multiway: corcondia – R documentation

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corcondia

Core Consistency Diagnostic

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.

Usage

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

##########   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)

multiway

Component Models for Multi-Way Data

v1.0-6

GPL (>= 2)

Authors