Nonnegative Orthogonal Locality Preserving Projection

Nonnegative Orthogonal Locality Preserving Projection (NOLPP) is a variant of OLPP where projection vectors - or, basis for learned subspace - contain no negative values.

do.nolpp(
  X,
  ndim = 2,
  type = c("proportion", 0.1),
  preprocess = c("null", "center", "scale", "cscale", "decorrelate", "whiten"),
  t = 1,
  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 "null". See also aux.preprocess for more details.

t

kernel bandwidth in \((0,\infty)\).

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.olpp

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 kernel bandwidths with 20% connectivity
out1 = do.nolpp(X, type=c("proportion",0.5), t=0.01)
out2 = do.nolpp(X, type=c("proportion",0.5), t=0.1)
out3 = do.nolpp(X, type=c("proportion",0.5), t=1)

## visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(out1$Y, col=label, main="NOLPP::t=0.01")
plot(out2$Y, col=label, main="NOLPP::t=0.1")
plot(out3$Y, col=label, main="NOLPP::t=1")
par(opar)
}