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 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.

Learning setup

There are four common setups for similarity and metric distance learning.
; Regression similarity learning
; Classification similarity learning
; Ranking similarity learning
; Locality sensitive hashing
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.

Metric learning

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. In practice, metric learning algorithms ignore the condition of identity of indiscernibles and learn a pseudo-metric.
When the objects are vectors in, then any matrix in the symmetric positive semi-definite cone defines a distance pseudo-metric of the space of x through the form. When is a symmetric positive definite matrix, is a metric. Moreover, as any symmetric positive semi-definite matrix can be decomposed as where and, the distance function can be rewritten equivalently. The distance corresponds to the Euclidean distance between the projected feature vectors and.
Some well-known approaches for metric learning include Large margin nearest neighbor, Information theoretic metric learning.
In statistics, the covariance matrix of the data is sometimes used to define a distance metric called Mahalanobis distance.

Applications

Similarity learning is used in information retrieval for learning to rank, in face verification or face identification, and in recommendation systems. Also, many machine learning approaches rely on some metric. This includes unsupervised learning such as clustering, which groups together close or similar objects. It also includes supervised approaches like K-nearest neighbor algorithm which rely on labels of nearby objects to decide on the label of a new object. Metric learning has been proposed as a preprocessing step for many of these approaches.

Scalability

Metric and similarity learning naively scale quadratically with the dimension of the input space, as can easily see when the learned metric has a bilinear form. Scaling to higher dimensions can be achieved by enforcing a sparseness structure over the matrix model, as done with HDSL, and with COMET.