Andrews Transformation

Transforms a multivariate dataset into functional data using the Andrews Fourier expansion. Each row of the input matrix becomes a curve on \([-\pi, \pi]\) defined by $$f_i(t) = x_{i1}/\sqrt{2} + x_{i2}\sin(t) + x_{i3}\cos(t) + x_{i4}\sin(2t) + x_{i5}\cos(2t) + \ldots$$

Usage

andrews_transform(X, m = 200)

Arguments

X

Numeric matrix or data.frame (\(n \times p\)). Rows are observations, columns are variables. Coerced via as.matrix().

m

Number of grid points on \([-\pi, \pi]\) (default 200).

Value

An fdata object (\(n\) curves, \(m\) grid points) with additional attributes:

andrews_basis

The \(m \times p\) Fourier basis matrix.

andrews_varnames

Variable names (colnames(X) or paste0("V", 1:p) if NULL).

Details

The resulting fdata object carries the Fourier basis matrix and variable names as attributes, enabling andrews_loadings() to project FPCA eigenfunctions back to the original variable space.

See also

andrews_loadings(), fdata2pc()

Examples

X <- scale(iris[, 1:4])
fd <- andrews_transform(X)
plot(fd)