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.

- 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.

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.

Chiaromonte F, Martinelli J (2002).
“Dimension Reduction Strategies for Analyzing Global Gene Expression Data with a Response.”
*Mathematical Biosciences*, **176**(1), 123--144.
ISSN 0025-5564.

Zhong W, Zeng P, Ma P, Liu JS, Zhu Y (2005).
“RSIR: Regularized Sliced Inverse Regression for Motif Discovery.”
*Bioinformatics*, **21**(22), 4169--4175.

Bernard-Michel C, Gardes L, Girard S (2009).
“Gaussian Regularized Sliced Inverse Regression.”
*Statistics and Computing*, **19**(1), 85--98.

Bernard-Michel C, Douté S, Fauvel M, Gardes L, Girard S (2009).
“Retrieval of Mars Surface Physical Properties from OMEGA Hyperspectral Images Using Regularized Sliced Inverse Regression.”
*Journal of Geophysical Research*, **114**(E6).

```
## 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)
```