Transformation Coefficients — dot

The dimension of the original data set is n\*p. It can be projected onto a n\*k space. The functions below are to provide such transformations, e.g. the Andrews coefficient (a Fourier transformation) and the Legendre polynomials.

andrews(p = 4, k = 50 * (p - 1), ...)

legendre(p = 4, k = 50 * (p - 1), ...)

Arguments

p: The number of dimensions
k: The sequence length
...: Other arguments passed on to methods. Mainly used for customized transformation function

Value

A list contains two named components

vector: A length k vector (define the domain)
matrix: A p\*k transformed coefficient matrix

References

Andrews, David F. "Plots of high-dimensional data." Biometrics (1972): 125-136.

Abramowitz, Milton, and Irene A. Stegun, eds. "Chapter 8" Handbook of mathematical functions with formulas, graphs, and mathematical tables. Vol. 55. US Government printing office, 1948.

Examples

x <- andrews(p = 4)
dat <- iris[, -5]
proj <- t(as.matrix(dat) %*% x$matrix)
matplot(x$vector, proj,
        type = "l", lty = 1,
        col = "black",
        xlab = "x",
        ylab = "Andrews coefficients",
        main = "Iris")