Localized Sliced Inverse Regression

Localized SIR (SIR) is an extension of celebrated SIR method. As its name suggests, the locality concept is brought in that for each slice, only local data points are considered in order to discover intrinsic structure of the data.

do.lsir(
  X,
  response,
  ndim = 2,
  h = max(2, round(nrow(X)/5)),
  preprocess = c("center", "scale", "cscale", "decorrelate", "whiten"),
  ycenter = FALSE,
  numk = max(2, round(nrow(X)/10)),
  tau = 1
)

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.

ycenter

a logical; TRUE to center the response variable, FALSE otherwise.

numk

size of determining neighborhood via \(k\)-nearest neighbor selection.

tau

regularization parameter for adjusting rank-deficient scatter matrix.

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.

References

Wu Q, Liang F, Mukherjee S (2010). “Localized Sliced Inverse Regression.” Journal of Computational and Graphical Statistics, 19(4), 843--860.

See also

do.sir

Author

Kisung You

Examples

## generate swiss roll with auxiliary dimensions
## it follows reference example from LSIR paper.
set.seed(100)
n     = 123
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 different number of neighborhoods
out1 = do.lsir(X, y, numk=5)
out2 = do.lsir(X, y, numk=10)
out3 = do.lsir(X, y, numk=25)

## visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(out1$Y, main="LSIR::nbd size=5")
plot(out2$Y, main="LSIR::nbd size=10")
plot(out3$Y, main="LSIR::nbd size=25")

par(opar)