SDAAP: Sparse Discriminant Analysis solved via Accelerated Proximal...

In accSDA: Accelerated Sparse Discriminant Analysis

Sparse Discriminant Analysis solved via Accelerated Proximal Gradient

Description

Applies accelerated proximal gradient algorithm to the optimal scoring formulation of sparse discriminant analysis proposed by Clemmensen et al. 2011.

Usage

SDAAP(x, ...)

## Default S3 method:
SDAAP(
  Xt,
  Yt,
  Om,
  gam,
  lam,
  q,
  PGsteps,
  PGtol,
  maxits,
  tol,
  selector = rep(1, dim(Xt)[2]),
  initTheta,
  bt = FALSE,
  L,
  eta,
  rankRed = FALSE
)

Arguments

Xt	n by p data matrix, (not a data frame, but a matrix)
Yt	n by K matrix of indicator variables (Yij = 1 if i in class j). This will later be changed to handle factor variables as well. Each observation belongs in a single class, so for a given row/observation, only one element is 1 and the rest is 0.
Om	p by p parameter matrix Omega in generalized elastic net penalty.
gam	Regularization parameter for elastic net penalty.
lam	Regularization parameter for l1 penalty, must be greater than zero.
q	Desired number of discriminant vectors.
PGsteps	Maximum number if inner proximal gradient algorithm for finding beta.
PGtol	Stopping tolerance for inner APG method.
maxits	Number of iterations to run
tol	Stopping tolerance for proximal gradient algorithm.
selector	Vector to choose which parameters in the discriminant vector will be used to calculate the regularization terms. The size of the vector must be *p* the number of predictors. The default value is a vector of all ones. This is currently only used for ordinal classification.
initTheta	Option to set the initial theta vector, by default it is a vector of all ones for the first theta.
bt	Boolean to indicate whether backtracking should be used, default false.
L	Initial estimate for Lipshitz constant used for backtracking.
eta	Scalar for Lipshitz constant.
rankRed	Boolean indicating whether Om is in factorized form, such that R^t*R = mO

Value

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

call

The matched call.

B

p by q matrix of discriminant vectors.

Q

K by q matrix of scoring vectors.

subits

Total number of iterations in proximal gradient subroutine.

totalits

Number coordinate descent iterations for all discriminant vectors

NULL

See Also

SDAAPcv, SDAP and SDAD

accSDA documentation built on Sept. 5, 2022, 5:05 p.m.