A fundamental data-mining problem is to examine data for “similar” items. We shall take up applications in Section 3.1, but an example would be looking at a collection of Web pages and finding near-duplicate pages. These pages could be plagiarisms, for example, or they could be mirrors that have almost the same content but differ in information about the host and about other mirrors.

We begin by phrasing the problem of similarity as one of finding sets with a relatively large intersection. We show how the problem of finding textually similar documents can be turned into such a set problem by the technique known as “shingling.” Then, we introduce a technique called “minhashing,” which compresses large sets in such a way that we can still deduce the similarity of the underlying sets from their compressed versions. Other techniques that work when the required degree of similarity is very high are covered in Section 3.9.

Another important problem that arises when we search for similar items of any kind is that there may be far too many pairs of items to test each pair for their degree of similarity, even if computing the similarity of any one pair can be made very easy. That concern motivates a technique called “locality-sensitive hashing,” for focusing our search on pairs that are most likely to be similar.

Finally, we explore notions of “similarity” that are not expressible as intersection of sets. This study leads us to consider the theory of distance measures in arbitrary spaces. It also motivates a general framework for locality-sensitive hashing that applies for other definitions of “similarity.”