SZVDcv {accSDA}

Cross-validation of sparse zero variance discriminant analysis

Description

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

Usage

SZVDcv(Atrain, ...)

## Default S3 method:
SZVDcv(
  Atrain,
  Aval,
  k,
  num_gammas,
  g_mults,
  D,
  sparsity_pen,
  scaling,
  penalty,
  beta,
  tol,
  ztol,
  maxits,
  quiet,
  ...
)

Arguments

Atrain

Training data set.

...

Parameters passed to SZVD.default.

Aval

Validation set.

k

Number of classes within training and validation sets.

num_gammas

Number of gammas to train on.

g_mults

Parameters defining range of gammas to train, g_max*(c_min, c_max). Note that it is an array/vector with two elements.

D

Penalty dictionary basis matrix.

sparsity_pen

weight defining validation criteria as weighted sum of misclassification error and cardinality of discriminant vectors.

scaling

Whether to rescale data so each feature has variance 1.

penalty

Controls whether to apply reweighting of l1-penalty (using sigma = within-class std devs)

beta

Parameter for augmented Lagrangian term in the ADMM algorithm.

tol

Stopping tolerances for the ADMM algorithm, must have tol$rel and tol$abs.

ztol

Threshold for truncating values in DVs to zero.

maxits

Maximum number of iterations used in the ADMM algorithm.

quiet

Controls display of intermediate results.

Details

This function might require a wrapper similar to ASDA.

Value

SZVDcv returns an object of class "SZVDcv" including a list with the following named components:

DVs

Discriminant vectors for the best choice of gamma.

all_DVs

Discriminant vectors for all choices of gamma.

l0_DVs

Discriminant vectors for gamma minimizing cardinality.

mc_DVs

Discriminant vector minimizing misclassification.

gamma

Choice of gamma minimizing validation criterion.

gammas

Set of all gammas trained on.

max_g

Maximum value of gamma guaranteed to yield a nontrivial solution.

ind

Index of best gamma.

w0

unpenalized zero-variance discriminants (initial solutions) plus B and W, etc. from ZVD

NULL

See Also

Non CV version: SZVD.

Examples

  P <- 300 # Number of variables
  N <- 50 # 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)))
 Xval <- 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 <- rep(1:3,each=N)
  Yval <- rep(1:3,each=N)


  # Train the classifier and increase the sparsity parameter from the default
  # so we penalize more for non-sparse solutions.

  res <- accSDA::SZVDcv(cbind(Ytrain,Xtrain),cbind(Yval,Xval),num_gammas=4,
                        g_mults = c(0,1),beta=2.5,
                        D=diag(P), maxits=100,tol=list(abs=1e-3,rel=1e-3), k = 3,
                        ztol=1e-4,sparsity_pen=0.3,quiet=FALSE,penalty=TRUE,scaling=TRUE)