Package 'MGSDA'

Title: Multi-Group Sparse Discriminant Analysis
Description: Implements Multi-Group Sparse Discriminant Analysis proposal of I.Gaynanova, J.Booth and M.Wells (2016), Simultaneous sparse estimation of canonical vectors in the p>>N setting, JASA <doi:10.1080/01621459.2015.1034318>.
Authors: Irina Gaynanova
Maintainer: Irina Gaynanova <[email protected]>
License: GPL (>= 2)
Version: 1.6.1
Built: 2024-11-06 06:13:06 UTC
Source: https://github.com/cran/MGSDA

Help Index


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)

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 VtWVV^tWV. If some eigenvalues are less than tol, the low-rank version of V is used for classification.

Details

For a new observation with the value x, the classification is performed based on the smallest Mahalanobis distance in the projected space:

min1gG(VtxZg)(VtWV)1(VtxZg)\min_{1\le g \le G}(V^tx-Z_g)(V^tWV)^{-1}(V^tx-Z_g)

where ZgZ_g are the group-specific means of the training dataset in the projected space and WW is the sample within-group covariance matrix.

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

Value

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

Author(s)

Irina Gaynanova

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)

Cross-validation for MGSDA

Description

Chooses optimal tuning parameter lambda for function dLDA based on the m-fold cross-validation mean squared error

Usage

cv.dLDA(Xtrain, Ytrain, lambdaval = NULL, nl = 100, msep = 5, eps = 1e-6,
    l_min_ratio = ifelse(n<p,0.1,0.0001),myseed=NULL,prior=TRUE,rho=1)

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

lambdaval

Optional user-supplied sequence of tuning parameters; the default value is NULL and cv.dLDA chooses its own sequence

nl

Number of lambda values; the default value is 50

msep

Number of cross-validation folds; the default value is 5

eps

Tolerance level for the convergence of the optimization algorithm; the default value is 1e-6

l_min_ratio

Smallest value for lambda, as a fraction of lambda.max, the data-derived value for which all coefficients are zero; the default value is 0.1 if the number of samples n is larger than the number of variables p, and is 0.001 otherwise.

myseed

Optional specification of random seed for generating the folds; the default value is NULL.

prior

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

rho

A scalar that ensures the objective function is bounded from below; the default value is 1.

Value

lambdaval

The sequence of tuning parameters used

error_mean

The mean cross-validated number of misclassified observations - a vector of length length(lambdaval)

error_se

The standard error associated with each value of error_mean

lambda_min

The value of tuning parameter that has the minimal mean cross-validation error

f

The mean cross-validated number of non-zero features - a vector of length length(lambdaval)

Author(s)

Irina Gaynanova

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
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 optimal tuning parameter
out.cv=cv.dLDA(xtrain,ytrain)
# find V
V=dLDA(xtrain,ytrain,lambda=out.cv$lambda_min)
# number of non-zero features
sum(rowSums(V)!=0)

Estimate the matrix of discriminant vectors using L_1 penalty on the rows

Description

Solve Multi-Group Sparse Discriminant Anlalysis problem for the supplied value of the tuning parameter lambda.

Usage

dLDA(xtrain, ytrain, lambda, Vinit = NULL,eps=1e-6,maxiter=1000,rho=1)

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.

lambda

Tuning parameter.

Vinit

A px(G-1) optional initial value for the optimization algorithm; the default value is NULL.

eps

Tolerance level for the convergence of the optimization algorithm; the default value is 1e-6.

maxiter

Maximal number of iterations for the optimization algorithm; the default value is 1000.

rho

A scalar that ensures the objective function is bounded from below; the default value is 1.

Details

Solves the following optimization problem:

minV12Tr(VtWV+ρVtDDtV)Tr(DtV)+λi=1pvi2\min_V \frac12 Tr(V^tWV+\rho V^tDD^tV)-Tr(D^tV)+\lambda\sum_{i=1}^p\|v_i\|_2

Here W is the within-group sample covariance matrix and D is the matrix of orthogonal contrasts between the group means, both are constructed based on the supplied values of xtrain and ytrain.

When G=2G=2, the row penalty reduces to vector L_1 penalty.

Value

Returns a px(G-1) matrix of canonical vectors V.

Author(s)

Irina Gaynanova

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
n=10
p=100
G=3
ytrain=rep(1:G,each=n)
set.seed(1)
xtrain=matrix(rnorm(p*n*G),n*G,p)
V=dLDA(xtrain,ytrain,lambda=0.1)
sum(rowSums(V)!=0) # number of non-zero rows