Optimize kernel beta for nmfae by cross-validation

nmfae.kernel.beta.cv selects the optimal beta parameter of the kernel function by evaluating nmf.rrr.cv for each candidate value. The kernel matrix \(A = K(U, V; \beta)\) replaces \(Y_2\) in the three-layer NMF model.

When beta = NULL, candidate values are automatically generated via nmfkc.kernel.beta.nearest.med.

Usage

nmf.rrr.kernel.beta.cv(
  Y1,
  rank1 = 2,
  rank2 = NULL,
  U,
  V = NULL,
  beta = NULL,
  plot = TRUE,
  ...
)

Arguments

Y1

Output matrix \(Y_1\) (P1 x N). Non-negative.

rank1

Integer. Rank of the response basis. Default is 2.

rank2

Integer. Rank of the covariate basis. Default (NULL) = rank1.

U

Covariate matrix \(U\) (K x M). Rows are features, columns are samples (or knot points for non-symmetric kernels).

V

Covariate matrix \(V\) (K x N). If NULL (default), V = U and a symmetric kernel is used.

beta

Numeric vector of candidate beta values. If NULL, automatically determined via nmfkc.kernel.beta.nearest.med.

plot

Logical. If TRUE (default), plots the objective function curve.

...

Additional arguments. Kernel-specific args (kernel, degree) are passed to nmfkc.kernel; all others (div, seed, shuffle, epsilon, maxit, etc.) are passed to nmf.rrr.cv. Also accepts cores to evaluate the candidate beta values in parallel (default getOption("mc.cores", 1L)); each inner CV then runs sequentially, and because results are gathered in order the selected beta is identical for any cores. For backward compatibility, Q and R are accepted as aliases for rank and rank.encoder.

Rank aliases accepted here for backward compatibility: Q for rank1, R for rank2.

Value

A list with components:

beta

The beta value that minimizes the cross-validation objective.

objfunc

Named numeric vector of objective function values for each candidate beta.

See also

nmf.rrr.cv, nmfkc.kernel, nmfkc.kernel.beta.cv

Examples

Y <- matrix(cars$dist, nrow = 1)
U <- matrix(cars$speed, nrow = 1)
res <- nmf.rrr.kernel.beta.cv(Y, rank1 = 1, rank2 = 1, U = U,
                             beta = c(0.01, 0.02, 0.05), nfolds = 5)
#> beta=0.01...
#> 0.1sec
#> beta=0.02...
#> 0.2sec
#> beta=0.05...
#> 0.1sec

res$beta
#> [1] 0.05