The isometric SPE (ISPE) adopts the idea of approximating geodesic distance on embedded manifold when two data points are close enough. It introduces the concept of cutoff where the learning process is only applied to the pair of data points whose original proximity is small enough to be considered as mutually local whose distance should be close to geodesic distance.

do.ispe(
X,
ndim = 2,
proximity = function(x) {
dist(x, method = "euclidean")
},
C = 50,
S = 50,
lambda = 1,
drate = 0.9,
cutoff = 1
)

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.

proximity

a function for constructing proximity matrix from original data dimension.

C

the number of cycles to be run; after each cycle, learning parameter

S

the number of updates for each cycle.

lambda

initial learning parameter.

drate

multiplier for lambda at each cycle; should be a positive real number in $$(0,1).$$

cutoff

cutoff threshold value.

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

Agrafiotis DK, Xu H (2002). “A Self-Organizing Principle for Learning Nonlinear Manifolds.” Proceedings of the National Academy of Sciences, 99(25), 15869--15872.

Kisung You

Examples

## load iris data
data(iris)
set.seed(100)
subid = sample(1:150,50)
X     = as.matrix(iris[subid,1:4])
label = as.factor(iris[subid,5])

## compare with original SPE
outSPE <- do.spe(X, ndim=2)
out1 <- do.ispe(X, ndim=2, cutoff=0.5)
out2 <- do.ispe(X, ndim=2, cutoff=5)
out3 <- do.ispe(X, ndim=2, cutoff=50)

## Visualize
plot(outSPE$Y, pch=19, col=label, main="SPE") plot(out1$Y,   pch=19, col=label, main="ISPE::cutoff=0.5")
plot(out2$Y, pch=19, col=label, main="ISPE::cutoff=5") plot(out3$Y,   pch=19, col=label, main="ISPE::cutoff=50")