MGSDA (version 1.6.1)

classifyV: Classification for MGSDA

Description

Classify observations in the test set using the supplied matrix of canonical vectors V and the training set.

Usage

classifyV(Xtrain, Ytrain, Xtest, V, prior = TRUE, tol1 = 1e-10)

Value

Returns a vector of length M with predicted group labels for the test set.

Arguments

Xtrain

A Nxp data matrix; N observations on the rows and p features on the columns.

Ytrain

A N vector containing the group labels. Should be coded as 1,2,...,G, where G is the number of groups.

Xtest

A Mxp data matrix; M test observations on the rows and p features on the columns.

V

A pxr matrix of canonical vectors that is used to classify observations.

prior

A logical indicating whether to put larger weights to the groups of larger size; the default value is TRUE.

tol1

Tolerance level for the eigenvalues of \(V^tWV\). If some eigenvalues are less than tol, the low-rank version of V is used for classification.

Author

Irina Gaynanova

Details

For a new observation with the value x, the classification is performed based on the smallest Mahalanobis distance in the projected space: $$\min_{1\le g \le G}(V^tx-Z_g)(V^tWV)^{-1}(V^tx-Z_g)$$ where \(Z_g\) are the group-specific means of the training dataset in the projected space and \(W\) is the sample within-group covariance matrix.

If prior=T, then the above distance is adjusted by \(-2\log\frac{n_g}{N}\), where \(n_g\) is the size of group g.

References

I.Gaynanova, J.Booth and M.Wells (2016) "Simultaneous Sparse Estimation of Canonical Vectors in the p>>N setting.", JASA, 111(514), 696-706.

Examples

### Example 1
# generate training data
n=10
p=100
G=3
ytrain=rep(1:G,each=n)
set.seed(1)
xtrain=matrix(rnorm(p*n*G),n*G,p)
# find V
V=dLDA(xtrain,ytrain,lambda=0.1)
sum(rowSums(V)!=0)
# generate test data
m=20
set.seed(3)
xtest=matrix(rnorm(p*m),m,p)
# perform classification
ytest=classifyV(xtrain,ytrain,xtest,V)