KhatriRao {Matrix} | R Documentation |
Computes Khatri-Rao products for any kind of matrices.
The Khatri-Rao product is a column-wise Kronecker product. Originally introduced by Khatri and Rao (1968), it has many different applications, see Liu and Trenkler (2008) for a survey. Notably, it is used in higher-dimensional tensor decompositions, see Bader and Kolda (2008).
KhatriRao(X, Y = X, FUN = "*", make.dimnames = FALSE)
X,Y |
matrices of with the same number of columns. |
FUN |
the (name of the) |
make.dimnames |
logical indicating if the result should inherit
|
a "CsparseMatrix"
, say R
, the Khatri-Rao
product of X
(n x k) and Y
(m x k), is of dimension (n*m) x k,
where the j-th column, R[,j]
is the kronecker product
kronecker(X[,j], Y[,j])
.
The current implementation is efficient for large sparse matrices.
Michael Cysouw, Univ. Marburg; minor tweaks by Martin Maechler.
Khatri, C. G., and Rao, C. Radhakrishna (1968) Solutions to Some Functional Equations and Their Applications to Characterization of Probability Distributions. Sankhya: Indian J. Statistics, Series A 30, 167–180.
Liu, Shuangzhe, and Gõtz Trenkler (2008) Hadamard, Khatri-Rao, Kronecker and Other Matrix Products. International J. Information and Systems Sciences 4, 160–177.
Bader, Brett W, and Tamara G Kolda (2008) Efficient MATLAB Computations with Sparse and Factored Tensors. SIAM J. Scientific Computing 30, 205–231.
## Example with very small matrices: m <- matrix(1:12,3,4) d <- diag(1:4) KhatriRao(m,d) KhatriRao(d,m) dimnames(m) <- list(LETTERS[1:3], letters[1:4]) KhatriRao(m,d, make.dimnames=TRUE) KhatriRao(d,m, make.dimnames=TRUE) dimnames(d) <- list(NULL, paste0("D", 1:4)) KhatriRao(m,d, make.dimnames=TRUE) KhatriRao(d,m, make.dimnames=TRUE) dimnames(d) <- list(paste0("d", 10*1:4), paste0("D", 1:4)) KhatriRao(m,d, make.dimnames=TRUE) KhatriRao(d,m, make.dimnames=TRUE) nm <- as(m,"nMatrix") nd <- as(d,"nMatrix") KhatriRao(nm,nd, make.dimnames=TRUE) KhatriRao(nd,nm, make.dimnames=TRUE) stopifnot(dim(KhatriRao(m,d)) == c(nrow(m)*nrow(d), ncol(d)))