do.rsir {Rdimtools}

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

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).

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)