trajectory_pred

Trajectory Prediction with SCCNN

This is a README file for the task of trajectory prediction based on the SCCNN proposed in the paper Convolutional Learning on Simplicial Complexes.

Note that the algorithm of trajectory prediction performed in a simplicial complex is introduced by paper, Principled Simplicial Neural Networks PSNN for Trajectory Prediction, with its code available at https://github.com/nglaze00/SCoNe_GCN. Based on PSNN, we applied the SCCNN to this prediction task, together with SNN, SCNN and Bunch Model for comparisons.

Requirements

Our implementation requires the same packages as in PSNN, detailed in https://github.com/nglaze00/SCoNe_GCN, including, Python 3; numpy, matplotlib, scipy, networkx, jax, jaxlib, treelib

Data

We first use the python file trajectory_analysis/synthetic_data_gen.py to generate a synthetic simplicial complexes, together with trajectories, which was proposed in Schaub et al. Specifically, we considered the construction with two holes defiend by 400 points, and generated 1000 trajectories based on random walks in edge spaces, following the same procedures as in PSNN. We also randomly split these trajectories into 10 training-test sets. One can do so by specifying the rlz_id and random_split_id in the python file, e.g.,

for rlz_id in [2]: #trajectories realiation index
    for random_split_id in [1,2,3,4,5,6,7,8,9,10]: #training-test data spli indices
        folder_suffix = 'working'+str(rlz_id)+'_'+str(random_split_id)  
        generate_dataset(400, 1000, rlz_id, random_split_id, folder_suffix)

Trajectory Prediction Algorithm

We refer to PSNN for the details of trajectory prediction algorithm.

SCCNN Models

As described in the paper, we considered SCCNN-Node and SCCNN-Edge with SCF orders $T=1$ and $T=2$, which are written in the python file trajectory_analysis/trajectory_experiments.py. Function sccnn_func_1_n is for SCCNN-Node of order $T=1$, and sccnn_func_2_e is for SCCNN-Edge of order $T=2$.

To apply the model, one needs to specify the hyperparameters. For example, to use SCCNN-Node of order one, one can set the two parameters 'model' and 'hidden_layers' as follows, where tuple (15,16) denotes there are 15 shift matrices in total for all node, edge and triangle signals, and 16 features per layer and three tuples make three layers.

hyperparams = {'model':'sccnn1_n','hidden_layers':[(15,16),(15,16),(15,16)]}

Or, one can specify the parameters in the prompt as follows

python ./trajectory_analysis/trajectory_experiments.py -model sccnn1_n -hidden_layers 15_16_15_16_15_16

Other Models

We also built the code for other models, including

1. Bunch Model with prediction performed through node and edge features. For a three-layer Bunch-Node, it can be applied by settting

   hyperparams={'model':'bunch','hidden_layers':[(7,16),(7,16),(7,16)]}

   and a Bunch-Edge can be applied by setting the 'model' as bunch_2.
2. PSNN: which can be applied by setting

   hyperparams={'model':'scone','hidden_layers':[(3,16),(3,16),(3,16)]}

3. SCNN: for different orders $T_{\rm{d}}$ and $T_{\rm{u}}$, we can set

   hyperparams={'model':'scnn31','hidden_layers':[(3,16),(3,16),(3,16)],'k1_scnn':3,'k2_scnn':1}

   to obtain perform an SCNN of orders $3,1$, where 'hidden_layers' does not need to change, automated by 'k1_scnn' and 'k2_scnn'.
4. SNN: for SNN of order $T=3$, we can set

   hyperparams={'model':'ebli','hidden_layers':[(4,16),(4,16),(4,16)]}

Integral Lipschitz regularization

We also applied the integral Lipschitz regularizer to the model SCNN and PSNN to study if it can help with the stability. Specifically, files trajectory_analysis/stability_experiment_with_il_rgl.py and trajectory_analysis/stability_experiment_no_il_rgl.py implemented the stability experimetns with and without the regularizer.

By specifying the 'perturbation' parameter, one can add perturbations with different norms to the Hodge Laplacians based on the relative perturbation model. For example, we can study the stability of SCNN of orders $T_{\rm{d}}=T_{\rm{u}}=3$ with a regularization weight $0.5$ and perturbation level (norm) $0.5$.

python ./trajectory_analysis/trajectory_stability_experiment.py -model scnn3 -hidden_layers 3_16_3_16_3_16 -weight_il 0.5 -k1_scnn 3 -k2_scnn 3 -perturbation 0.5 

Using trajectory_analysis/il_constant_with_rgl.py and trajectory_analysis/il_constant_no_rgl.py we can visualize the integral lipschitz property of the trained SCNN with and without the regularizer.