psvmSDR (version 2.0.1)

npsdr: A unified Principal sufficient dimension reduction method via kernel trick

Description

Principal Sufficient Dimension Reduction method

Usage

npsdr(
  x,
  y,
  loss = "svm",
  h = 10,
  lambda = 1,
  b = floor(length(y)/3),
  eps = 1e-05,
  max.iter = 100,
  eta = 0.1,
  mtype,
  plot = TRUE
)

Value

An object with S3 class "npsdr". Details are listed below.

evalues

Eigenvalues of the estimated working matrix M.

evectors

Eigenvectors of the estimated working matrix M, the first d leading eigenvectors consists the basis of the central subspace.

Arguments

x

data matrix

y

either continuous or (+1,-1) typed binary response vector

loss

pre-specified loss functions belongs to "svm", "logit", "l2svm", "wsvm", "qr", "asls", "wlogit", "wl2svm", "lssvm", "wlssvm", and user-defined loss function object also can be used formed by inside double (or single) quotation mark. Default is 'svm'.

h

the number of slices. default value is 10

lambda

hyperparameter for the loss function. default value is 1

b

number of basis functions for a kernel trick, floor(length(y)/3) is default

eps

threshold for stopping iteration with respect to the magnitude of derivative, default value is 1.0e-4

max.iter

maximum iteration number for the optimization process. default value is 30

eta

learning rate for gradient descent method. default value is 0.1

mtype

type of margin, either "m" or "r" refer margin and residual, respectively (See, Table 1 in the pacakge manuscript). When one use user-defined loss function this argument should be specified. Default is "m".

plot

If TRUE then it produces scatter plots of \(Y\) versus the first sufficient predictor. The default is FALSE.

Author

Jungmin Shin, , Seung Jun Shin, , Andreas Artemiou

References

Artemiou, A. and Dong, Y. (2016) Sufficient dimension reduction via principal lq support vector machine, Electronic Journal of Statistics 10: 783–805.
Artemiou, A., Dong, Y. and Shin, S. J. (2021) Real-time sufficient dimension reduction through principal least squares support vector machines, Pattern Recognition 112: 107768.
Kim, B. and Shin, S. J. (2019) Principal weighted logistic regression for sufficient dimension reduction in binary classification, Journal of the Korean Statistical Society 48(2): 194–206.
Li, B., Artemiou, A. and Li, L. (2011) Principal support vector machines for linear and nonlinear sufficient dimension reduction, Annals of Statistics 39(6): 3182–3210.
Soale, A.-N. and Dong, Y. (2022) On sufficient dimension reduction via principal asymmetric least squares, Journal of Nonparametric Statistics 34(1): 77–94.
Wang, C., Shin, S. J. and Wu, Y. (2018) Principal quantile regression for sufficient dimension reduction with heteroscedasticity, Electronic Journal of Statistics 12(2): 2114–2140.
Shin, S. J., Wu, Y., Zhang, H. H. and Liu, Y. (2017) Principal weighted support vector machines for sufficient dimension reduction in binary classification, Biometrika 104(1): 67–81.
Li, L. (2007) Sparse sufficient dimension reduction, Biometrika 94(3): 603–613.

See Also

npsdr_x, psdr, rtpsdr

Examples

# \donttest{
set.seed(1)
n <- 200;
p <- 5;
x <- matrix(rnorm(n*p, 0, 2), n, p)
y <- 0.5*sqrt((x[,1]^2+x[,2]^2))*(log(x[,1]^2+x[,2]^2))+ 0.2*rnorm(n)
obj_kernel <- npsdr(x, y, plot=FALSE)
print(obj_kernel)
plot(obj_kernel)
# }