selectA | R Documentation |
Select a random embedding matrix
selectA(
d,
D,
type = "isotropic",
control = list(n = 30, maxit = 100, maxit2 = 10)
)
d |
small dimension |
D |
high dimension |
type |
method of random sampling of coefficients or selection procedure, one of
|
control |
list to be passed to |
randomly selected matrix with orthogonal columns and normalized rows (except for standard)
Mickael Binois
M. Binois (2015), Uncertainty quantification on Pareto fronts and high-dimensional strategies in Bayesian optimization, with applications in multi-objective automotive design, PhD thesis, Mines Saint-Etienne.
## Example of orthogonal projections
d <- 2; D <- 6
A1 <- selectA(d, D, type = 'Gaussian')
A2 <- selectA(d, D, type = 'isotropic')
A3 <- selectA(d, D, type = 'optimized')
n <- 10000
size <- 10
Y <- size * (2 * matrix(runif(n * d), n) - 1)
Z1 <- ortProj(randEmb(Y, A1), t(A1))
Z2 <- ortProj(randEmb(Y, A2), t(A2))
Z3 <- ortProj(randEmb(Y, A3), t(A3))
par(mfrow = c(1, 3))
plot(Z1, asp = 1)
plot(Z2, asp = 1)
plot(Z3, asp = 1)
par(mfrow = c(1, 1))
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