Given a set of training data, this function builds the Shrinkage-based Diagonal Quadratic Discriminant Analysis (SDQDA) classifier, which is based on the DQDA classifier, often attributed to Dudoit et al. (2002). The DQDA classifier belongs to the family of Naive Bayes classifiers, where the distributions of each class are assumed to be multivariate normal. To improve the estimation of the class variances, Pang et al. (2009) proposed the SDQDA classifier which uses a shrinkage-based estimators of each class covariance matrix.
The SDQDA classifier is a modification to QDA, where the off-diagonal elements of the pooled sample covariance matrix are set to zero. To improve the estimation of the pooled variances, we use a shrinkage method from Pang et al. (2009).
qda_shrink_cov(x, ...) # S3 method for default qda_shrink_cov(x, y, prior = NULL, num_alphas = 101, ...) # S3 method for formula qda_shrink_cov(formula, data, prior = NULL, num_alphas = 101, ...) # S3 method for qda_shrink_cov predict(object, newdata, type = c("class", "prob", "score"), ...)
Matrix or data frame containing the training data. The rows are the sample observations, and the columns are the features. Only complete data are retained.
additional arguments (not currently used).
Vector of class labels for each training observation. Only complete data are retained.
Vector with prior probabilities for each class. If NULL (default), then equal probabilities are used. See details.
the number of values used to find the optimal amount of shrinkage
A formula of the form
data frame from which variables specified in
Fitted model object
Matrix or data frame of observations to predict. Each row corresponds to a new observation.
Prediction type: either `"class"`, `"prob"`, or `"score"`.
qda_shrink_cov object that contains the trained SDQDA classifier
The DQDA classifier is a modification to the well-known QDA classifier, where the off-diagonal elements of the pooled covariance matrix are assumed to be zero -- the features are assumed to be uncorrelated. Under multivariate normality, the assumption uncorrelated features is equivalent to the assumption of independent features. The feature-independence assumption is a notable attribute of the Naive Bayes classifier family. The benefit of these classifiers is that they are fast and have much fewer parameters to estimate, especially when the number of features is quite large.
The matrix of training observations are given in
x. The rows of
x contain the sample observations, and the columns contain the
features for each training observation.
The vector of class labels given in
y are coerced to a
The length of
y should match the number of rows in
An error is thrown if a given class has less than 2 observations because the variance for each feature within a class cannot be estimated with less than 2 observations.
prior, contains the a priori class membership for
each class. If
prior is NULL (default), the class membership
probabilities are estimated as the sample proportion of observations
belonging to each class. Otherwise,
prior should be a vector with the
same length as the number of classes in
probabilities should be nonnegative and sum to one.
Dudoit, S., Fridlyand, J., & Speed, T. P. (2002). "Comparison of Discrimination Methods for the Classification of Tumors Using Gene Expression Data," Journal of the American Statistical Association, 97, 457, 77-87.
Pang, H., Tong, T., & Zhao, H. (2009). "Shrinkage-based Diagonal Discriminant Analysis and Its Applications in High-Dimensional Data," Biometrics, 65, 4, 1021-1029.
library(modeldata) data(penguins) pred_rows <- seq(1, 344, by = 20) penguins <- penguins[, c("species", "body_mass_g", "flipper_length_mm")]#' set.seed(42) sdqda_out <- qda_shrink_cov(species ~ ., data = penguins[-pred_rows, ]) predicted <- predict(sdqda_out, penguins[pred_rows, -1], type = "class") sdqda_out2 <- qda_shrink_cov(x = penguins[-pred_rows, -1], y = penguins$species[-pred_rows]) predicted2 <- predict(sdqda_out2, penguins[pred_rows, -1], type = "class") all.equal(predicted, predicted2)#>  TRUE