corcondia function

Core Consistency Diagnostic

Calculates Bro and Kiers's core consistency diagnostic (CORCONDIA) for a fit parafac or parafac2 model. For Parafac2, the diagnostic is calculated after transforming the data.

corcondia(X, object, divisor = c("nfac","core"))

Arguments

• X: Three-way data array with dim=c(I,J,K) or four-way data array with dim=c(I,J,K,L). Can also input a list of two-way or three-way arrays (for Parafac2).
• object: Object of class "parafac" (output from parafac) or class "parafac2" (output from parafac2).
• divisor: Divide by number of factors (default) or core sum of squares.

Returns

Returns CORCONDIA value.

References

Bro, R., & Kiers, H.A.L. (2003). A new efficient method for determining the number of components in PARAFAC models. Journal of Chemometrics, 17, 274-286. tools:::Rd_expr_doi("10.1002/cem.801")

Author(s)

Nathaniel E. Helwig helwig@umn.edu

Details

The core consistency diagnostic is defined as

where G is the least squares estimate of the Tucker core array, S is a super-diagonal core array, and divisor is the sum of squares of either S ("nfac") or G ("core"). A value of 100 indiciates a perfect multilinear structure, and smaller values indicate greater violations of multilinear structure.

Examples

##########   EXAMPLE   ##########

# create random data array with Parafac structure
set.seed(3)
mydim <- c(50,20,5)
nf <- 2
Amat <- matrix(rnorm(mydim[1]*nf),mydim[1],nf)
Bmat <- matrix(runif(mydim[2]*nf),mydim[2],nf)
Cmat <- matrix(runif(mydim[3]*nf),mydim[3],nf)
Xmat <- array(tcrossprod(Amat,krprod(Cmat,Bmat)),dim=mydim)
Emat <- array(rnorm(prod(mydim)),dim=mydim)
Emat <- nscale(Emat, 0, ssnew = sumsq(Xmat))   # SNR=1
X <- Xmat + Emat

# fit Parafac model (1-4 factors)
pfac1 <- parafac(X,nfac=1,nstart=1)
pfac2 <- parafac(X,nfac=2,nstart=1)
pfac3 <- parafac(X,nfac=3,nstart=1)
pfac4 <- parafac(X,nfac=4,nstart=1)

# check corcondia
corcondia(X, pfac1)
corcondia(X, pfac2)
corcondia(X, pfac3)
corcondia(X, pfac4)