fps: Fantope Projection and Selection

In vqv/fps: Fantope Projection and Selection

Description

This function computes a solution path of the Fantope Projection and Selection (FPS) estimator. It takes a symmetric matrix S as input and returns an object containing a list of projection matrices estimated by FPS over a sequence of regularization parameter values.

Fantope Project and Select

Usage

fps(S, ndim, nsol = 50L, maxnvar = -1L, lambdamin = -1,
  lambda = as.numeric(c()), maxiter = 100L, tolerance = 0.001,
  verbose = 0L)

Arguments

S	Input matrix (assumed to be symmetric)
ndim	Target subspace dimension (can be fractional)
nsol	Number of solutions to compute
maxnvar	Suggested maximum number of variables to include (ignored if maxnvar <= 0)
lambdamin	Minimum value of lambda (set automatically if lambdamin < 0)
lambda	Vector of regularization parameter values; overrides //' nsol, maxnvar, and lambdamin if nonempty
maxiter	Maximum number of iterations for each solution
tolerance	Convergence threshold
verbose	Level of verbosity; Silent if verbose = 0, otherwise display more messages and progress indicators as verbose increases

Details

By default, a sensible minimum value of the regularization parameter is automatically chosen so that the minimally regularized solution is different from PCA.

For large input matrices (1000-by-1000 or larger) it is recommended that the maxnvar argument be set to a reasonably small number.

Value

An S3 object of class fps which is a list with the following components:

ndim	trace (dimension) of the estimate
lambda	a vector containing the regularization parameters of each estimate
projection	a list containing the the projection matrix estimates
leverage	a matrix whose columns are the diagonal entries of the projection matrix estimates
L1	a vector of the sum of absolute values of each estimate
var.explained	variance explained by each estimate (trace inner product of the projection and S)
var.total	total variance (trace of S)
niter	a vector containing the number of ADMM iterations for each estimate

Examples

# Apply FPS to the standardized wine data from the UCI ML repository
data(wine)
out <- fps(cor(wine), ndim = 2)
print(out)
plot(out)

# Create a synthetic dataset by adding noise variables to the wine data
j <- sample(1:ncol(wine), size = 500 - ncol(wine), replace = TRUE)
noise <- apply(wine[, j], 2, sample, replace = TRUE)
colnames(noise) <- rep('noise', ncol(noise))
x <- cbind(wine, noise)
out <- fps(cor(x), ndim = 2, maxnvar = 50, verbose = 1)

## Not run: 
# Choose lambda by cross-validation (this may take a few minutes)
cvout <- cv(out, x, FUN = cor, verbose = 1)
plot(cvout)
v <- coef(out, lambda = cvout$lambda.cv)
print(v)

## End(Not run)

vqv/fps documentation built on May 3, 2019, 6:41 p.m.