curvilinear {singR}

Curvilinear algorithm with r0 joint components

Description

The curvilinear algorithm is modified from Wen and Yin paper.

Usage

curvilinear(
  Ux,
  Uy,
  xData,
  yData,
  invLx,
  invLy,
  rho,
  tau = 0.01,
  alpha = 0.8,
  maxiter = 1000,
  tol = 1e-06,
  rj
)

Arguments

Ux

Matrix with n.comp x n, initial value of Ux, comes from greedyMatch.

Uy

Matrix with n.comp x n, initial value of Uy, comes from greedyMatch.

xData

matrix with n x px, Xw = Lx %*% Xc.

yData

matrix with n x py, Yw = Ly %*% Yc.

invLx

Inverse matrix of Lx, matrix n x n.

invLy

Inverse matrix of Ly, matrix n x n.

rho

the weight parameter of matching relative to non-gaussianity.

tau

initial step size, default value is 0.01

alpha

controls weighting of skewness and kurtosis. Default value is 0.8, which corresponds to the Jarque-Bera test statistic with 0.8 weighting on squared skewness and 0.2 on squared kurtosis.

maxiter

default value is 1000

tol

the threshold of change in Ux and Uy to stop the curvlinear function

rj

the joint rank, comes from greedyMatch.

Value

a list of matrices:

Ux

Optimized Ux with matrix n.comp x n.

Uy

Optimized Uy with matrix n.comp x n.

tau

step size

iter

number of iterations.

error

PMSE(Ux,Uxnew)+PMSE(Uy,Uynew)

obj

Objective Function value