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In statistics and related fields, a similarity measure or similarity function or similarity metric is a real-valued function that quantifies the similarity between two objects. Although no single definition of a similarity exists, usually such measures are in some sense the inverse of distance metrics : they take on large values for similar ...
The term is also frequently used metaphorically [1] to mean a measurement of the amount of difference between two similar objects (such as statistical distance between probability distributions or edit distance between strings of text) or a degree of separation (as exemplified by distance between people in a social network).
In statistics, probability theory, and information theory, a statistical distance quantifies the distance between two statistical objects, which can be two random variables, or two probability distributions or samples, or the distance can be between an individual sample point and a population or a wider sample of points.
In computer science and statistics, the Jaro–Winkler similarity is a string metric measuring an edit distance between two sequences. It is a variant of the Jaro distance metric [ 1 ] (1989, Matthew A. Jaro) proposed in 1990 by William E. Winkler .
Data can be binary, ordinal, or continuous variables. It works by normalizing the differences between each pair of variables and then computing a weighted average of these differences. The distance was defined in 1971 by Gower [1] and it takes values between 0 and 1 with smaller values indicating higher similarity.
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 (or the triangle inequality). In practice, metric learning algorithms ignore ...
Bhattacharyya distance related, for measuring similarity between data sets (and not between a point and a data set) Hamming distance identifies the difference bit by bit of two strings; Hellinger distance, also a measure of distance between data sets; Similarity learning, for other approaches to learn a distance metric from examples.
In this scenario, the similarity between the two baskets as measured by the Jaccard index would be 1/3, but the similarity becomes 0.998 using the SMC. In other contexts, where 0 and 1 carry equivalent information (symmetry), the SMC is a better measure of similarity.