do.lpmip {Rdimtools}

Locality-Preserved Maximum Information Projection

Description

Locality-Preserved Maximum Information Projection (LPMIP) is an unsupervised linear dimension reduction method to identify the underlying manifold structure by learning both the within- and between-locality information. The parameter alpha is balancing the tradeoff between two and the flexibility of this model enables an interpretation of it as a generalized extension of LPP.

Usage

do.lpmip(
  X,
  ndim = 2,
  type = c("proportion", 0.1),
  preprocess = c("null", "center", "scale", "cscale", "whiten", "decorrelate"),
  sigma = 10,
  alpha = 0.5
)

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.

type

a vector of neighborhood graph construction. Following types are supported; c("knn",k), c("enn",radius), and c("proportion",ratio). Default is c("proportion",0.1), connecting about 1/10 of nearest data points among all data points. See also aux.graphnbd for more details.

preprocess

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

sigma

bandwidth parameter for heat kernel in (0,\infty).

alpha

balancing parameter between two locality information 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.

projection

a (p\times ndim) whose columns are basis for projection.

Author(s)

Kisung You

References

Haixian Wang, Sibao Chen, Zilan Hu, Wenming Zheng (2008). “Locality-Preserved Maximum Information Projection.” IEEE Transactions on Neural Networks, 19(4), 571–585.

Examples

## use iris dataset
data(iris)
set.seed(100)
subid <- sample(1:150, 50)
X     <- as.matrix(iris[subid,1:4])
lab   <- as.factor(iris[subid,5])

## try different neighborhood size
out1 <- do.lpmip(X, ndim=2, type=c("proportion",0.10))
out2 <- do.lpmip(X, ndim=2, type=c("proportion",0.25))
out3 <- do.lpmip(X, ndim=2, type=c("proportion",0.50))

## Visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(out1$Y, pch=19, col=lab, main="10% connected")
plot(out2$Y, pch=19, col=lab, main="25% connected")
plot(out3$Y, pch=19, col=lab, main="50% connected")
par(opar)