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Deep learning based Koopman operator for graph dynamical systems.

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DeepGraphDMD

This repository contains code for the method "DeepGraphDMD: Interpretable Spatio-Temporal Decomposition of Non-linear Functional Brain Network Dynamics" which is accepted in MICCAI 2023. Illustration

Installation

To run the module in this repository, create a docker image from docker/docker_command.sh and run the code inside the running docker instance. Alternatively, install requirements from docker/requirements.txt in a virtual environment.

Dataset

Download HCP resting-state data from HCP1200 Parcellation+Timeseries+Netmats (PTN). The time-series data used in this project resides in the folder HCP_PTN1200/node_timeseries/3T_HCP1200_MSMAll_d{parcel}_ts2 (for the experiments in the paper, parcel=50 but other values can also be used).

Training

To train the model, SparseEdgeKoopman/trainer.py file is used in the following manner:

python3 -m src.SparseEdgeKoopman.trainer --weight 1 10 0.5 --hidden_dim 64 -g 1 -m 500 -d 0.1 --lr 1e-4 --mode train --write_dir SparseEdgeKoopman/megatrawl/win=16_lkis=64 --window 16 --lkis_window 64 --batch_size 16 --stride 4 --latent_dim 32 &

Prediction (Generate latent network embedding that has linear dynamics)

After the model is trained, generate a latent network sequence for every subject using the following command:

python3 -m src.SparseEdgeKoopman.predict --subject_id <subject_id> --window 16 --stride 4 --trial 0

Applying GraphDMD to extract DMD modes and their frequency

Run the Matlab script: src/GraphDMD/batch_wise_DeepgDMD.m to generate DMD modes Phi and their frequency Psi for every lkis window.

batch_wise_DeepgDMD(<subject_id>)

To aggregate Phi across all lkis windows and generate a set of average Phi_avg for each subject, run the following python script:

python3 -m src.GraphDMD.cluster_gdmd_modes --subject_id <subject_id> --trial 0 --min_K 8 --max_K 15 --min_psi 0 --max_psi 0.15

Now, the aggregated Phi_avg can be used to do downstream tasks such as predicting behavioral measures. However, before that run the following script to align the Phi_avg modes across subjects (Phi_aligned):

python3 -m src.GraphDMD.cluster_group_gdmd --min_psi <lower_freq> --max_psi <upper_freq>

Regression Analysis of Behavioral Measures from HCP

Train an ElasticNet regressor, to regress various behavioral measures of HCP data using the aligned DMD modes Phi_aligned:

python3 -m src.HCP1200.training-cv --target <behavioral_measure_name> --corr_type gDMD_multi --l_freq <lower_freq> --r_freq <upper_freq> --q 0.4' --output=training-cv-gDMD_multi_<behavioral_measure_name>_<lower_freq>-<upper_freq>.txt

Example: python3 -m src.HCP1200.training-cv --target CogTotalComp_AgeAdj --corr_type gDMD_multi --l_freq 0.07 --r_freq 0.08 --q 0.4' --output=training-cv-gDMD_multi_CogTotalComp_AgeAdj_0.07-0.08_aligned.txt

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