Week 10: Matrix Factorization and Collaborative Filtering

Overview

This week explores Singular Value Decomposition (SVD) and its applications in collaborative filtering, with a focus on recommendation systems and matrix factorization techniques.

Learning Objectives

• Understand SVD fundamentals
• Master collaborative filtering concepts
• Implement matrix factorization methods
• Apply recommendation system techniques
• Evaluate filtering performance

1. Collaborative Filtering Basics

• Core Concepts
  • User-item interactions
  • Rating matrices
  • Similarity measures
• Types of Filtering
  • Memory-based
  • Model-based
  • Hybrid approaches
• Netflix Problem
  • Rating prediction
  • Missing value handling
  • Scale considerations

2. SVD Fundamentals

• Mathematical Foundation
  • Matrix decomposition
  • Singular values
  • Left/right singular vectors
• Applications
  • Dimensionality reduction
  • Data compression
  • Feature extraction

3. Implementation Approaches

• Item-Based Methods
  • Item-item similarity
  • Neighborhood selection
  • Rating prediction
  • Computational efficiency
• Matrix Factorization
  • Low-rank approximation
  • Latent factor models
  • Optimization techniques
  • Regularization strategies

4. Advanced Topics

• System Design
  • Cold start problem
  • Sparsity handling
  • Scalability issues
• Evaluation Methods
  • Rating prediction accuracy
  • Ranking metrics
  • Coverage analysis