Inner product in the Hilbert space of U-centered distance matrices
Stand-alone function to compute the inner product in the Hilbert space of U-centered distance matrices, as in the definition of partial distance covariance.
U_product(U, V)
U |
U-centered distance matrix |
V |
U-centered distance matrix |
Note that pdcor, etc. functions include the centering and
projection operations, so that these stand alone versions are not
needed except in case one wants to check the internal computations.
Exported from U_product.cpp.
U_product returns the inner product, a scalar.
Maria L. Rizzo mrizzo@bgsu.edu and Gabor J. Szekely
Szekely, G.J. and Rizzo, M.L. (2014),
Partial Distance Correlation with Methods for Dissimilarities,
Annals of Statistics, Vol. 42, No. 6, pp. 2382-2412.
https://projecteuclid.org/euclid.aos/1413810731
x <- iris[1:10, 1:4] y <- iris[11:20, 1:4] M1 <- as.matrix(dist(x)) M2 <- as.matrix(dist(y)) U <- U_center(M1) V <- U_center(M2) U_product(U, V) dcovU_stats(M1, M2)
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