Tensor Analysis with n-Mode Generalized Difference Subspace

This repository implements the n-mode Generalized Difference Subspace (GDS) method for tensor classification based on:

Gatto, B. B., dos Santos, E. M., Koerich, A. L., Fukui, K., & Júnior, W. S. S. (2021). Tensor analysis with n-mode generalized difference subspace. Expert Systems with Applications, 171, 114559. https://doi.org/10.1016/j.eswa.2020.114559

Overview

Multi-dimensional data (tensors) arise naturally in applications such as video analysis, hyperspectral imaging, and multi-sensor time series. Traditional subspace methods lack discriminative power when applied to tensor data. This project:

• Introduces an n-mode GDS projection to extract class-separating features per tensor mode.
• Embeds the resulting subspaces into a product Grassmann manifold for unified classification.
• Defines a reworked Fisher score for tensor separability and a weighted geodesic distance.

Repository Structure

├── nModeGDS_main.m       % Entry script: training, testing, visualization
├── train_nModeGDS.m      % Computes class bases and per-mode GDS projections
├── classify_nModeGDS.m   % Classifies test samples via weighted canonical-sum
├── Tensor_rep.m          % Mode-wise tensor unfolding (3-mode example)
├── gds_utils.m           % EVD and canonical-sum utilities
└── LICENSE               % MIT License

Requirements

• MATLAB R2019b or later
• Image Processing Toolbox (for imresize3)
• Statistics and Machine Learning Toolbox (for Fisher score, optional)

Usage

1. Clone the repository

git clone https://github.com/bernardo-gatto/nModeGDS.git cd nModeGDS

2. **Run classification**
```matlab
% Adjust parameters in nModeGDS_main.m if needed
nModeGDS_main;

3. Inspect results

   • A confusion matrix (imagesc) visualizes classification performance across classes.

Citation

If you use this code, please cite:

@article{gatto2021tensor,
  title={Tensor analysis with n-mode generalized difference subspace},
  author={Gatto, Bernardo B and dos Santos, Eulanda M and Koerich, Alessandro L and Fukui, Kazuhiro and Junior, Waldir SS},
  journal={Expert Systems with Applications},
  volume={171},
  pages={114559},
  year={2021},
  publisher={Elsevier}
}

License

This project is licensed under the MIT License. See the LICENSE file for details.