linear_RSIR: Regularized Sliced Inverse Regression

In Rdimtools: Dimension Reduction and Estimation Methods

Regularized Sliced Inverse Regression

Description

One of possible drawbacks in SIR method is that for high-dimensional data, it might suffer from rank deficiency of scatter/covariance matrix. Instead of naive matrix inversion, several have proposed regularization schemes that reflect several ideas from various incumbent methods.

Usage

do.rsir(
  X,
  response,
  ndim = 2,
  h = max(2, round(nrow(X)/5)),
  preprocess = c("center", "scale", "cscale", "decorrelate", "whiten"),
  regmethod = c("Ridge", "Tikhonov", "PCA", "PCARidge", "PCATikhonov"),
  tau = 1,
  numpc = ndim
)

Arguments

X	an (n\times p) matrix or data frame whose rows are observations and columns represent independent variables.
response	a length-n vector of response variable.
ndim	an integer-valued target dimension.
h	the number of slices to divide the range of response vector.
preprocess	an additional option for preprocessing the data. Default is "center". See also aux.preprocess for more details.
regmethod	type of regularization scheme to be used.
tau	regularization parameter for adjusting rank-deficient scatter matrix.
numpc	number of principal components to be used in intermediate dimension reduction scheme.

Value

a named list containing

Y

an (n\times ndim) matrix whose rows are embedded observations.

trfinfo

a list containing information for out-of-sample prediction.

projection

a (p\times ndim) whose columns are basis for projection.

Author(s)

Kisung You

References

\insertRef

chiaromonte_dimension_2002Rdimtools

\insertRef

zhong_rsir_2005Rdimtools

\insertRef

bernard-michel_gaussian_2009Rdimtools

\insertRef

bernard-michel_retrieval_2009Rdimtools

See Also

do.sir

Examples

## generate swiss roll with auxiliary dimensions
## it follows reference example from LSIR paper.
set.seed(100)
n     = 50
theta = runif(n)
h     = runif(n)
t     = (1+2*theta)*(3*pi/2)
X     = array(0,c(n,10))
X[,1] = t*cos(t)
X[,2] = 21*h
X[,3] = t*sin(t)
X[,4:10] = matrix(runif(7*n), nrow=n)

## corresponding response vector
y = sin(5*pi*theta)+(runif(n)*sqrt(0.1))

## try with different regularization methods
## use default number of slices
out1 = do.rsir(X, y, regmethod="Ridge")
out2 = do.rsir(X, y, regmethod="Tikhonov")
outsir = do.sir(X, y)

## visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(out1$Y,   main="RSIR::Ridge")
plot(out2$Y,   main="RSIR::Tikhonov")
plot(outsir$Y, main="standard SIR")
par(opar)

Rdimtools documentation built on Dec. 28, 2022, 1:44 a.m.