Autoencoder regularisation

Legendre-Latent-Space Regularisation ensures Toplogical Data-Structure Preservation under Autoencoder Compression

This repo contains code and supplementary material of the corresponding article, available here: TBA

Datasets

• Fashion MNIST
• MRI brain scans : Open Access Series of Imaging Studies (OASIS)
• synthetic datasets of points on high-dimensional circle and torus

The repository consists of the following autoencoder models:

• MLP-AE : Multilayer perceptron autoencoder
• AE-REG : Regularized autoencoder (proposed AE with Jacobian regularization)
• Hybrid AE-REG : Hybrid regularized autoencoder (Proposed AE with hybridization through orthogonal polynomial interpolation and Jacobian regularization)
• CNN-AE : Convolutional neural network autoencoder
• Contra AE : Contractive Autoencoder
• MLP-VAE : Multilayer perceptron-based variational autoencoder
• CNN-VAE : Convolutional neural network-based variational autoencoder

Topology retention experiments using synthetic datasets of points on high-dimensional circles and tori

Before running any files in the repository, change the directory to ./autoencoder-regularisation- using cd ./autoencoder-regularisation-

The libraries required to run the code are listed in environment.yml. Install the libraries using conda env create -f environment.yml and activate the environment using conda activate followed by the name of the environment.`

Then train the autoencoders with the following data using the corresponding commands:

• 15-dimensional circle: python ./cycle_tori_experiments/circle_exp.py
• 15-dimensional torus: python ./cycle_tori_experiments/tori_exp.py
• 1024-dimensional torus: python ./cycle_tori_experiments/tori_dim_1024_exp.py

The image shows different autoencoder embeddings of high-dimensional tori to their intrinsic three-dimensional space

Preprocessing of MRI brain scans dataset

From Open Access Series of Imaging Studies (OASIS) dataset images in the format .dwi (Diffusion-weighted imaging) were considered with a chosen single channel from each image. These three-dimensional images were sliced into two-dimensional cross-sections to generate the MRI brain scan image dataset used in the experiments performed.

Orthogonal polynomial regression step for Hybrid AE-REG before training

This step before training of the proposed Hybrid AE-REG involves fitting involves extraction of the coefficients for the fitted orthogonal polynomial series

• Run python ./coefficients_computation_for_fitted_polynomials/FashionMNIST/parallel_0_to_10_dq25.py to perform polynomial regression over the Fashion MNIST dataset. Set no_images and deg_quad as required or keep the default values.

• Run python ./coefficients_computation_for_fitted_polynomials/FashionMNIST/LSTSQparallel_fmnsit_train_dq20.py to extract coefficients in parallel using multiple cores.

• Similarly run python ./coefficients_computation_for_fitted_polynomials/MRI_scans/parallel_0_to_10.py and other files in ./coefficients_computation_for_fitted_polynomials/MRI_scans/ to extract fitted polynomial coefficients for MRI brain scan dataset.

Training all the autoencoders

Fashion MNIST dataset

• MLP-AE and AE-REG : python ./train_nonHybrid_MLPAE_AEREG_FashionMNIST/mlpae_aereg_FMNIST.py
• Hybrid AE-REG : python ./train_Hybrid_AEs_FashionMNIST/Hybrid_AE_REG_fmnist.py
• CNN-AE : python ./train_CNN_AE_FMNIST_MRI/convAE_FMNIST.py
• Contra AE : python ./train_ContraAE_FMNIST_MRI/contraAE_FMNIST.py
• MLP-VAE : python ./train_MLP_VAE_FMNIST_MRI/vae_mlp_FMNIST.py
• CNN-VAE : python ./train_CNN_VAE_FMNIST_MRI/vae_cnn_FMNIST.py

Dataset of two-dimensional slices of MRI brain scans

To pre-save the MRI dataset to later enumerate through it while training, run python ./DataPreprocessing/MRI/getSingleTensorTreainTestDatasets.py which saves the train and test image dataset as /savedData/trainDataSet.pt and ./savedData/testDataSet.pt

• MLP-AE and AE-REG : python ./train_nonHybrid_MLPAE_AEREG_MRI/train_full_data/MRI_train_call10.py to train over the whole dataset or run python ./train_nonHybrid_MLPAE_AEREG_MRI/train_var_TDA/MRI_train_call10.py to flexibly change the training data amount(TDA) considered
• Hybrid AE-REG : python ./train_Hybrid_AEs_MRI/Hybrid_AEREG_MRI.py
• CNN-AE : python ./train_CNN_AE_FMNIST_MRI/convAE_MRI.py
• Contra AE : python ./train_ContraAE_FMNIST_MRI/contraAE_MRI.py
• MLP-VAE : python ./train_MLP_VAE_FMNIST_MRI/vae_mlp_MRI.py
• CNN-VAE : python ./train_CNN_VAE_FMNIST_MRI/vae_cnn_MRI.py

Reconstruction quality box plots

To replicate the box plots for reconstruction qualities of different autoencoders against perturbations for Fashion MNIST dataset, run python ./reconstruction_quality_all_AE_box_plots/FashionMNIST_box_plotting.py and for MRI brains scans run python ./reconstruction_quality_all_AE_box_plots/MRI_box_plotting.py. THe coefficients of hybrid autoencoders are required to be precomputed and loaded to get the box plots by running the above codes.

The plots would be found in ./all_results/FinalResultsPSNR_SSIM_FashionMNIST/ and ./all_results/MRI_box_plots/after running the files.

Perturbation experiments

Perturbation experiments are performed on the Fashion MNIST and MRI datasets. To replicate the results, run python ./perturbation_experiments/FashionMNIST_perturbation_experiments.py for Fashion MNIST dataset and python ./perturbation_experiments/MRI_perturbation_experiments.py for MRI dataset.

The outputs of perturbation experiments are saved in ./all_results/FashionMNIST_perturbation_results/ and ./all_results/MRI_perturbation_results/ respectively.

Geodesic experiments

Files for the code of geodesic computation and plotting are in ./topological_analysis_in_latent_space/FashionMNIST_geodesics/ and ./topological_analysis_in_latent_space/MRI_geodesics/ respectively.