Nonnegative Orthogonal Neighborhood Preserving Projections

Nonnegative Orthogonal Neighborhood Preserving Projections (NONPP) is a variant of ONPP where projection vectors - or, basis for learned subspace - contain no negative values.

do.nonpp(
  X,
  ndim = 2,
  type = c("proportion", 0.1),
  preprocess = c("null", "center", "decorrelate", "whiten"),
  maxiter = 1000,
  reltol = 1e-05
)

Arguments

X

an \((n\times p)\) matrix or data frame whose rows are observations.

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" and other options of "decorrelate" and "whiten" are supported. See also aux.preprocess for more details.

maxiter

number of maximum iteraions allowed.

reltol

stopping criterion for incremental relative error.

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

Zafeiriou S, Laskaris N (2010). “Nonnegative Embeddings and Projections for Dimensionality Reduction and Information Visualization.” In 2010 20th International Conference on Pattern Recognition, 726--729.

See also

do.onpp

Author

Kisung You

Examples

if (FALSE) {
## 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])

## use different levels of connectivity
out1 = do.nonpp(X, type=c("proportion",0.1))
out2 = do.nonpp(X, type=c("proportion",0.2))
out3 = do.nonpp(X, type=c("proportion",0.5))

## visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(out1$Y, col=label, main="NONPP::10% connected")
plot(out2$Y, col=label, main="NONPP::20% connected")
plot(out3$Y, col=label, main="NONPP::50% connected")
par(opar)
}