MinLambda: Numerical optimization for finding appropriate smoothing...
In romanflury/mrbsizeR: Scale Space Multiresolution Analysis of Random Signals

Description Usage Arguments Details Value Examples

Numerical optimization of an objective function G is carried out to find appropriate signal-dependent smoothing levels (λ's). This is easier than visual inspection via the signal-dependent tapering function in TaperingPlot.

1	MinLambda(Xmu, mm, nn, nGrid, nLambda = 2, lambda, sphere = FALSE)

`Xmu`	Posterior mean of the input object as a vector.
`mm`	Number of rows of the original input object.
`nn`	Number of columns of the original input object.
`nGrid`	Size of grid where objective function is evaluated (nGrid-by-nGrid). This argument is ignorded if a sequence `lambda` is specified.
`nLambda`	Number of lambdas to minimize over. Possible arguments: 2 (default) or 3.
`lambda`	λ-sequence which is used for optimization. If nothing is provided, `lambda <- 10^seq(-3, 10, len = nGrid)` is used for data on a grid and `lambda <- 10^seq(-6, 1, len = nGrid)` is used for spherical data.
`sphere`	`TRUE` or `FALSE`: Is the input object defined on a sphere?

As signal-dependent tapering functions are quiet irregular, it is hard to find appropriate smoothing values only by visual inspection of the tapering function plot. A more formal approach is the numerical optimization of an objective function.

Optimization can be carried out with 2 or 3 smoothing parameters. As the smoothing parameters 0 and ∞ are always added, this results in a mrbsizeR analysis with 4 or 5 smoothing parameters.

Sometimes, not all features of the input object can be extracted using the smoothing levels proposed by MinLambda. It might then be necessary to include additional smoothing levels.

plot.minLambda creates a plot of the objective function G on a grid. The minimum is indicated with a white point. The minimum values of the λ's can be extracted from the output of MinLambda, see examples.

A list with 3 objects:

G Value of objective function G.

lambda Evaluated smoothing parameters λ.

minind Index of minimal λ's. lambda[minind] gives the minimal values.

# Artificial sample data
set.seed(987)
sampleData <- matrix(stats::rnorm(100), nrow = 10)
sampleData[4:6, 6:8] <- sampleData[4:6, 6:8] + 5

# Minimization of two lambdas on a 20-by-20-grid
minlamOut <- MinLambda(Xmu = c(sampleData), mm = 10, nn = 10, 
                       nGrid = 20, nLambda = 2)

# Minimal lambda values
minlamOut$lambda[minlamOut$minind]