fpc (version 2.2-9)

# ncoord: Neighborhood based discriminant coordinates

## Description

Neighborhood based discriminant coordinates as defined in Hastie and Tibshirani (1996) and a robustified version as defined in Hennig (2003). The principle is to maximize the projection of a between classes covariance matrix, which is defined by averaging the between classes covariance matrices in the neighborhoods of all points.

## Usage

ncoord(xd, clvecd, nn=50, weighted=FALSE,
sphere="mcd", orderall=TRUE, countmode=1000, ...)

## Arguments

xd

the data matrix; a numerical object which can be coerced to a matrix.

clvecd

integer vector of class numbers; length must equal nrow(xd).

nn

integer. Number of points which belong to the neighborhood of each point (including the point itself).

weighted

logical. FALSE corresponds to the original method of Hastie and Tibshirani (1996). If TRUE, the between classes covariance matrices B are weighted by w/trace B, where w is some weight depending on the sizes of the classes in the neighborhood. Division by trace B reduces the effect of outliers. TRUE cooresponds to WNC as defined in Hennig (2003).

sphere

a covariance matrix or one of "mve", "mcd", "classical", "none". The matrix used for sphering the data. "mcd" and "mve" are robust covariance matrices as implemented in cov.rob. "classical" refers to the classical covariance matrix. "none" means no sphering and use of the raw data.

orderall

logical. By default, the neighborhoods are computed by ordering all points each time. If FALSE, the neighborhoods are computed by selecting nn times the nearest point from the remaining points, which may be faster sometimes.

countmode

optional positive integer. Every countmode algorithm runs ncoord shows a message.

...

no effect

## Value

List with the following components

ev

eigenvalues in descending order.

units

columns are coordinates of projection basis vectors. New points x can be projected onto the projection basis vectors by x %*% units

proj

projections of xd onto units.

## References

Hastie, T. and Tibshirani, R. (1996). Discriminant adaptive nearest neighbor classification. IEEE Transactions on Pattern Analysis and Machine Intelligence 18, 607-616.

Hennig, C. (2004) Asymmetric linear dimension reduction for classification. Journal of Computational and Graphical Statistics 13, 930-945 .

Hennig, C. (2005) A method for visual cluster validation. In: Weihs, C. and Gaul, W. (eds.): Classification - The Ubiquitous Challenge. Springer, Heidelberg 2005, 153-160.

plotcluster for straight forward discriminant plots. discrproj for alternatives. rFace for generation of the example data used below.

## Examples

# NOT RUN {
set.seed(4634)
face <- rFace(600,dMoNo=2,dNoEy=0)
grface <- as.integer(attr(face,"grouping"))
ncf <- ncoord(face,grface)
plot(ncf\$proj,col=grface)
ncf2 <- ncoord(face,grface,weighted=TRUE)
plot(ncf2\$proj,col=grface)
# ...done in one step by function plotcluster.
# }