mdmp: The Minimum Distance Rule using Moore-Penrose Inverse (MDMP)...

In ramhiser/sparsediscrim: Sparse and Regularized Discriminant Analysis

Description

Given a set of training data, this function builds the MDMP classifier from Srivistava and Kubokawa (2007). The MDMP classifier is an adaptation of the linear discriminant analysis (LDA) classifier that is designed for small-sample, high-dimensional data. Srivastava and Kubokawa (2007) have proposed a modification of the standard maximum likelihood estimator of the pooled covariance matrix, where only the largest 95 their corresponding eigenvectors are kept. The value of 95 and can be changed via the eigen_pct argument.

The MDMP 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. Srivastava and Kubokawa (2007) have proposed a modification of the standard maximum likelihood estimator of the pooled covariance matrix, where only the largest 95 their corresponding eigenvectors are kept.

Usage

mdmp(x, ...)

## Default S3 method:
mdmp(x, y, prior = NULL, eigen_pct = 0.95, ...)

## S3 method for class 'formula'
mdmp(formula, data, prior = NULL, ...)

## S3 method for class 'mdmp'
predict(object, newdata, ...)

Arguments

x	matrix containing the training data. The rows are the sample observations, and the columns are the features.
...	additional arguments
y	vector of class labels for each training observation
prior	vector with prior probabilities for each class. If NULL (default), then equal probabilities are used. See details.
eigen_pct	the percentage of eigenvalues kept
formula	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	data frame from which variables specified in formula are preferentially to be taken.
object	trained mdmp object
newdata	matrix of observations to predict. Each row corresponds to a new observation.

Details

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.

Value

mdmp object that contains the trained MDMP classifier

list predicted class memberships of each row in newdata

References

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.

Examples

n <- nrow(iris)
train <- sample(seq_len(n), n / 2)
mdmp_out <- mdmp(Species ~ ., data = iris[train, ])
predicted <- predict(mdmp_out, iris[-train, -5])$class

mdmp_out2 <- mdmp(x = iris[train, -5], y = iris[train, 5])
predicted2 <- predict(mdmp_out2, iris[-train, -5])$class
all.equal(predicted, predicted2)

ramhiser/sparsediscrim documentation built on May 26, 2019, 10:14 p.m.