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Classical Recommender Systems

Recommender systems dictate modern internet consumption—they power YouTube homepages, Amazon product suggestions, and TikTok feeds.

The Two Primary Paradigms​

  1. Content-Based Filtering: Recommends items based on item features. (e.g., If you watch an action movie starring Tom Cruise, the system recommends another action movie starring Tom Cruise).
  2. Collaborative Filtering: Recommends items based on user behavior and interactions. (e.g., "Users who bought this also bought...").

Matrix Factorization​

The core engine of classical Collaborative Filtering is Matrix Factorization (which won the famous $1M Netflix Prize).

Imagine a massive, sparse matrix where Rows are Users, Columns are Movies, and the cells are Ratings (1-5 stars). Most cells are empty. Matrix Factorization uses linear algebra (specifically SVD - Singular Value Decomposition) to split this giant matrix into two smaller, dense matrices:

  1. A User Embedding matrix.
  2. An Item Embedding matrix.

When you take the dot product of a User Embedding and an Item Embedding, you get the predicted rating that the user would give that movie!

Python Implementation: Matrix Factorization​

import numpy as np
from sklearn.decomposition import TruncatedSVD

# Simulated User-Item Rating Matrix (Users x Items)
# 0 means unrated.
ratings_matrix = np.array([
    [5, 3, 0, 1],
    [4, 0, 0, 1],
    [1, 1, 0, 5],
    [1, 0, 0, 4],
    [0, 1, 5, 4],
])

# Perform Singular Value Decomposition (Matrix Factorization)
# We compress the items into 2 latent features
svd = TruncatedSVD(n_components=2)
user_embeddings = svd.fit_transform(ratings_matrix)
item_embeddings = svd.components_

# Reconstruct the matrix to see the predicted ratings for unrated items!
predicted_ratings = np.dot(user_embeddings, item_embeddings)

print("Original Matrix:\n", ratings_matrix)
print("\nPredicted Ratings Matrix:\n", np.round(predicted_ratings, 1))