Geometric Matrix Completion Eval

---
name: geometric-matrix-completion-eval
description: Evaluates a model's ability to perform geometric matrix completion on multi-network recommendation datasets. It probes how well graph neural networks and low-rank representations can integrate cross-network and within-network features to predict missing user-item ratings. Use when the user wants to benchmark on Douban, Flixster, YahooMusic, ML-100K, ML-1M, or asks about evaluating this task. Reports RMSE.
metadata:
  skill_kind: dataset_eval
  source_arxiv: 2206.09477
  bibtex_key: du2022geometric
  confidence: high
---

# geometric-matrix-completion-eval

> Geometric Matrix Completion via Sylvester Multi-Graph Neural Network — Du et al. (2022) (arXiv:2206.09477, 2022)

## What this evaluates

Evaluates a model's ability to perform geometric matrix completion on multi-network recommendation datasets. It probes how well graph neural networks and low-rank representations can integrate cross-network and within-network features to predict missing user-item ratings.

## Datasets

- **Douban** — total 136891; splits: train (-1), test (-1)
- **Flixster** — total 26173; splits: train (-1), test (-1)
- **YahooMusic** — total 5335; splits: train (-1), test (-1)
- **ML-100K** — total 100000; splits: train (-1), test (-1)
- **ML-1M** — total 1000209; splits: train (-1), test (-1)

## Metrics

- `RMSE` **(primary)** — range: other
  - Root Mean Squared Error: the square root of the average of squared differences between predicted and actual ratings over the test set.

## Input / output format

**Input**: Sparse user-item rating matrix, plus user-user and item-item interaction networks represented as adjacency matrices. For datasets lacking one network type, an identity matrix is used as a placeholder.

**Output**: Predicted rating values for all unobserved user-item pairs in the test set.

## Scoring recipe

```python
import numpy as np
def compute_rmse(y_true, y_pred):
    return np.sqrt(np.mean((y_true - y_pred) ** 2))
```

## Common pitfalls

- The exact train/test split is not specified in the paper; it relies on a fixed partition adopted by prior works (Yao et al. 2018, Monti et al. 2017), making exact reproduction difficult without consulting those citations.
- For ML-100K and ML-1M, user-user and item-item interaction networks are constructed via k-NN search on features with k=10 or k=12, which acts as a critical hyperparameter affecting performance.
- Douban and YahooMusic only provide one type of interaction network (user-user or item-item respectively); the missing network must be replaced with an identity matrix, which is easy to overlook.

## Evidence (verbatim from paper)

> The metric for comparison is the widely adopted rooted mean squared error (RMSE).

## Citation

```bibtex
@misc{du2022geometric,
  title={Geometric Matrix Completion via Sylvester Multi-Graph Neural Network},
  author={Du et al. (2022)},
  year={2022},
  note={arXiv:2206.09477}
}
```

- arXiv: 2206.09477