# fda: Factorial discriminant analysis In mlesnoff/rnirs: Dimension reduction, Regression and Discrimination for Chemometrics

 fda R Documentation

## Factorial discriminant analysis

### Description

Functions `fda` and `fdasvd` fit a factorial discriminant analysis (FDA). The functions maximize the compromise `p'Bp / p'Wp`, i.e. `max p'Bp` with constraint `p'Wp = 1`. Vectors `p` are the linear discrimant coefficients "LD".

Function `fda` uses an eigen decomposition of `W^(-1)B` (if `W` is singular, W^(-1) can be replaced by a pseudo-inverse, with argument `pseudo`), and function `fdasvd` a weighted SVD decomposition of the matrix of the class centers. See the code for details.

### Usage

``````
fda(Xr, Yr, Xu = NULL, ncomp = NULL, pseudo = FALSE)

fdasvd(Xr, Yr, Xu = NULL, ncomp = NULL, ...)

``````

### Arguments

 `Xr` A `n x p` matrix of reference (= training) observations. `Yr` A vector of length `n` of reference (= training) responses (class membership). `Xu` A `m x p` matrix or data frame of new (= test) observations to be projected in the calculated reference FDA score space (`Xu` is not used in the calculation of this score space). Default to `NULL`. `ncomp` The maximum number of components to consider (`ncomp <= min(p, nb. classes - 1)`). `pseudo` For function `fda`. Logical indicating if matrix `W` has to be inverted by pseudo-inverse. Default to `FALSE`. `...` For function `fdasvd`. Optionnal arguments to pass in function `pca`.

### Value

A list of outputs (see examples), such as:

 `Tr` The Xr-score matrix (`n x ncomp`). `Tu` The Xu-score matrix (`m x ncomp`). `Tcenters` The Xr-class centers score matrix (`nb. classes x ncomp`). `P` The Xr-loadings matrix (`p x ncomp`). Coefficients of linear discriminants: P = "LD" of `lda` of package `MASS`. `explvar` Proportions of explained variance by PCA of the class centers in transformed scale.

And other outputs ("z" outputs relate on transformed data; see the code).

### References

Saporta G., 2011. ProbabilitÃ©s analyse des donnÃ©es et statistique. Editions Technip, Paris, France.

### Examples

``````
data(iris)

Xr <- iris[, 1:4]
yr <- iris[, 5]

fm <- fda(Xr, yr)
names(fm)

# Xr-scores

# Xr-class centers scores
fm\$Tcenters

# = coefficients of linear discriminants
# = "LD" of function lda of MASS package
fm\$P

# Explained variance by PCA of the class centers
# in transformed scale
fm\$explvar

plotxy(fm\$Tr, group = yr, ellipse = TRUE)
points(fm\$Tc, pch = 8, col = "blue")

# Object Tcenters is the projection of the class centers in the score space
fm <- fda(Xr, yr)
fm\$Tcenters
centers <- centr(Xr, yr)\$centers
centers
fm <- fda(Xr, yr, centers)
fm\$Tu

``````

mlesnoff/rnirs documentation built on April 24, 2023, 4:17 a.m.