Matrix Factorization for Movie Recommendation: A Dimensionality Reduction Approach

Overview

This project develops an intelligent movie recommendation system using low-rank matrix factorization and dimensionality reduction. User–movie interactions are represented as a sparse rating matrix, where missing entries correspond to unrated movies. By applying matrix factorization with bias terms, both users and movies are embedded into a shared latent feature space. The system then predicts missing ratings and generates personalized Top-$N$ recommendations. The project evaluates performance using error-based metrics (RMSE, MAE) and ranking-based metrics (Precision@N, Recall@N), while also analyzing challenges such as cold-start and overfitting.

Suitable For

• BS Mathematics – applications of linear algebra, optimization, and matrix completion

• BS Computer Science / Artificial Intelligence / Data Science – recommender algorithms, personalization, and machine learning implementation

• BS Software Engineering / IT – system design, evaluation, and application development

Technologies Used

• Programming Language: Python

• Libraries & Tools: NumPy, Pandas, Matplotlib, Scikit-learn

• Optimization Methods: Stochastic Gradient Descent (SGD), Alternating Least Squares (ALS)

• Evaluation Metrics: RMSE, MAE, Precision@N, Recall@N, NDCG

Techniques

• Matrix completion using low-rank factorization with biases

• Dimensionality reduction to learn latent user and movie features

• Regularization to avoid overfitting

• Baseline comparisons with global mean and bias-only models

• Ranking-based evaluation for Top-$N$ recommendations

Visualization

• User–movie rating matrix with observed vs. missing entries

• Training loss and validation RMSE curves

• Comparison of predicted vs. actual ratings

• Top-$N$ recommendation lists for sample users

Features

• Mathematical formulation of recommendation as a matrix completion problem

• Step-by-step implementation: data masking, initialization, optimization, evaluation

• Low-rank latent factor learning with bias adjustments

• Prediction of missing ratings and personalized recommendations

• Comparison with baseline approaches for clarity

• Error and ranking metrics for model assessment

Deliverables

• Python source code implementing matrix factorization (SGD/ALS)

• LaTeX project documentation with theory, methodology, and results

• Evaluation tables showing RMSE, MAE, Precision@N, Recall@N

• Top-$N$ recommendations generated for each user

• Figures/plots: training vs. validation error, observed vs. predicted ratings

Support

• Guidance on setting up small-scale synthetic rating matrices

• Help with interpreting error metrics (RMSE, MAE) vs. ranking metrics (Precision@N, Recall@N)

• Assistance in understanding cold-start and scalability challenges

• Extension ideas: hybrid recommendation (collaborative + content-based)

Benefits for Students

• Gain practical experience applying linear algebra to real-world personalization problems

• Understand the link between matrix factorization and machine learning

• Learn to evaluate predictive models using both error metrics and ranking metrics

• Build skills in Python programming, optimization, and data visualization

• Develop a strong capstone project connecting mathematics, computing, and recommender systems