crda: Compressive regularized discriminant analysis (CRDA) approach...

In mntabassm/compressiveRDA: Compressive Regularized Discriminant Analysis (CRDA)

Description

CRDA approach performs simultaneous feature selection and classification of high-dimensional data. The function crda classifies each column of the test data set Xt (p x N) into one of the G classes. Test data set Xt and training data set X must have the same number of rows (features or variables). Vector y is a class variable of training data. Its unique values define classes; each element defines the class to which the corresponding column of X belongs. The input y is a numeric vector with integer elements ranging from 1,2,..,G, where G is the number of classes. Note that y must have the same number of rows as there are columns in X. The output yhat indicates the class to which each column of Xt has been assigned. Also yhat is Nx1 vector of integers ranging from 1,2,...,G. CRDA approach aims to address three facets of high-dimensional classification: namely, accuracy, computational complexity, and interpretability.

Usage

crda(X, y, Xt = NULL, q = "cv", prior = "uniform", kgrid = NULL,
  nK = 10, nfolds = 5, centerX = TRUE)

Arguments

X	Training dataset, a pxn matrix with n-samples each having p-features.
y	Labels for training dataset, an nx1 vector of whole numbers.
Xt	Test dataset, a pxnt matrix with nt-samples each of p-features.
q	scalar (>=1) or string 'var' or 'inf' or 'cv'. If q is a real scalar, then it must be >= 1 and it denotes the L_q-norm to be used in the hard thresholding operator H_K(B,phi) in the CRDA method. If q is equal to a string 'inf' (or 'var') then L_infty norm will be used (or sample variance) will be used as the hard-thresholding selector function. If q is equal to a string 'cv', then CV is used to select the best hard-thresholding selector function among the L_1-, L_2-, L_inf-norm and the sample variance.
prior	Type of prior class probabilities, either 'uniform' (default) or 'estimated'.
kgrid	A grid of candidate values for joint-sparsity level.
nK	Number of candidate values in the grid of joint-sparsity level.
nfolds	Number of folds for cross-validation scheme.
centerX	Flag for grand-mean centering of test dataset using grand-mean of training dataset.

Details

crda

Value

An object obj of class crda with the following attributes:

funCall	The call to the crda function.
prior	Prior class probabilities.
B	Coefficient matrix before feature selection.
M	Group-means matrix.
Ind	Indices of the length of the row vectors of B organized in descending order, where the length is determined by optional argument 'q'.
K	Joint-sparsity level.
yhat	Predicted labels for test dataset
muX	Optional: Grand-mean, i.e., row (feature) wise mean of training dataset.

Author(s)

Muhammad Naveed Tabassum and Esa Ollila, 2019.

See Also

crda.auxfuns, crda.demo

Examples

crda(X,y)
crda(X,y, Xt = testdata)
crda(X,y, Xt = testdata, q = 1)
crda(X,y, Xt = Xt, q = 2, centerX = FALSE)
crda(X,y, Xt = Xt, prior = 'estimated', centerX = TRUE)

mntabassm/compressiveRDA documentation built on Oct. 15, 2019, 6:41 p.m.