Recommender Systems with SVD and NMF

The project explores recommendation modeling using:

• Algebraic SVD
• Surprise SVD
• Surprise NMF
• User similarity analysis in latent space
• Data poisoning attacks on recommender systems

Repository Contents

• Data_CollabFilter.xlsx — input ratings dataset
• *.ipynb — Google Colab / Jupyter notebooks used for the analysis
• *.pdf — exported notebook/report files
• README.md — project overview and usage instructions

Assignment Tasks

1. Algebraic SVD Decomposition

Performed algebraic SVD on the user-item matrix using 2 and 5 latent factors.

For each case:

• computed matrices P, Sigma, and Q
• reconstructed the matrix
• calculated RMSE
• identified the top 3 cells contributing most to RMSE
• compared the improvement from 2 to 5 factors

2. Surprise SVD

Used the Surprise package to train SVD recommender models with 2 and 5 latent factors.

For each case:

• extracted latent matrices P and Q
• generated the latent interaction matrix P × Qᵀ
• generated the full predicted rating matrix
• computed:
  • RMSE on known ratings
  • RMSE on all cells (after filling missing entries with 0)
• generated top 3 recommendations for each user
• compared recommendation differences between 2 and 5 factors

3. Surprise NMF

Used the Surprise package’s NMF model with 2 and 5 latent factors.

For each case:

• extracted matrices W and H
• generated the latent interaction matrix W × Hᵀ
• generated the full predicted rating matrix
• computed:
  • RMSE on known ratings
  • RMSE on all cells
• generated top 3 recommendations for each user
• compared NMF against SVD

4. Similar Users in Latent Space

Using the 2-factor Surprise SVD result:

• found three users whose top-3 recommendations overlap the most
• extracted their latent user vectors
• computed:
  • Euclidean distance
  • Cosine similarity
• analyzed which similarity measure better reflects their recommendation overlap

5. Data Poisoning Attack

Simulated poisoning of the recommendation system by adding fake users designed to push:

item7 → item8, item9, item10

Two cases were tested:

• adding one fictitious user
• adding three fictitious users

Then:

• retrained the Surprise SVD model
• measured how top recommendations changed
• analyzed how effective the poisoning attack was

Main Findings

• Increasing latent factors improved algebraic SVD reconstruction quality.
• For Surprise SVD, increasing factors from 2 to 5 produced only a small improvement.
• For Surprise NMF, increasing factors from 2 to 5 produced a much larger improvement.
• NMF outperformed SVD in RMSE for this dataset.
• Recommendation overlap can be analyzed using latent user vectors.
• Recommender systems based on matrix factorization are vulnerable to data poisoning, although the attack in this assignment only partially achieved the intended effect.

Environment / Requirements

This project was developed in Google Colab using Python.

Suggested packages:

pip install pandas numpy scikit-learn openpyxl
pip install "numpy<2" scikit-surprise

Note: scikit-surprise may require NumPy < 2 in Colab/runtime environments.

How to Run

1. Upload the dataset file Data_CollabFilter.xlsx
2. Open the notebook in Google Colab
3. Run the cells in order:
   • data loading and preprocessing
   • Task 1: Algebraic SVD
   • Task 2: Surprise SVD
   • Task 3: Surprise NMF
   • Task 4: Similarity analysis
   • Task 5: Poisoning experiment

Learning Outcomes

This project demonstrates:

• matrix factorization for recommender systems
• reconstruction and prediction error analysis
• recommendation generation from latent factor models
• comparison of SVD and NMF methods
• latent-space user similarity analysis
• recommender system robustness and poisoning attacks

Author

Mansurbek Satarov