Quadratic discrimination

The function returns the elements needed to calculate the quadratic discrimination in (11.48). Use the output from this function in predict_qda (Section A.3.2) to find the predicted groups.

qda(x, y)

Arguments

x

The \(N \times P\) data matrix.

y

The \(N\)-vector of group identities, assumed to be given by the numbers 1,...,\(K\) for \(K\) groups.

Value

A `list` with the following components:

Mean

A \(P \times K\) matrix, where column \(K\) contains the coefficents \(a_k\) for (11.31). The final column is all zero.

Sigma

A \(K \times P \times P\) array, where the Sigma[k,,] contains the sample covariance matrix for group \(k\), \(\hat{\Sigma_k}\).

c

The \(K\)-vector of constants \(c_k\) for (11.48).

See also

predict_qda and lda

Examples

# Load Iris Data
data(iris)

# Iris example
x.iris <- as.matrix(iris[, 1:4])

# Gets group vector (1, ... , 1, 2, ... , 2, 3, ... , 3)
y.iris <- rep(1:3, c(50, 50, 50))

# Perform QDA
qd.iris <- qda(x.iris, y.iris)