Implementation for Normed Spaces for Graph Embeddings

Available Spaces

• Euclidean-l1, Euclidean-l2, Euclidean-linf
• Poincare, Lorentz, Sphere, Pseudo-Euclidean
• Poincare x Euclidean-l1, Poincare x Euclidean-l2, Poincare x Euclidean-linf, Euclidean-l1 x Euclidean-linf
• Upper-riem, Upper-f1, Upper-finf, Bounded-riem, Bounded-f1, Bounded-finf
• SPD

Usage

Below are the instructions about running experiments in the l1 and linf normed spaces.

Graph Reconstruction

python run_dis.py --model euclidean --metric l1 --dims 20 --learning_rate 0.01 --batch_size 2048 --epoch 3000 --graph grid

python run_dis.py --model euclidean --metric linf --dims 20 --learning_rate 0.01 --batch_size 2048 --epoch 3000 --graph tree

python run_dis.py --model prod-eueu --metric l1,linf --dims 20 --learning_rate 0.01 --batch_size 2048 --epoch 3000 --graph tree

python run_dis.py --model pesudo-eueu --metric l2,l2 --dims 20 --learning_rate 0.01 --batch_size 2048 --epoch 3000 --graph grid

Link Prediction on GNNs

python run_lp_gnn.py --dims 64 --graph cora --model euclidean --metric l1 --gnn gcn --learning_rate 0.01 --batch_size -1 --epoch 1000

python run_lp_gnn.py --dims 64 --graph cora --model prod-eueu --metric l1,linf --gnn gcn --learning_rate 0.01 --batch_size -1 --epoch 1000

Recommendation (cd recosys/)

python run.py --dims 20 --model prod-hyeu --metric l1 --loss hinge --graph lastfm --learning_rate 5e-2 --batch_size 1024 --epoch 500 --val_every 30 --max_grad_norm 10

python run.py --dims 20 --model euclidean --metric l1 --loss bce --graph mupnyc --learning_rate 5e-2 --batch_size 512 --epoch 500 --val_every 30 --max_grad_norm 5

Below is the way to visualize embedding distortion in the linf normed space.

python visual.py --model euclidean --metric linf --dims 20 --graph grid

Datasets

• Grid Tree TreexTree Tree o Grid Grid o Tree Fullerenes
• Margulis Paley Chordal
• USCA312 Biseasome CSPHD EuroRoad Facebook
• ML-100k LastFM MeetUp-NYC
• Cora Citeseer

Requirements

• Python == 3.8
• scikit-learn == 1.0.1
• torch == 1.12.1
• torch-geometric == 2.1.0
• geoopt == 0.5.0
• networkit == 10.0
• networkx == 2.6.3