Similarity learning

Similarity learning is an area of supervised machine learning in artificial intelligence. It is closely related to regression and classification, but the goal is to learn from examples a similarity function that measures how similar or related two objects are. It has applications in ranking, in recommendation systems, visual identity tracking, face verification, and speaker verification.

There are four common setups for similarity and metric distance learning.

A common approach for learning similarity, is to model the similarity function as a bilinear form. For example, in the case of ranking similarity learning, one aims to learn a matrix W that parametrizes the similarity function ${\displaystyle f_{W}(x,z)=x^{T}Wz}$.

Similarity learning is closely related to distance metric learning. Metric learning is the task of learning a distance function over objects. A metric or distance function has to obey four axioms: non-negativity, Identity of indiscernibles, symmetry and subadditivity / triangle inequality. In practice, metric learning algorithms ignore the condition of identity of indiscernibles and learn a pseudo-metric.

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