Geometry Aware Inductive Matrix Completion (GeoIMC)

GeoIMC is an inductive matrix completion algorithm based on the works by Jawanpuria et al. (2019)

Consider the case of MovieLens-100K (ML100K), Let $X \in R^{m \times d_1}, Z \in R^{n \times d_2} $ be the features of users and movies respectively. Let $M \in R^{m \times n}$, be the partially observed ratings matrix. GeoIMC models this matrix as $M = XUBV^TZ^T$, where $U \in R^{d_1 \times k}, V \in R^{d_2 \times k}, B \in R^{k \times k}$ are Orthogonal, Orthogonal, Symmetric Positive-Definite matrices respectively. This Optimization problem is solved by using Pymanopt.

This notebook provides an example of how to utilize and evaluate GeoIMC implementation in recommenders

python

import tempfile
import zipfile
import pandas as pd
import numpy as np

from recommenders.datasets import movielens
from recommenders.models.geoimc.geoimc_data import ML_100K
from recommenders.models.geoimc.geoimc_algorithm import IMCProblem
from recommenders.models.geoimc.geoimc_predict import Inferer
from recommenders.evaluation.python_evaluation import rmse, mae
from recommenders.utils.notebook_utils import store_metadata

python

# Choose the MovieLens dataset
MOVIELENS_DATA_SIZE = '100k'
# Normalize user, item features
normalize = True
# Rank (k) of the model
rank = 300
# Regularization parameter
regularizer = 1e-3

# Parameters for algorithm convergence
max_iters = 150000
max_time = 1000
verbosity = 1

1. Download ML100K dataset and features

python

# Create a directory to download ML100K
dp = tempfile.mkdtemp(suffix='-geoimc')
movielens.download_movielens(MOVIELENS_DATA_SIZE, f"{dp}/ml-100k.zip")
with zipfile.ZipFile(f"{dp}/ml-100k.zip", 'r') as z:
    z.extractall(dp)

2. Load the dataset using the example features provided in helpers

The features were generated using the same method as the work by Xin Dong et al. (2017)

python

dataset = ML_100K(
    normalize=normalize,
    target_transform='binarize'
)

python

dataset.load_data(f"{dp}/ml-100k/")

python

print(f"""Characteristics:

              target: {dataset.training_data.data.shape}
              entities: {dataset.entities[0].shape}, {dataset.entities[1].shape}

              training: {dataset.training_data.get_data().data.shape}
              training_entities: {dataset.training_data.get_entity("row").shape}, {dataset.training_data.get_entity("col").shape}

              testing: {dataset.test_data.get_data().data.shape}
              test_entities: {dataset.test_data.get_entity("row").shape}, {dataset.test_data.get_entity("col").shape}
""")

3. Initialize the IMC problem

python

np.random.seed(10)
prblm = IMCProblem(
    dataset.training_data,
    lambda1=regularizer,
    rank=rank
)

python

# Solve the Optimization problem
prblm.solve(
    max_time,
    max_iters,
    verbosity
)

python

# Initialize an inferer
inferer = Inferer(
    method='dot'
)

python

# Predict using the parametrized matrices
predictions = inferer.infer(
    dataset.test_data,
    prblm.W
)

python

# Prepare the test, predicted dataframes
user_ids = dataset.test_data.get_data().tocoo().row
item_ids = dataset.test_data.get_data().tocoo().col
test_df = pd.DataFrame(
    data={
        "userID": user_ids,
        "itemID": item_ids,
        "rating": dataset.test_data.get_data().data
    }
)
predictions_df = pd.DataFrame(
    data={
        "userID": user_ids,
        "itemID": item_ids,
        "prediction": [predictions[uid, iid] for uid, iid in list(zip(user_ids, item_ids))]
    }
)

python

# Calculate RMSE
RMSE = rmse(
    test_df,
    predictions_df
)
# Calculate MAE
MAE = mae(
    test_df,
    predictions_df
)
print(f"""
RMSE: {RMSE}
MAE: {MAE}
""")

python

# Record results for tests - ignore this cell
store_metadata("rmse", RMSE)
store_metadata("mae", MAE)

References

[1] Pratik Jawanpuria, Arjun Balgovind, Anoop Kunchukuttan, Bamdev Mishra. Learning Multilingual Word Embeddings in Latent Metric Space: A Geometric Approach. Transaction of the Association for Computational Linguistics (TACL), Volume 7, p.107-120, 2019.

[2] Xin Dong, Lei Yu, Zhonghuo Wu, Yuxia Sun, Lingfeng Yuan, Fangxi Zhang. A Hybrid Collaborative Filtering Model withDeep Structure for Recommender Systems. Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence (AAAI-17), p.1309-1315, 2017.