The simplest way of out-of-sample extension might be linear regression even though the original embedding is not the linear type by solving $$\textrm{min}_{\beta} \|X_{old} \beta - Y_{old}\|_2^2$$ and use the estimate $$\hat{beta}$$ to acquire $$Y_{new} = X_{new} \hat{\beta}$$.

oos.linproj(Xold, Yold, Xnew)

## Arguments

Xold

an $$(n\times p)$$ matrix of data in original high-dimensional space.

Yold

an $$(n\times ndim)$$ matrix of data in reduced-dimensional space.

Xnew

an $$(m\times p)$$ matrix for out-of-sample extension.

## Value

an $$(m\times ndim)$$ matrix whose rows are embedded observations.

Kisung You

## Examples

# \donttest{
## generate sample data and separate them
data(iris, package="Rdimtools")
X   = as.matrix(iris[,1:4])
lab = as.factor(as.vector(iris[,5]))
ids = sample(1:150, 30)

Xold = X[setdiff(1:150,ids),]  # 80% of data for training
Xnew = X[ids,]                 # 20% of data for testing

## run PCA for train data & use the info for prediction
training = do.pca(Xold,ndim=2)
Yold     = training$Y Ynew = Xnew%*%training$projection
Yplab    = lab[ids]

## perform out-of-sample prediction
Yoos  = oos.linproj(Xold, Yold, Xnew)

## visualize