Gram matrix
Consider -vectors . The Gram matrix of the collection is the matrix with elements . The matrix can be expressed compactly in terms of the matrix , as
Assume that each vector is normalized: . Then the coefficient can be expressed as
where is the angle between the vectors and .
Thus is a measure of how similar and are.
The matrix arises for example in text document classification, with a measure of similarity between the -th and -th document, and their respective bag-of-words representation (normalized to have Euclidean norm ).
See also:
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