R KhatriRao Khatri-Rao 矩阵积

说明

计算任何类型矩阵的 Khatri-Rao 乘积。

Khatri-Rao 产品是按列的克罗内克产品。它最初由 Khatri 和 Rao (1968) 提出，有许多不同的应用，请参阅 Liu 和 Trenkler (2008) 的调查。值得注意的是，它用于高维张量分解，参见 Bader 和 Kolda (2008)。

用法

KhatriRao(X, Y = X, FUN = "*", sparseY = TRUE, make.dimnames = FALSE)

参数

X , Y	具有相同列数的矩阵。
FUN	用于按列克罗内克乘积的(名称)function，请参阅 kronecker ，默认为通常的乘法。
sparseY	逻辑指定是否应强制 Y 并将其视为 sparseMatrix 。将其设置为 FALSE ，例如，以区分结构零和零条目。
make.dimnames	逻辑指示结果是否应该以简单的方式从X和Y继承dimnames。

值

"CsparseMatrix" ，比如 R ， X ( n \times k ) 和 Y ( m \times k ) 的 Khatri-Rao 乘积的维度为 (n\cdot m) \times k ，其中 j-th 列，R[,j] 是克罗内克积 kronecker(X[,j], Y[,j]) 。

注意

当前的实现对于大型稀疏矩阵是有效的。

例子

## 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))
(Kmd <- KhatriRao(m,d, make.dimnames=TRUE))
(Kdm <- KhatriRao(d,m, make.dimnames=TRUE))

nm <- as(m, "nsparseMatrix")
nd <- as(d, "nsparseMatrix")
KhatriRao(nm,nd, make.dimnames=TRUE)
KhatriRao(nd,nm, make.dimnames=TRUE)

stopifnot(dim(KhatriRao(m,d)) == c(nrow(m)*nrow(d), ncol(d)))
## border cases / checks:
zm <- nm; zm[] <- FALSE # all FALSE matrix
stopifnot(all(K1 <- KhatriRao(nd, zm) == 0), identical(dim(K1), c(12L, 4L)),
          all(K2 <- KhatriRao(zm, nd) == 0), identical(dim(K2), c(12L, 4L)))

d0 <- d; d0[] <- 0; m0 <- Matrix(d0[-1,])
stopifnot(all(K3 <- KhatriRao(d0, m) == 0), identical(dim(K3), dim(Kdm)),
	  all(K4 <- KhatriRao(m, d0) == 0), identical(dim(K4), dim(Kmd)),
	  all(KhatriRao(d0, d0) == 0), all(KhatriRao(m0, d0) == 0),
	  all(KhatriRao(d0, m0) == 0), all(KhatriRao(m0, m0) == 0),
	  identical(dimnames(KhatriRao(m, d0, make.dimnames=TRUE)), dimnames(Kmd)))

## a matrix with "structural" and non-structural zeros:
m01 <- new("dgCMatrix", i = c(0L, 2L, 0L, 1L), p = c(0L, 0L, 0L, 2L, 4L),
           Dim = 3:4, x = c(1, 0, 1, 0))
D4 <- Diagonal(4, x=1:4) # "as" d
DU <- Diagonal(4)# unit-diagonal: uplo="U"
(K5  <- KhatriRao( d, m01))
K5d  <- KhatriRao( d, m01, sparseY=FALSE)
K5Dd <- KhatriRao(D4, m01, sparseY=FALSE)
K5Ud <- KhatriRao(DU, m01, sparseY=FALSE)
(K6  <- KhatriRao(diag(3),     t(m01)))
K6D  <- KhatriRao(Diagonal(3), t(m01))
K6d  <- KhatriRao(diag(3),     t(m01), sparseY=FALSE)
K6Dd <- KhatriRao(Diagonal(3), t(m01), sparseY=FALSE)
stopifnot(exprs = {
    all(K5 == K5d)
    identical(cbind(c(7L, 10L), c(3L, 4L)),
              which(K5 != 0, arr.ind = TRUE, useNames=FALSE))
    identical(K5d, K5Dd)
    identical(K6, K6D)
    all(K6 == K6d)
    identical(cbind(3:4, 1L),
              which(K6 != 0, arr.ind = TRUE, useNames=FALSE))
    identical(K6d, K6Dd)
})

作者

Original by Michael Cysouw, Univ. Marburg; minor tweaks, bug fixes etc, by Martin Maechler.

参考

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.

Bader, Brett W, and Tamara G Kolda (2008) Efficient MATLAB Computations with Sparse and Factored Tensors. SIAM J. Scientific Computing 30, 205-231.

也可以看看

kronecker 。