Locality Pursuit Embedding (LPE) is an unsupervised linear dimension reduction method. It aims at preserving local structure by solving a variational problem that models the local geometrical structure by the Euclidean distances.

do.lpe(
X,
ndim = 2,
preprocess = c("center", "scale", "cscale", "decorrelate", "whiten"),
numk = max(ceiling(nrow(X)/10), 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 "center". See also aux.preprocess for more details.

numk

size of $$k$$-nn neighborhood in original dimensional space.

## 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

Min W, Lu K, He X (2004). “Locality Pursuit Embedding.” Pattern Recognition, 37(4), 781--788.

Kisung You

## Examples

# \donttest{
## generate swiss roll with auxiliary dimensions
set.seed(100)
n     = 100
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)

## try with different neighborhood sizes
out1 = do.lpe(X, numk=5)
out2 = do.lpe(X, numk=10)
out3 = do.lpe(X, numk=25)

## visualize
plot(out1$Y, main="LPE::numk=5") plot(out2$Y, main="LPE::numk=10")