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Graph Recommender Systems

The focus of the project is to implement and compare the traditional Matrix Factorization (numerical linear algebra) approach and IGMC (SOTA) approach across various metrics.

Matrix Factorization The code for the matrix factorization is available under the folder MF. It is a jupyter notebook with instructions/comments to run added towards every step.

The description of various hyper-parameters is given below.

  • Learning rate (alpha) = 0.001
  • Regularization Coefficient (l) = 0.01
  • Number of steps of gradient descent (steps) = 40
  • Number of latent features (lf) = 10

To find the best possible number of latent factors, the matrix factorization model was trained for different values of lf (10, 15, 20, 25). The graph for comparison of Test MSE and Number of Latent Factors is given below.

Alt text

The results are summarized in the table below:

Number of Latent Features Final Training MSE MSE on test set
10 0.8495 0.9045
15 0.8536 0.9162
20 0.8551 0.9211
25 0.8554 0.9223

IGMC The code for the IGMC model is available under the folder IGMC. The commands used to run the train and test the model is given below

python from Main import train Params = {'Epochs':40, 'Batch_Size':50, 'LR': 1e-3, 'LR_Decay_Step' : 20, 'LR_Decay_Value' : 10, 'Max_Nodes_Per_Hop':200} losses, model, test_loader, test_ratings = train(params = Params) test(model, test_loader, test_ratings, topK=10)

The description of various hyper-parameters is given below.

  • Epochs - The number of iterations a model is set to train
  • Batch_Size - size of the mini batch used to split the dataset (train/test)
  • LR - Learning rate of the model
  • LR_Decay_Step - Epoch at which learning rate will be reduced
  • LR_Decay_Value - The amount by which learning rate will be reduced
  • Max_Nodes_Per_Hop - Maximum number of hops considered in extracting sub graphs

The Hyperparameter testing on Max_Nodes_Per_Hop has been performed by keeping values of others as constant. Below is the graph depicting the relation of training loss across various Max_Nodes_Per_Hop configurations.

Alt text

It can be seen that as the maximum nodes increase, loss values tends to decrease for a specific number of epochs.

The comparison of various metrics over the test set on different max_nodes_per_hop is given in the below table.

Metric 10-Nodes 50-Nodes 100-Nodes 200-Nodes
MSE 1.032 0.8701 0.8492 0.8371
Precision@10 0.5578 0.6521 0.6655 0.7095
Recall@10 0.3876 0.4435 0.4219 0.4446
F1 Score 0.4762 0.5279 0.5164 0.5466
Time per Epoch 50 sec 90 sec 125 sec 200 sec

Matrix Factorization vs IGMC Results

MSE Precision@10 Recall@10 F1 Score Time Per Epoch
MF 0.9045 0.55 0.47 0.4902 5 sec
IGMC 0.8371 0.7095 0.4446 0.5466 200 sec

Libraries

The project uses pytorch-geometric and sparse. We were facing some issues in downloading the correct version during the project. Please use the below script if you are facing any issues with the libraries.

import torch

def format_pytorch_version(version):
  return version.split('+')[0]

TORCH_version = torch.__version__
TORCH = format_pytorch_version(TORCH_version)

def format_cuda_version(version):
  return 'cu' + version.replace('.', '')

CUDA_version = torch.version.cuda
CUDA = format_cuda_version(CUDA_version)

!pip install torch-scatter     -f https://pytorch-geometric.com/whl/torch-{TORCH}+{CUDA}.html
!pip install torch-sparse      -f https://pytorch-geometric.com/whl/torch-{TORCH}+{CUDA}.html
!pip install torch-cluster     -f https://pytorch-geometric.com/whl/torch-{TORCH}+{CUDA}.html
!pip install torch-spline-conv -f https://pytorch-geometric.com/whl/torch-{TORCH}+{CUDA}.html
!pip install torch-geometric