# lda_schafer: Linear Discriminant Analysis using the Schafer-Strimmer... In sparsediscrim: Sparse and Regularized Discriminant Analysis

## Description

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 `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).

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10``` ```lda_schafer(x, ...) ## Default S3 method: lda_schafer(x, y, prior = NULL, ...) ## S3 method for class 'formula' lda_schafer(formula, data, prior = NULL, ...) ## S3 method for class 'lda_schafer' predict(object, newdata, ...) ```

## Arguments

 `x` matrix containing the training data. The rows are the sample observations, and the columns are the features. `...` additional arguments passed to `invcov.shrink` `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. `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 lda_schafer 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

`lda_schafer` object that contains the trained classifier

list predicted class memberships of each row in newdata

## 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.

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

 ```1 2 3 4 5 6 7 8``` ```n <- nrow(iris) train <- sample(seq_len(n), n / 2) lda_schafer_out <- lda_schafer(Species ~ ., data = iris[train, ]) predicted <- predict(lda_schafer_out, iris[-train, -5])\$class lda_schafer_out2 <- lda_schafer(x = iris[train, -5], y = iris[train, 5]) predicted2 <- predict(lda_schafer_out2, iris[-train, -5])\$class all.equal(predicted, predicted2) ```

sparsediscrim documentation built on Aug. 14, 2017, 5:10 p.m.