Constrained Graph Embedding

Constrained Graph Embedding (CGE) is a semi-supervised embedding method that incorporates partially available label information into the graph structure that find embeddings consistent with the labels.

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

Arguments

X

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

label

a length-\(n\) vector of data class labels. It should contain NA elements for missing label.

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.

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.

References

He X, Ji M, Bao H (2009). “Graph Embedding with Constraints.” In IJCAI.

Author

Kisung You

Examples

## use iris data
data(iris)
X     = as.matrix(iris[,2:4])
label = as.integer(iris[,5])
lcols = as.factor(label)

## copy a label and let 10% of elements be missing
nlabel = length(label)
nmissing = round(nlabel*0.10)
label_missing = label
label_missing[sample(1:nlabel, nmissing)]=NA

## try different neighborhood sizes
out1 = do.cge(X, label_missing, type=c("proportion",0.10))
out2 = do.cge(X, label_missing, type=c("proportion",0.25))
out3 = do.cge(X, label_missing, type=c("proportion",0.50))

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

par(opar)