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Computes the cosine (Ochiai) similarity of two inputs over their q-gram multisets.

public static double Similarity(ReadOnlySpan<char> a, ReadOnlySpan<char> b, int qval = 1, TextElement element = TextElement.Utf16Unit)

Parameters — a and b are the two inputs to compare; a string converts implicitly, and swapping them does not change the answer. qval is how many characters make one gram, 1 by default; it must be at least 1. element says what counts as one character: TextElement.Utf16Unit by default, or TextElement.CodePoint to match Python outside the Basic Multilingual Plane.

Returns — double in [0, 1]. 1 when the two bags hold the same grams in the same proportions, 0 when they share none.

Exceptions — ArgumentOutOfRangeException when qval is below 1.

Example — single characters by default, and bigrams when qval says so.

using Lodestar.Text.Similarity;

double related = Cosine.Similarity("apple", "pineapple");  // => 0.7453…
double bigrams = Cosine.Similarity("night", "nacht", qval: 2);  // => 0.25

Remarks — qval: 2 is worth knowing about here, and the example shows why. As single characters, "night" and "nacht" share three of five; as bigrams they share only ht, and the score collapses from a passing 0.6 to 0.25. Longer grams carry the order of the characters inside them, which is most of what a bag of single characters throws away — and the usual fix when set similarity reports two anagrams as identical.

The cost is that grams get rarer as qval grows, so scores fall across the board and a threshold belongs to the qval it was chosen for.

Two empty inputs give 1; one empty input against a non-empty one gives 0. An input shorter than qval holds no gram and counts as empty, except that two such inputs score 1 only when they are equal — "a" against "b" at qval: 2 gives 0, where textdistance divides by zero.

Applies to — net10.0, netstandard2.0.

See also — Overlap.Similarity, Jaccard.Similarity, the Python equivalence table.