Asymmetric weighted discriminant coordinates as defined in Hennig (2003). Asymmetric discriminant projection means that there are two classes, one of which is treated as the homogeneous class (i.e., it should appear homogeneous and separated in the resulting projection) while the other may be heterogeneous. The principle is to maximize the ratio between the projection of a between classes separation matrix and the projection of the covariance matrix within the homogeneous class. Points are weighted according to their (robust) Mahalanobis distance to the homogeneous class.

```
awcoord(xd, clvecd, clnum=1, mahal="square", method="classical",
clweight=switch(method,classical=FALSE,TRUE),
alpha=0.99, subsample=0, countmode=1000, ...)
```

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)`

.

clnum

integer. Number of the homogeneous class.

mahal

"md" or "square". If "md", the points are weighted by the
square root of the `alpha`

-quantile of the
corresponding chi squared distribution
over the roots of their Mahalanobis distance to the
homogeneous class, unless
this is smaller than 1. If "square" (which is recommended), the
(originally squared) Mahalanobis distance and the
unrooted quantile is used.

method

one of
"mve", "mcd" or "classical". Covariance matrix used within the
homogeneous class and for the computation of the Mahalanobis distances.
"mcd" and "mve" are robust covariance matrices as implemented
in `cov.rob`

. "classical" refers to the classical
covariance matrix.

clweight

logical. If `FALSE`

, only the points of the
heterogeneous class are weighted. This, together with
`method="classical"`

, computes AWC as defined in Hennig (2003). If
`TRUE`

, all points are weighted. This, together with
`method="mcd"`

, computes ARC as defined in Hennig (2003).

alpha

numeric between 0 and 1. The corresponding quantile of the chi squared distribution is used for the downweighting of points. Points with a smaller Mahalanobis distance to the homogeneous class get full weight.

subsample

integer. If 0, all points are used. Else, only a
subsample of `subsample`

of the points is used.

countmode

optional positive integer. Every `countmode`

algorithm runs `awcoord`

shows a message.

...

no effect

List with the following components

eigenvalues in descending order.

columns are coordinates of projection basis vectors.
New points `x`

can be projected onto the projection basis vectors
by `x %*% units`

projections of `xd`

onto `units`

.

The square root of the homogeneous classes covariance matrix
is inverted by use of
`tdecomp`

, which can be expected to give
reasonable results for singular within-class covariance matrices.

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.

# NOT RUN { set.seed(4634) face <- rFace(600,dMoNo=2,dNoEy=0) grface <- as.integer(attr(face,"grouping")) awcf <- awcoord(face,grface==1) # awcf2 <- ancoord(face,grface==1, method="mcd") plot(awcf$proj,col=1+(grface==1)) # plot(awcf2$proj,col=1+(grface==1)) # ...done in one step by function plotcluster. # }