const.control function

Auxiliary for Controlling Multi-Way Constraints

Auxiliary function for controlling the const argument of the mcr, parafac, and parafac2 functions. Applicable when using smoothness constraints.

const.control(const, df = NULL, degree = NULL, intercept = NULL)

Arguments

• const: Character vector of length 3 or 4 giving the constraints for each mode. See const for the 24 available options.
• df: Integer vector of length 3 or 4 giving the degrees of freedom to use for the spline basis in each mode. Can also input a single number giving the common degrees of freedom to use for each mode. Defaults to 7 degrees of freedom for each applicable mode.
• degree: Integer vector of length 3 or 4 giving the polynomial degree to use for the spline basis in each mode. Can also input a single number giving the common polynomial degree to use for each mode. Defaults to degree 3 (cubic) polynomials for each applicable mode.
• intercept: Logical vector of length 3 or 4 indicating whether the spline basis should contain an intercept. Can also input a single logical giving the common intercept indicator to use for each mode. Defaults to TRUE for each applicable mode.

Returns

Returns a list with elements: const, df, degree, and intercept.

Author(s)

Nathaniel E. Helwig helwig@umn.edu

Details

The mcr, parafac, and parafac2 functions pass the input const to this function to determine the fitting options when using smoothness constraints.

The const function (from CMLS package) describes the available constraint options.

Examples

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

# create random data array with Parafac structure
set.seed(4)
mydim <- c(30, 10, 8, 10)
nf <- 4
aseq <- seq(-3, 3, length.out = mydim[1])
Amat <- cbind(dnorm(aseq), dchisq(aseq+3.1, df=3),
              dt(aseq-2, df=4), dgamma(aseq+3.1, shape=3, rate=1))
Bmat <- svd(matrix(runif(mydim[2]*nf), nrow = mydim[2], ncol = nf), nv = 0)$u
Cmat <- matrix(runif(mydim[3]*nf), nrow = mydim[3], ncol = nf)
Cstruc <- Cmat > 0.5
Cmat <- Cmat * Cstruc
Dmat <- matrix(runif(mydim[4]*nf), nrow = mydim[4], ncol = nf)
Xmat <- tcrossprod(Amat, krprod(Dmat, krprod(Cmat, Bmat)))
Xmat <- array(Xmat, dim = mydim)
Emat <- array(rnorm(prod(mydim)), dim = mydim)
Emat <- nscale(Emat, 0, ssnew = sumsq(Xmat))   # SNR = 1
X <- Xmat + Emat

# fit Parafac model (unimodal and smooth A, orthogonal B, 
#                    non-negative and structured C, non-negative D)
set.seed(123)
pfac <- parafac(X, nfac = nf, nstart = 1, Cstruc = Cstruc, 
                const = c("unismo", "orthog", "nonneg", "nonneg"))
pfac

# same as before, but add some options to the unimodality contraints...
# more knots (df=10), quadratic splines (degree=2), and enforce non-negativity
cvec <- c("unsmno", "orthog", "nonneg", "nonneg")
ctrl <- const.control(cvec, df = 10, degree = 2)
set.seed(123)
pfac <- parafac(X, nfac = nf, nstart = 1, Cstruc = Cstruc,
                const = cvec, control = ctrl)
pfac