*Moins il y a de distance entre deux hommes, plus ils sont pointilleux pour le faire remarquer* (The shorter the distance between two men, the greater their insistence that it should be noticed)

Antoine Rivarol, 1788

In this chapter, we consider ways in which similarity may be measured, including metrics and distances, alongside a number of other techniques used in the context of recommender systems. The approaches presented in the following sections are those discussed elsewhere in this book and correspond to defined contexts. This chapter does not aim to provide an exhaustive list of all existing methods but simply gives an overview of the most widely used methods in the context of recommender systems (see the previous chapter). Table 3.1 shows the contexts of use of the approaches discussed in the previous chapters. Note that many approaches may be used in a variety of contexts.

Similarity measures generally take the form of functions quantifying the relationship between two objects, compared on the basis of their similarities and differences. The two objects must, clearly, be of the same type. However, the value given for a measure of similarity between *x* and *y* may be different to that given between *y* and *x*. Thus, not all similarity measures are metrics. In mathematical terms, a metric, or a distance, is a value function within the set of real numbers which defines the distance between the elements of a set *X*, such that d : ...

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