FIT5202 · Data Processing for Big Data
Machine Learning: Collaborative Filtering
Week 8 of Monash FIT5202 covers recommender systems: content-based versus collaborative filtering, user-based and item-based CF using cosine similarity, predicted ratings as a similarity-weighted aggregate, and model-based CF via matrix factorization (Spark MLlib's ALS). It also introduces the cold-start problem. Computing cosine similarity and a predicted rating is a reliable written-response item, and matrix factorization/ALS reasoning appears in the multiple-choice question.
What this chapter covers
- 01Recommender approaches: content-based vs collaborative filtering (memory-based vs model-based)
- 02User-based CF: find similar users, predict from their ratings, recommend top-N
- 03Cosine similarity over co-rated items: sim(u,u') = Σ rᵤᵢ·rᵤ'ᵢ / (√Σ rᵤᵢ² · √Σ rᵤ'ᵢ²)
- 04Predicted rating rᵤᵢ = k·Σ sim(u,u')·rᵤ'ᵢ with k = 1/Σ|sim(u,u')|
- 05Item-based CF as the transpose view of user-based CF
- 06Model-based CF: matrix factorization R ≈ U × V with r latent features (rank)
- 07Alternating Least Squares (ALS): fix U, solve V; fix V, solve U; minimise RMSE
- 08The cold-start problem for new users and new items
User-based collaborative filtering with cosine similarity
- +1Cosine similarity of Alice and Bob over the co-rated movies {Matrix, Inception, Interstellar}: numerator = 5·4 + 3·2 + 4·5 = 20 + 6 + 20 = 46.
- +1Denominator = √(5²+3²+4²)·√(4²+2²+5²) = √50·√45 = 7.071·6.708 ≈ 47.43, so sim(Alice, Bob) = 46 / 47.43 ≈ 0.97.
- +1Similarity of Alice and Carol: numerator = 5·5 + 3·3 + 4·3 = 25 + 9 + 12 = 46; denominator = √50·√(5²+3²+3²) = √50·√43 = 7.071·6.557 ≈ 46.37, so sim(Alice, Carol) ≈ 0.99.
- +1Normaliser k = 1 / (|sim(Alice, Bob)| + |sim(Alice, Carol)|) = 1 / (0.97 + 0.99) = 1 / 1.96 ≈ 0.510.
- +1Predicted rating = k · [sim(Alice, Bob)·R(Bob, Dune) + sim(Alice, Carol)·R(Carol, Dune)] = 0.510 · [0.97·5 + 0.99·4] = 0.510 · [4.85 + 3.96] = 0.510 · 8.81.
- +1= 4.49 ≈ 4.5. Both neighbours are highly similar to Alice and rate Dune well, so Dune is a strong recommendation.
Key terms
- Collaborative filtering (CF)
- Predicting a user's preferences from the preferences of many users. Memory-based CF (user- or item-based) uses similarity directly; model-based CF learns latent factors.
- Cosine similarity
- The similarity of two rating vectors over co-rated items: sim(u,u') = Σ rᵤᵢ·rᵤ'ᵢ / (√Σ rᵤᵢ² · √Σ rᵤ'ᵢ²). It measures the angle between the vectors, ignoring their length.
- User-based CF
- Recommend items by finding users with similar rating patterns to the target user and aggregating their ratings of items the target has not seen.
- Matrix factorization
- Model-based CF that factors the N×M rating matrix R into a user matrix U (N×r) and item matrix V (r×M), with r latent features, so R ≈ U × V.
- ALS (Alternating Least Squares)
- The optimisation Spark MLlib uses to learn U and V: alternately fix one and solve the other by least squares, iterating to minimise the RMSE between predicted and actual ratings.
- Cold-start problem
- The difficulty of recommending for a brand-new user or item that has few or no ratings, so similarity- and factor-based methods have little to work with.
Machine Learning: Collaborative Filtering FAQ
Why compute cosine similarity only over co-rated items?
Because a similarity is only meaningful where two users have both expressed a preference. Including items only one of them rated would compare a rating against a missing value. So you restrict the sums in the cosine formula to the items both users rated, then use those similarities to weight predictions.
What is the difference between memory-based and model-based CF?
Memory-based CF (user- or item-based) computes similarities directly from the rating matrix at prediction time. Model-based CF learns a compact model first — matrix factorization factors R into user and item latent-factor matrices via ALS — and predicts from that model, which scales better to large, sparse matrices.
What causes the cold-start problem and how is it handled?
A new user or item has too few ratings for similarity or factorization to work, so CF cannot place them. Common mitigations are falling back to content-based features, asking new users for a few initial ratings, or recommending popular items until enough data accumulates.
Can AI help me with collaborative filtering calculations?
Yes. Sia can compute cosine similarities and similarity-weighted predictions with you, explain matrix factorization and ALS, and quiz you on the cold-start problem — step by step, checking your working. It does not complete your graded assessment, and Monash academic-integrity rules apply.
Exam move
Make the two-formula routine automatic: cosine similarity over co-rated items, then a similarity-weighted prediction normalised by k = 1/Σ|sim|. Practise until you never forget the normaliser, and always sanity-check that a predicted rating lands inside the rating scale. Understand matrix factorization and ALS conceptually — factor R into U and V, alternate least squares, minimise RMSE — for the multiple-choice question, and be able to define the cold-start problem. Rehearse a full prediction on Moodle problems through SWOTVAC and ask Sia for fresh rating matrices.
Working through Machine Learning: Collaborative Filtering in FIT5202? Sia is AskSia’s AI Information Technology tutor — ask any FIT5202 Machine Learning: Collaborative Filtering question and get a clear, step-by-step explanation grounded in how FIT5202 is taught and assessed. Read this chapter free, then take your hardest questions to Sia.
