nonlinear_ISPE: Isometric Stochastic Proximity Embedding

In kisungyou/Rdimtools: Dimension Reduction and Estimation Methods

Isometric Stochastic Proximity Embedding

Description

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.

Usage

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.

Author(s)

Kisung You

References

\insertRef

agrafiotis_selforganizing_2002Rdimtools

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
opar <- par(no.readonly=TRUE)
par(mfrow=c(2,2))
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")
par(opar)

kisungyou/Rdimtools documentation built on Jan. 2, 2023, 9:55 a.m.