Orthogonal Neighborhood Preserving Projections

Source: R/linear_ONPP.R

Orthogonal Neighborhood Preserving Projection (ONPP) is an unsupervised linear dimension reduction method. It constructs a weighted data graph from LLE method. Also, it develops LPP method by preserving the structure of local neighborhoods.

do.onpp(
  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

Kokiopoulou E, Saad Y (2007). “Orthogonal Neighborhood Preserving Projections: A Projection-Based Dimensionality Reduction Technique.” IEEE Transactions on Pattern Analysis and Machine Intelligence, 29(12), 2143--2156.

Author

Kisung You

Examples

## use 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])

## try different numbers for neighborhood size
out1 = do.onpp(X, type=c("proportion",0.10))
out2 = do.onpp(X, type=c("proportion",0.25))
out3 = do.onpp(X, type=c("proportion",0.50))

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

par(opar)