Locally Principal Component Analysis by Yang et al. (2006)

Locally Principal Component Analysis (LPCA) is an unsupervised linear dimension reduction method. It focuses on the information brought by local neighborhood structure and seeks the corresponding structure, which may contain useful information for revealing discriminative information of the data.

do.lpca2006(
  X,
  ndim = 2,
  type = c("proportion", 0.1),
  preprocess = c("center", "scale", "cscale", "decorrelate", "whiten")
)

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 "center". See also aux.preprocess for more details.

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

Yang J, Zhang D, Yang J (2006). “Locally Principal Component Learning for Face Representation and Recognition.” Neurocomputing, 69(13-15), 1697--1701.

Author

Kisung You

Examples

# \donttest{
## use iris dataset
data(iris)
set.seed(100)
subid = sample(1:150,100)
X     = as.matrix(iris[subid,1:4])
lab   = as.factor(iris[subid,5])

## try different neighborhood size
out1 <- do.lpca2006(X, ndim=2, type=c("proportion",0.25))
out2 <- do.lpca2006(X, ndim=2, type=c("proportion",0.50))
out3 <- do.lpca2006(X, ndim=2, type=c("proportion",0.75))

## Visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(out1$Y, pch=19, col=lab, main="LPCA2006::25% connected")
plot(out2$Y, pch=19, col=lab, main="LPCA2006::50% connected")
plot(out3$Y, pch=19, col=lab, main="LPCA2006::75% connected")

par(opar)
# }