Local Linear Laplacian Eigenmaps

Local Linear Laplacian Eigenmaps is an unsupervised manifold learning method as an extension of Local Linear Embedding (do.lle). It is claimed to be more robust to local structure and noises. It involves the concept of artificial neighborhood in constructing the adjacency graph for reconstruction of the approximated manifold.

do.llle(
  X,
  ndim = 2,
  preprocess = c("null", "center", "scale", "cscale", "decorrelate", "whiten"),
  K = round(nrow(X)/2),
  P = max(round(nrow(X)/4), 2),
  bandwidth = 0.2
)

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.

preprocess

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

K

size of near neighborhood for each data point.

P

size of artifical neighborhood.

bandwidth

scale parameter for Gaussian kernel. It should be in \((0,1)\).

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

Liu F, Zhang W, Gu S (2016). “Local Linear Laplacian Eigenmaps: A Direct Extension of LLE.” Pattern Recognition Letters, 75, 30--35.

See also

do.lle

Author

Kisung You

Examples

if (FALSE) {
## use iris data
data(iris)
X     = as.matrix(iris[,1:4])
label = as.integer(iris$Species)

# see the effect bandwidth
out1 = do.llle(X, bandwidth=0.1, P=20)
out2 = do.llle(X, bandwidth=0.5, P=20)
out3 = do.llle(X, bandwidth=0.9, P=20)

# visualize the results
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(out1$Y, col=label, main="bandwidth=0.1")
plot(out2$Y, col=label, main="bandwidth=0.5")
plot(out3$Y, col=label, main="bandwidth=0.9")
par(opar)
}