Novel CNN-Based Approach with Tensor Subspace Learning and HOWSVD-MD](https://mlsanity.com/paper/2405.20058/) (2024)
- [Automatic inspection of cultural monuments using deep and tensor-based learning on hyperspectral imagery](https://mlsanity.com/paper/2207.02163/) (2022)
- [Marine Debris Detection in Satellite Surveillance using Attention Mechanisms](https://mlsanity.com/paper/2307.04128/) (2023)
- [Prototype-Rule Neurosymbolic Regularization for Rank-Constrained Tensor Neural Networks under Label Scarcity](https://mlsanity.com/paper/2609.40131/) (2026)

## Abstract (arXiv)

An increasing number of emerging applications in data science and engineering are based on multidimensional and structurally rich data. The irregularities, however, of high-dimensional data often compromise the effectiveness of standard machine learning algorithms. We hereby propose the Rank-R Feedforward Neural Network (FNN), a tensor-based nonlinear learning model that imposes Canonical/Polyadic decomposition on its parameters, thereby offering two core advantages compared to typical machine learning methods. First, it handles inputs as multilinear arrays, bypassing the need for vectorization, and can thus fully exploit the structural information along every data dimension. Moreover, the number of the model's trainable parameters is substantially reduced, making it very efficient for small sample setting problems. We establish the universal approximation and learnability properties of Rank-R FNN, and we validate its performance on real-world hyperspectral datasets. Experimental evaluations show that Rank-R FNN is a computationally inexpensive alternative of ordinary FNN that achieves state-of-the-art performance on higher-order tensor data.