Linear Discriminant Analysis using the Schafer-Strimmer Covariance Matrix Estimator

Source: R/lda-schafer.r

Given a set of training data, this function builds the Linear Discriminant Analysis (LDA) classifier, where the distributions of each class are assumed to be multivariate normal and share a common covariance matrix. When the pooled sample covariance matrix is singular, the linear discriminant function is incalculable. This function replaces the inverse of pooled sample covariance matrix with an estimator proposed by Schafer and Strimmer (2005). The estimator is calculated via corpcor::invcov.shrink().

The Linear Discriminant Analysis (LDA) classifier involves the assumption that the distributions of each class are assumed to be multivariate normal and share a common covariance matrix. When the pooled sample covariance matrix is singular, the linear discriminant function is incalculable. Here, the inverse of the pooled sample covariance matrix is replaced with an estimator from Schafer and Strimmer (2005).

lda_schafer(x, ...)

# S3 method for default
lda_schafer(x, y, prior = NULL, ...)

# S3 method for formula
lda_schafer(formula, data, prior = NULL, ...)

# S3 method for lda_schafer
predict(object, newdata, type = c("class", "prob", "score"), ...)

Arguments

x

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.
...

Options passed to corpcor::invcov.shrink()
y

Vector of class labels for each training observation. Only complete data are retained.
prior

Vector with prior probabilities for each class. If NULL (default), then equal probabilities are used. See details.
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

Fitted model object
newdata

Matrix or data frame of observations to predict. Each row corresponds to a new observation.
type

Prediction type: either `"class"`, `"prob"`, or `"score"`.

Value

lda_schafer object that contains the trained classifier

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.

References

Schafer, J., and Strimmer, K. (2005). "A shrinkage approach to large-scale covariance estimation and implications for functional genomics," Statist. Appl. Genet. Mol. Biol. 4, 32.

Examples

library(modeldata)
data(penguins)
pred_rows <- seq(1, 344, by = 20)
penguins <- penguins[, c("species", "body_mass_g", "flipper_length_mm")]
lda_schafer_out <- lda_schafer(species ~ ., data = penguins[-pred_rows, ])
predicted <- predict(lda_schafer_out, penguins[pred_rows, -1], type = "class")

lda_schafer_out2 <- lda_schafer(x = penguins[-pred_rows, -1], y = penguins$species[-pred_rows])
predicted2 <- predict(lda_schafer_out2, penguins[pred_rows, -1], type = "class")
all.equal(predicted, predicted2)

#> [1] TRUE