| Type: | Package |
| Title: | Multi-Group Sparse Discriminant Analysis |
| Version: | 1.6.1 |
| Date: | 2023-09-03 |
| Author: | Irina Gaynanova |
| Maintainer: | Irina Gaynanova <irinagn@umich.edu> |
| 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>. |
| Imports: | MASS, stats |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| RoxygenNote: | 7.2.3 |
| NeedsCompilation: | yes |
| Packaged: | 2023-09-03 20:15:39 UTC; irinag |
| Repository: | CRAN |
| Date/Publication: | 2023-09-03 21:00:05 UTC |
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 |
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.
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 |
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 |
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 |
error_se |
The standard error associated with each value of |
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 |
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:
\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=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