Given a set of training data, this function builds the MDEB classifier from Srivistava and Kubokawa (2007). The MDEB classifier is an adaptation of the linear discriminant analysis (LDA) classifier that is designed for small-sample, high-dimensional data. Rather than using the standard maximum likelihood estimator of the pooled covariance matrix, Srivastava and Kubokawa (2007) have proposed an Empirical Bayes estimator where the eigenvalues of the pooled sample covariance matrix are shrunken towards the identity matrix: the shrinkage constant has a closed form and is quick to calculate.
The MDEB classifier from Srivistava and Kubokawa (2007) is an adaptation of the linear discriminant analysis (LDA) classifier that is designed for small-sample, high-dimensional data. Rather than using the standard maximum likelihood estimator of the pooled covariance matrix, Srivastava and Kubokawa (2007) have proposed an Empirical Bayes estimator where the eigenvalues of the pooled sample covariance matrix are shrunken towards the identity matrix: the shrinkage constant has a closed form and is quick to calculate
mdeb(x, ...)# S3 method for default
mdeb(x, y, prior = NULL, ...)
# S3 method for formula
mdeb(formula, data, prior = NULL, ...)
# S3 method for mdeb
predict(object, newdata, ...)
matrix containing the training data. The rows are the sample observations, and the columns are the features.
additional arguments
vector of class labels for each training observation
vector with prior probabilities for each class. If NULL (default), then equal probabilities are used. See details.
A formula of the form groups ~ x1 + x2 + ... That is,
the response is the grouping factor and the right hand side specifies the
(non-factor) discriminators.
data frame from which variables specified in formula are
preferentially to be taken.
trained mdeb object
matrix of observations to predict. Each row corresponds to a new observation.
mdeb object that contains the trained MDEB classifier
list predicted class memberships of each row in newdata
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 factor.
The length of y should match the number of rows in x.
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.
The vector, 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 y. The prior probabilities should be
nonnegative and sum to one.
Srivastava, M. and Kubokawa, T. (2007). "Comparison of Discrimination Methods for High Dimensional Data," Journal of the Japanese Statistical Association, 37, 1, 123-134.
Srivastava, M. and Kubokawa, T. (2007). "Comparison of Discrimination Methods for High Dimensional Data," Journal of the Japanese Statistical Association, 37, 1, 123-134.
# NOT RUN {
n <- nrow(iris)
train <- sample(seq_len(n), n / 2)
mdeb_out <- mdeb(Species ~ ., data = iris[train, ])
predicted <- predict(mdeb_out, iris[-train, -5])$class
mdeb_out2 <- mdeb(x = iris[train, -5], y = iris[train, 5])
predicted2 <- predict(mdeb_out2, iris[-train, -5])$class
all.equal(predicted, predicted2)
# }
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