Amazon.com Recommendations Item to Item Collaborative Filtering (2003)
August 16, 2025When the journal IEEE Internet Computing was celebrating its 20th anniversary in 2017, its editorial board selected Amazon.com Recommendations: Item-to-Item Collaborative Filtering, published in 2003, as the paper that best stood the test of time. The paper views traditional collaborative filtering as the approach of finding users similar to the target user and recommending items those users have selected but the user has not. Let \(N\) be the number of the items. In the traditional approach, each user is represented as an \(N\)-dimensional vector to measure the similarity between users, the item to item collaborative filtering constructs an \(N\) x \(N\) matrix, where each component represents the similarity between two items. By computing the item to item matrix offline, the proposed approach can recommend similar items in time independent of both \(N\) and the number of users \(M\).
The item to item similarity matrix is based on the pairs of items that each user selected:
For each item in product catalog, I1
For each customer C who purchased I1
For each item I2 purchased by customer C
Record that a customer purchased I1 and I2
For each item I2
Compute the similarity between I1 and I2
Cosine similarity is commonly used as the similarity metric. Although the worst-case time complexity is \(O(N^2M)\), in practice it is closer to \(O(NM)\), since each user typically selects only a small number of items.