Core Consistency Diagnostic

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Description

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 by pfac$A$H.

Usage

1
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.

Details

The core consistency diagnostic is defined as

100 * ( 1 - sum( (G-S)^2 ) / divisor )

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.

Value

Returns CORCONDIA value.

Author(s)

Nathaniel E. Helwig <helwig@umn.edu>

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.

Examples

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##########   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,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)