Locally Linear Embedded Eigenspace Analysis

Locally Linear Embedding (LLE) is a powerful nonlinear manifold learning method. This method, Locally Linear Embedded Eigenspace Analysis - LEA, in short - is a linear approximation to LLE, similar to Neighborhood Preserving Embedding. In our implementation, the choice of weight binarization is removed in order to respect original work. For 1-dimensional projection, which is rarely performed, authors provided a detour for rank correcting mechanism but it is omitted for practical reason.

do.lea(
  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.

projection

a \((p\times ndim)\) whose columns are basis for projection.

References

Fu Y, Huang TS (2005). “Locally Linear Embedded Eigenspace Analysis.” IFP-TR, UIUC, 2005, 2--05.

See also

do.npe

Author

Kisung You

Examples

if (FALSE) {
## use iris dataset
data(iris)
set.seed(100)
subid <- sample(1:150, 50)
X     <- as.matrix(iris[subid,1:4])
lab   <- as.factor(iris[subid,5])

## compare LEA with LLE and another approximation NPE
out1 <- do.lle(X, ndim=2)
out2 <- do.npe(X, ndim=2)
out3 <- do.lea(X, ndim=2)

## visual comparison
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(out1$Y, pch=19, col=lab, main="LLE")
plot(out2$Y, pch=19, col=lab, main="NPE")
plot(out3$Y, pch=19, col=lab, main="LEA")
par(opar)
}