1. The user–item matrix
A recommendation system begins with a matrix. Rows are users, columns are items, and blank entries are unknown preferences.
Blank entries are missing values, not zero ratings.
2. Cosine similarity between users
Centered cosine similarity:
Similarity is computed only on items both users rated, after subtracting each user's average rating.
3. Predict a missing rating from neighbors
4. Latent factor geometry
In a low-rank recommender, each user and item receives hidden coordinates. A predicted rating is a dot product.
Predicted score $p_u\cdot q_i$:
5. Rank and hidden taste
Move the two hidden taste sliders. The table below is generated by a rank-2 model: user vectors times item vectors.
6. Ethics reflection
Recommendation systems are not neutral tables. They shape what users see next.
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