Industry Report Amazon.com Recommendations Item-to-Item Collaborative Filtering Greg Linden, Brent Smith, and Jeremy York • Amazon.com ecommendation algorithms are best There are three common approaches to solving the known for their use on e-commerce Web recommendation problem: traditional collabora- R sites,1 where they use input about a cus- tive filtering, cluster models, and search-based tomer’s interests to generate a list of recommend- methods. Here, we compare these methods with ed items. Many applications use only the items our algorithm, which we call item-to-item collab- that customers purchase and explicitly rate to rep- orative filtering. Unlike traditional collaborative resent their interests, but they can also use other filtering, our algorithm’s online computation scales attributes, including items viewed, demographic independently of the number of customers and data, subject interests, and favorite artists. number of items in the product catalog. Our algo- At Amazon.com, we use recommendation algo- rithm produces recommendations in realtime, rithms to personalize the online store for each cus- scales to massive data sets, and generates high- tomer. The store radically changes based on cus- quality recommendations. tomer interests, showing programming titles to a software engineer and baby toys to a new mother. Recommendation Algorithms The click-through and conversion rates — two Most recommendation algorithms start by finding important measures of Web-based and email a set of customers whose purchased and rated advertising effectiveness — vastly exceed those of items overlap the user’s purchased and rated untargeted content such as banner advertisements items.2 The algorithm aggregates items from these and top-seller lists. similar customers, eliminates items the user has E-commerce recommendation algorithms often already purchased or rated, and recommends the operate in a challenging environment. For example: remaining items to the user. Two popular versions of these algorithms are collaborative filtering and • A large retailer might have huge amounts of cluster models. Other algorithms — including data, tens of millions of customers and millions search-based methods and our own item-to-item of distinct catalog items. collaborative filtering — focus on finding similar • Many applications require the results set to be items, not similar customers. For each of the user’s returned in realtime, in no more than half a purchased and rated items, the algorithm attempts second, while still producing high-quality rec- to find similar items. It then aggregates the simi- ommendations. lar items and recommends them. • New customers typically have extremely limit- ed information, based on only a few purchases Traditional Collaborative Filtering or product ratings. A traditional collaborative filtering algorithm rep- • Older customers can have a glut of information, resents a customer as an N-dimensional vector of based on thousands of purchases and ratings. items, where N is the number of distinct catalog • Customer data is volatile: Each interaction pro- items. The components of the vector are positive vides valuable customer data, and the algorithm for purchased or positively rated items and nega- must respond immediately to new information. tive for negatively rated items. To compensate for 76 JANUARY • FEBRUARY 2003 Published by the IEEE Computer Society 1089-7801/03/$17.00©2003 IEEE IEEE INTERNET COMPUTING Amazon.com Recommendations best-selling items, the algorithm typically multi- Unfortunately, all these methods also reduce plies the vector components by the inverse fre- recommendation quality in several ways. First, if quency (the inverse of the number of customers the algorithm examines only a small customer who have purchased or rated the item), making less sample, the selected customers will be less similar well-known items much more relevant.3 For almost to the user. Second, item-space partitioning all customers, this vector is extremely sparse. restricts recommendations to a specific product or The algorithm generates recommendations subject area. Third, if the algorithm discards the based on a few customers who are most similar to most popular or unpopular items, they will never the user. It can measure the similarity of two cus- appear as recommendations, and customers who tomers, A and B, in various ways; a common have purchased only those items will not get rec- method is to measure the cosine of the angle ommendations. Dimensionality reduction tech- between the two vectors: 4 niques applied to the item space tend to have the same effect by eliminating low-frequency items. rr Dimensionality reduction applied to the customer rr rr AB• similarity() A, B= cos() A , B = rr space effectively groups similar customers into AB* clusters; as we now describe, such clustering can also degrade recommendation quality. The algorithm can select recommendations from Cluster Models the similar customers’ items using various meth- To find customers who are similar to the user, clus- ods as well, a common technique is to rank each ter models