Local Tangent Space Alignment

Local Tangent Space Alignment, or LTSA in short, is a nonlinear dimensionality reduction method that mimicks the behavior of low-dimensional manifold embedded in high-dimensional space. Similar to LLE, LTSA computes tangent space using nearest neighbors of a given data point, and a multiple of tangent spaces are gathered to to find an embedding that aligns the tangent spaces in target dimensional space.

do.ltsa(
  X,
  ndim = 2,
  type = c("proportion", 0.1),
  symmetric = c("union", "intersect", "asymmetric"),
  preprocess = c("center", "scale", "cscale", "decorrelate", "whiten")
)

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.

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.

eigvals

a vector of eigenvalues from the final decomposition.

References

Zhang T, Yang J, Zhao D, Ge X (2007). “Linear Local Tangent Space Alignment and Application to Face Recognition.” Neurocomputing, 70(7-9), 1547--1553.

Author

Kisung You

Examples

# \donttest{
## generate data
set.seed(100)
X <- aux.gensamples(dname="cswiss",n=100)

## 1. use 10%-connected graph
output1 <- do.ltsa(X,ndim=2)

## 2. use 25%-connected graph
output2 <- do.ltsa(X,ndim=2,type=c("proportion",0.25))

## 3. use 50%-connected graph
output3 <- do.ltsa(X,ndim=2,type=c("proportion",0.50))

## Visualize three different projections
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(output1$Y, main="10%")
plot(output2$Y, main="25%")
plot(output3$Y, main="50%")

par(opar)
# }