In the previous chapter, we generated recommendations by analyzing the intrinsic properties of items. We now shift our focus from item attributes to user behavior with collaborative filtering. This technique operates on a simple, intuitive principle: users who agreed in the past are likely to agree in the future. Instead of asking "what is this item like?", we ask "who else liked this item?".

This chapter introduces neighborhood-based methods, which form the foundation of many collaborative filtering systems. We will begin by structuring our data into a user-item interaction matrix, a grid where each cell $R_{u,i}$ can represent the interaction between a user $u$ and an item $i$.

From there, you will learn to:

• Differentiate between user-based and item-based collaborative filtering.
• Find similar users or items by applying the k-Nearest Neighbors (k-NN) algorithm.
• Calculate similarity scores using metrics such as cosine similarity and Pearson correlation.
• Predict a user's potential rating for an item based on the ratings of their "neighbors".
• Address the common challenge of data sparsity in the interaction matrix.

By the end of this chapter, you will build a functional item-based collaborative filter, giving you a practical understanding of how to generate recommendations based purely on user interaction patterns.