oos.linproj {Rdimtools}

OOS : Linear Projection

Description

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}

.

Usage

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.

Author(s)

Kisung You

Examples

## 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
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,2))
plot(Ynew, pch=19, col=Yplab, main="true prediction")
plot(Yoos, pch=19, col=Yplab, main="OOS prediction")
par(opar)