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In probability and statistics, the Hellinger distance (closely related to, although different from, the Bhattacharyya distance) is used to quantify the similarity between two probability distributions. It is a type of f-divergence. The Hellinger distance is defined in terms of the Hellinger integral, which was introduced by Ernst Hellinger in 1909.
Ernst David Hellinger (September 30, 1883 – March 28, 1950) was a German mathematician and is primarily known for his works on statistics and probability. His works include Hellinger distance and Hellinger integral which were introduced by him in 1909.
Notably, except for total variation distance, all others are special cases of -divergence, or linear sums of -divergences. For each f-divergence D f {\displaystyle D_{f}} , its generating function is not uniquely defined, but only up to c ⋅ ( t − 1 ) {\displaystyle c\cdot (t-1)} , where c {\displaystyle c} is any real constant.
In mathematics, the Hellinger integral is an integral introduced by Hellinger that is a special case of the Kolmogorov integral. It is used to define the Hellinger distance in probability theory. References
A metric on a set X is a function (called the distance function or simply distance) d : X × X → R + (where R + is the set of non-negative real numbers). For all x , y , z in X , this function is required to satisfy the following conditions:
Jaro distance is commonly used in record linkage to compare first and last names to other sources. Edit distance; Levenshtein distance; Lee distance; Hamming distance; Jaro distance; Similarity between two probability distributions. Typical measures of similarity for probability distributions are the Bhattacharyya distance and the Hellinger ...
Hellinger is a surname. Notable people with the surname include: Ernst Hellinger (1883–1950), German mathematician Hellinger distance, used to quantify the similarity between two probability distributions; Hellinger integral, used to define the Hellinger distance in probability theory
The total variation distance (or half the norm) arises as the optimal transportation cost, when the cost function is (,) =, that is, ‖ ‖ = (,) = {(): =, =} = [], where the expectation is taken with respect to the probability measure on the space where (,) lives, and the infimum is taken over all such with marginals and , respectively.