Measuring the distance between users in the preference space

The two most recognizable types of collaborative filtering systems are user-based recommenders and item-based recommenders. If one were to imagine that the preference space is an n-dimensional feature space where either users or items are plotted, then we would say that similar users or items tend to cluster near each other in this preference space; hence, an alternative name for this type of collaborative filtering is nearest-neighbor recommenders.

A crucial step in this process is to come up with a similarity or distance metric with which we can compare critics to each other or mutually preferred items. This metric is then used to perform pairwise comparisons of a particular user to all other users, or conversely, for an item to be compared to all other items. Normalized comparisons are then used to determine recommendations. Although the computational space can become exceedingly large, distance metrics themselves are not difficult...