Multilinear Clustering via Tensor Fukunaga–Koontz Transform with Fisher Eigenspectrum Regularization

This repository contains MATLAB code supporting the experiments in the paper:

Gatto, B. B., dos Santos, E. M., Molinetti, M. A. F., & Fukui, K. (2021). Multilinear clustering via tensor Fukunaga–Koontz transform with Fisher eigenspectrum regularization. Applied Soft Computing, 113, 107899.

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Table of Contents

• Overview
• Dependencies
• Data
• Code Structure
• Usage
• Functions
• Example
• Citation
• License

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Overview

This project implements a multilinear subspace clustering approach based on the tensor Fukunaga–Koontz transform (FKT), enhanced with a Fisher eigenspectrum regularization. It applies the Mutual Subspace Method (MSM) over different tensor modes and combines the resulting similarity matrices to perform classification on video data under varying illumination settings.

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Dependencies

• MATLAB R2019b or later
• Image Processing Toolbox (for imresize3)

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Data

The dataset cambridge16x12.mat contains the preprocessed Cambridge hand-gesture video sequences:

load('cambridge16x12.mat')

• Data is a cell array of size nclass, each containing 100 video samples.
• Each video sample is a matrix of size d × t, where d = 12 × 16 pixels and t is the number of frames.

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Code Structure

├── cambridge16x12.mat      % Dataset file
├── main.m                  % Script to run training, testing, and plot confusion matrices
├── Tensor_rep.m            % Function to build mode-1, mode-2, mode-3 unfoldings for a video tensor
├── EVD.m                   % Function for eigenvalue decomposition and basis extraction
└── README.md               % This documentation file

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Usage

1. Configure parameters in main.m:

   • Number of classes (nclass)
   • Subspace dimensions (ri1, rd1, etc.)
   • Number of canonical angles (k, k3)

2. Run the script:

   clear all; close all;
   load('cambridge16x12.mat');
   main;  % or simply execute the content of main.m

3. View results:

   • Three confusion matrices (confusion1, confusion2, confusion3) for each tensor mode
   • Combined similarity matrix conf_total

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Functions

• [X1,X2,X3] = Tensor_rep(D)

  • Input: D (d × t data matrix)
  • Outputs: Mode-1 unfolding X1, Mode-2 unfolding X2, Mode-3 unfolding X3

• [eig_vec,eig_val] = EVD(D)

  • Input: D (d × n data matrix)
  • Outputs: Sorted eigenvectors and eigenvalues of the covariance matrix

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Example

The provided main.m script demonstrates:

• Extraction of tensor unfoldings from sample videos
• Basis computation via EVD
• Similarity scoring using MSM over three modes
• Weighted combination of similarity matrices
• Visualization of classification performance with imagesc

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Citation

If you use this code for your research, please cite:

@article{gatto2021multilinear,
  title={Multilinear clustering via tensor Fukunaga--Koontz transform with Fisher eigenspectrum regularization},
  author={Gatto, Bernardo B and dos Santos, Eulanda M and Molinetti, Marco AF and Fukui, Kazuhiro},
  journal={Applied Soft Computing},
  volume={113},
  pages={107899},
  year={2021},
  publisher={Elsevier}
}

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License

This code is released under the MIT License. See LICENSE for details.