Locality Pursuit Embedding

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.

Author

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
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(out1$Y, main="LPE::numk=5")
plot(out2$Y, main="LPE::numk=10")
plot(out3$Y, main="LPE::numk=25")

par(opar)
# }