Create sparse distance, covariance or correlation matrix from x, y

Exploit k-nearest neighbor algorithms to estimate a sparse matrix measuring the distance, correlation or covariance between two matched datasets. Critical to the validity of this function is the basic mathematical relationships between euclidean distance and correlation and between correlation and covariance. For applications of such matrices, one may see relevant publications by Mauro Maggioni and other authors.

sparseDistanceMatrixXY(
  x,
  y,
  k = 3,
  r = Inf,
  sigma = NA,
  kmetric = c("euclidean", "correlation", "covariance", "gaussian"),
  eps = 0.000001,
  kPackage = "FNN",
  ncores = NA
)

Arguments

x	input matrix, should be n (samples) by p (measurements)
y	input matrix second view, should be n (samples) by q (measurements)
k	number of neighbors
r	radius of epsilon-ball
sigma	parameter for kernel PCA.
kmetric	similarity or distance metric determining k nearest neighbors
eps	epsilon error for rapid knn
kPackage	name of package to use for knn
ncores	number of cores to use

Value

matrix sparse p by q matrix is output with p by k nonzero entries

References

http://www.math.jhu.edu/~mauro/multiscaledatageometry.html

Author

Avants BB

Examples

if (FALSE) {
set.seed(120)
mat = matrix( rnorm(60), nrow=6 )
mat2 = matrix( rnorm(120), nrow=6 )
smat = sparseDistanceMatrixXY( mat, mat2, 3 )
smat2 = sparseDistanceMatrixXY( mat2, mat, 3 )
testthat::expect_is(smat, "Matrix")
testthat::expect_is(smat, "dgCMatrix")
testthat::expect_is(smat2, "Matrix")
testthat::expect_is(smat2, "dgCMatrix")
testthat::expect_equal(sum(smat), 154.628961265087)
testthat::expect_equal(sum(smat2), 63.7344262003899)
}