Similarity metrics [1] are a mathematical construct which is particularly useful in natural language processing—especially in information retrieval. Let's first try to understand what a metric is. We can understand a metric as a function that defines a distance between each pair of elements of a set, or vector. It's clear how this would be useful to us - we can compare between how similar two documents would be based on the distance. A low value returned by the distance function would mean that the two documents are similar, and a high value would mean they are quite different.
While we mention documents in the example, we can technically compare any two elements in a set – this also means we can compare between two sets of topics created by a topic model, for example. We can check between the TF-IDF representations of documents and between LSI or LDA representations of documents.
Most of us would be aware of one distance or similarity metric already – the Euclideanmetric...
