Improved Local Tangent Space Alignment

Conventional LTSA method relies on PCA for approximating local tangent spaces. Improved LTSA (ILTSA) provides a remedy that can efficiently recover the geometric structure of data manifolds even when data are sparse or non-uniformly distributed.

do.iltsa(
  X,
  ndim = 2,
  type = c("proportion", 0.25),
  symmetric = c("union", "intersect", "asymmetric"),
  preprocess = c("center", "scale", "cscale", "decorrelate", "whiten"),
  t = 10
)

Arguments

X

an \((n\times p)\) matrix or data frame whose rows are observations and columns represent independent variables.

ndim

an integer-valued target dimension.

type

a vector of neighborhood graph construction. Following types are supported; c("knn",k), c("enn",radius), and c("proportion",ratio). Default is c("proportion",0.1), connecting about 1/10 of nearest data points among all data points. See also aux.graphnbd for more details.

symmetric

one of "intersect", "union" or "asymmetric" is supported. Default is "union". See also aux.graphnbd for more details.

preprocess

an additional option for preprocessing the data. Default is "center". See also aux.preprocess for more details.

t

heat kernel bandwidth parameter in \((0,\infty)\).

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.

References

Zhang P, Qiao H, Zhang B (2011). “An Improved Local Tangent Space Alignment Method for Manifold Learning.” Pattern Recognition Letters, 32(2), 181--189.

Author

Kisung You

Examples

# \donttest{
## load iris data
data(iris)
set.seed(100)
subid = sample(1:150,50)
X     = as.matrix(iris[subid,1:4])
label = as.factor(iris[subid,5])

## try different bandwidth size
out1 <- do.iltsa(X, t=1)
out2 <- do.iltsa(X, t=10)
out3 <- do.iltsa(X, t=100)

## Visualize two comparisons
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(out1$Y, pch=19, col=label, main="ILTSA::t=1")
plot(out2$Y, pch=19, col=label, main="ILTSA::t=10")
plot(out3$Y, pch=19, col=label, main="ILTSA::t=100")

par(opar)
# }