Latent Factor Models

## What "content-based" means A recommender is content-based when the score for a (user, item) pair is computed from a **description of the item itself** plus **that one user's own history**, and from nothing else. No other user's behaviour enters the calculation. The contrast is collaborative filtering, which ignores what an item is *about* and learns purely from the pattern of who interacted with what. That single design choice is why content-based methods are the standard answer to new-item cold start. A job board that publishes a posting at 09:00 with zero applications has, from a collaborative point of view, nothing at all to work with. From a content point of view it has everything it needs: the title, the seniority, the skill tags, the location. ## Half one: representing the item Every item is turned into a numeric feature vector over a fixed set of columns: - **Categorical attributes** — one column per skill tag, per category, per employment type; 1 if present, 0 otherwise. - **Ordinal or numeric attributes** — required years of experience, salary band midpoint, usually rescaled so one large-valued column does not dominate the similarity. - **Attributes derived from item text** — the free-text description has to be turned into numbers by some featurisation step before it can be used here. Once you have that vector, the recommender treats it exactly like any other block of columns. The quality ceiling of the whole approach is set here. If the only feature you record is a top-level category, every posting in that category looks identical to the model and it cannot rank within the category at all. ## Half two: representing the user The user profile lives in the *same* feature space as the items, which is what makes them comparable. The simplest construction is the centroid: average the feature vectors of the items the user engaged with positively. ``` profile = (1 / n) * sum(feature_vector(item) for item in liked_items) ``` Common refinements: - **Weight by strength of signal** — an application counts more than a page view; a 5-star rating counts more than a 3. - **Decay by recency** — a profile built from three-year-old behaviour describes a person who no longer exists. An exponential decay on the weights keeps it current. - **Use negative signal** — instead of averaging only the likes, fit a small discriminative model per user (a logistic regression over the item features, say) on liked versus skipped items. This can learn that the user wants Python *without* on-call, which a positives-only centroid cannot express. ## Scoring With both sides as vectors, the score is a similarity. Cosine dominates: ``` cos(u, i) = dot(u, i) / (norm(u) * norm(i)) ``` The normalisation matters. A raw dot product rewards items simply for having many non-zero features, so a posting that lists twenty skill tags outranks a precise match with three. Cosine measures the *angle* — how aligned the descriptions are — and is scale-free. For non-negative feature vectors it lands in `[0, 1]`; with signed features it ranges `[-1, 1]`. The alternative framing is per-user supervised learning: treat the user's history as a labelled dataset (item features as X, engaged/not as y), fit a small model, and score candidates with it. Same information, different bias-variance tradeoff — the classifier can learn feature interactions the centroid cannot, but it overfits fast on a user with eleven data points. ## What it buys and what it costs **Buys:** - **New items are scorable immediately.** No interaction history is required on the item side, which is the entire reason this leaf exists. On a news homepage where most inventory is hours old, this is not an edge case; it is the steady state. - **Explainability.** "Recommended because you applied to two other senior Python roles" falls straight out of which features drove the similarity. A latent-factor score has no such reading. - **Independence from other users.** A niche user with unusual taste is served as well as a mainstream one, because nobody has to resemble them. **Costs:** - **Overspecialisation.** The profile is built from what the user already chose, so recommendations stay in that neighbourhood. There is no mechanism by which an item unlike anything in the history can surface, and therefore little serendipity. - **A hard ceiling at feature quality.** Content similarity cannot capture "people who liked this also liked that" correlations that no recorded attribute encodes — production quality, writing style, how well a hiring manager actually treats people. - **It does not solve new-*user* cold start.** The profile still needs the user's own history. A subscriber who has clicked nothing has an empty profile, and content features do not help. - **Similarity is not preference.** Two postings can be near-identical in feature space and differ enormously in whether the user wants them. In practice this is why real systems are hybrids: content features carry an item until it has enough interactions for a collaborative signal to take over, and the two scores are blended with a weight that shifts as data accumulates.