How do you compute similarity between users or items?

To compute similarity between users or items, the most common approach involves analyzing interaction patterns or feature-based representations. For user similarity, this typically means comparing how users interact with items (e.g., ratings, clicks, purchases). For item similarity, it involves comparing how items are interacted with by users or analyzing their inherent attributes. The core idea is to quantify how closely two users or items align based on shared behaviors or characteristics.

One widely used method is cosine similarity, which measures the angle between vectors representing user preferences or item attributes. For example, in a user-item rating matrix, each user is represented as a vector of their ratings for items. Cosine similarity calculates how aligned two users’ rating vectors are, ignoring differences in rating scales. Suppose User A rates movies [5, 3, 0] and User B rates [4, 2, 1], where 0 means no rating. The similarity is computed by treating missing values as zeros and measuring the cosine of the angle between the vectors. For items, the same logic applies: if two movies are rated similarly by many users, their vectors will align closely. Other distance metrics like Pearson correlation adjust for user-specific biases (e.g., a user who rates everything higher), while Jaccard similarity is useful for binary data (e.g., purchased/not purchased).

Another approach involves matrix factorization or embedding-based methods. Techniques like Singular Value Decomposition (SVD) or neural embeddings (e.g., Word2Vec for items) reduce high-dimensional interaction data into dense vectors that capture latent patterns. For instance, collaborative filtering models in recommendation systems factorize the user-item matrix into user and item embeddings. Similarity is then computed using these lower-dimensional vectors. For text-based items (e.g., articles), embeddings from models like BERT can represent semantic content, and cosine similarity between embeddings measures content-based similarity. Hybrid methods combine interaction data and item features (e.g., genre, tags) to compute similarity, improving robustness for sparse datasets.

Practical considerations include handling sparse data and scalability. For example, in user-user similarity with sparse ratings, Pearson correlation might ignore unrated items, while cosine similarity treats missing values as zeros, which can skew results. Libraries like SciKit-Learn or NumPy provide efficient implementations for similarity computations. For large datasets, approximate nearest neighbor (ANN) algorithms like FAISS or ANNOY optimize speed by trading off exactness. Developers should also preprocess data (e.g., normalization, handling missing values) and validate similarity metrics against domain-specific goals (e.g., recommendation accuracy in A/B tests).