Collaborative filtering, generally speaking, is the process of filtering for information or patterns using techniques involving collaboration between multiple data points. Collaborative filtering methods have a wide breadth of applications, ranging from monitoring data such as logs, application on financial data, e-commerce recommendations, and different web applications such as news sites.

In collaborative filtering for recommendation, the underlying assumption of the approach is that if person A has the same opinion as person B on an issue, A is more likely to have B's opinion on a different issue, x, than the opinion on x of a randomly-chosen person. The idea behind collaborative filtering is the idea that people often get the best recommendations from someone with similar tastes like themselves. Collaborative filtering explores techniques for matching people with similar interests and making recommendations on this basis.

The primary input for any recommendation...