SZVD_kFold_cv: Cross-validation of sparse zero variance discriminant analysis

Description

Applies alternating direction methods of multipliers to solve sparse zero variance discriminant analysis.

Usage

SZVD_kFold_cv(X, ...)
# S3 method for default
SZVD_kFold_cv(
  X,
  Y,
  folds,
  gams,
  beta,
  D,
  q,
  maxits,
  tol,
  ztol,
  feat,
  penalty,
  quiet,
  ...
)

Value

SZVDcv returns an object of class "SZVDcv" including a list with the named components DVs and gambest. Where DVs are the discriminant vectors for the best l1 regularization parameter and gambest is the best regularization parameter found in the cross-validation.

NULL

Arguments

X: n by p data matrix, variables should be scaled to by sd
...: Parameters passed to SZVD.default.
Y: n by K indicator matrix.
folds: number of folds to use in K-fold cross-validation.
gams: Number of regularly spaced regularization parameters to try in [0,1]*max_gamma. See details for how max_gamma is computed in the function.
beta: Augmented Lagrangian parameter. Must be greater than zero.
D: Penalty dictionary basis matrix.
q: Desired number of discriminant vectors.
maxits: Number of iterations to run ADMM algorithm.
tol: Stopping tolerances for ADMM, must have tol$rel and tol$abs.
ztol: Rounding tolerance for truncating entries to 0.
feat: Maximum fraction of nonzero features desired in validation scheme.
penalty: Controls whether to apply reweighting of l1-penalty (using sigma = within-class std devs)
quiet: toggles between displaying intermediate statistics.

Details

Add how max_gamma is calculated from the ZVD solution. This function might require a wrapper similar to ASDA.

Examples

Run this code

  P <- 150 # Number of variables
  N <- 20 # Number of samples per class

  # Mean for classes, they are zero everywhere except the first 3 coordinates
  m1 <- rep(0,P)
  m1[1] <- 3

  m2 <- rep(0,P)
  m2[2] <- 3

  m3 <- rep(0,P)
  m3[3] <- 3

  # Sample dummy data
  Xtrain <- rbind(MASS::mvrnorm(n=N,mu = m1, Sigma = diag(P)),
                 MASS::mvrnorm(n=N,mu = m2, Sigma = diag(P)),
                MASS::mvrnorm(n=N,mu = m3, Sigma = diag(P)))


  # Generate the labels
  Ytrain <- cbind(c(rep(1,N),rep(0,2*N)),
                  c(rep(0,N),rep(1,N),rep(0,N)),
                  c(rep(0,2*N),rep(1,N)))

  # Normalize the data
  Xt <- accSDA::normalize(Xtrain)
  Xtrain <- Xt$Xc

  # Train the classifier and increase the sparsity parameter from the default
  # so we penalize more for non-sparse solutions.
  res <- accSDA::SZVD_kFold_cv(Xtrain,Ytrain,folds=2,gams=2,beta=2.5,q=1, D=diag(P),
                              maxits=50,tol=list(abs=1e-2,rel=1e-2),
                              ztol=1e-3,feat=0.3,quiet=FALSE,penalty=TRUE)