divide the customer base into many seg- item according to how many similar customers ments and treat the task as a classification problem. purchased it. The algorithm’s goal is to assign the user to the seg- Using collaborative filtering to generate recom- ment containing the most similar customers. It then mendations is computationally expensive. It is uses the purchases and ratings of the customers in O(MN) in the worst case, where M is the number the segment to generate recommendations. of customers and N is the number of product cat- The segments typically are created using a clus- alog items, since it examines M customers and up tering or other unsupervised learning algorithm, to N items for each customer. However, because although some applications use manually deter- the average customer vector is extremely sparse, mined segments. Using a similarity metric, a clus- the algorithm’s performance tends to be closer to tering algorithm groups the most similar customers O(M + N). Scanning every customer is approxi- together to form clusters or segments. Because mately O(M), not O(MN), because almost all cus- optimal clustering over large data sets is imprac- tomer vectors contain a small number of items, tical, most applications use various forms of regardless of the size of the catalog. But there are greedy cluster generation. These algorithms typi- a few customers who have purchased or rated a cally start with an initial set of segments, which significant percentage of the catalog, requiring often contain one randomly selected customer O(N) processing time. Thus, the final performance each. They then repeatedly match customers to the of the algorithm is approximately O(M + N). Even existing segments, usually with some provision for so, for very large data sets — such as 10 million or creating new or merging existing segments.6 For more customers and 1 million or more catalog very large data sets — especially those with high items — the algorithm encounters severe perfor- dimensionality — sampling or dimensionality mance and scaling issues. reduction is also necessary. It is possible to partially address these scaling Once the algorithm generates the segments, it issues by reducing the data size.4 We can reduce M computes the user’s similarity to vectors that sum- by randomly sampling the customers or discarding marize each segment, then chooses the segment customers with few purchases, and reduce N by dis- with the strongest similarity and classifies the user carding very popular or unpopular items. It is also accordingly. Some algorithms classify users into possible to reduce the number of items examined multiple segments and describe the strength of by a small, constant factor by partitioning the item each relationship.7 space based on product category or subject classi- Cluster models have better online scalability fication. Dimensionality reduction techniques such and performance than collaborative filtering3 as clustering and principal component analysis can because they compare the user to a controlled reduce M or N by a large factor.5 number of segments rather than the entire cus- IEEE INTERNET COMPUTING http://computer.org/internet/ JANUARY • FEBRUARY 2003 77 Industry Report form well. For users with thousands of purchases, however, it’s impractical to base a query on all the items. The algorithm must use a subset or summa- ry of the data, reducing quality. In all cases, rec- ommendation quality is relatively poor. The rec- ommendations are often either too general (such as best-selling drama DVD titles) or too narrow (such as all books by the same author). Recom- mendations should help a customer find and dis- Figure 1. The “Your Recommendations”feature on the Amazon.com cover new, relevant, and interesting items. Popu- homepage. Using this feature, customers can sort recommendations lar items by the same author or in the same subject and add their own product ratings. category fail to achieve this goal. Item-to-Item Collaborative Filtering Amazon.com uses recommendations as a targeted marketing tool in many email campaigns and on most of its Web sites’ pages, including the high- traffic Amazon.com homepage. Clicking on the “Your Recommendations” link leads customers to an Figure 2. Amazon.com shopping cart recommendations. The recom- area where they can filter their recommendations by mendations are based on the items in the customer’s cart: The product line and subject area, rate the recommended Pragmatic Programmer and Physics for Game Developers. products, rate their previous purchases, and see why items are recommended (see Figure 1). As Figure 2 shows, our shopping cart recom- tomer base. The complex and expensive clustering mendations, which offer customers product sug- computation is run offline. However, recommen- gestions based on the items in their shopping cart. dation quality is low.1 Cluster models group The feature is similar to the impulse items in a numerous customers together in a segment, match supermarket checkout line, but our impulse items a user to a segment, and then consider all cus- are targeted to each customer.