Asymmetric discriminant coordinates
Asymmetric 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.
adcoord(xd, clvecd, clnum=1)
xd |
the data matrix; a numerical object which can be coerced to a matrix. |
clvecd |
integer vector of class numbers; length must equal
|
clnum |
integer. Number of the homogeneous class. |
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.
List with the following components
ev |
eigenvalues in descending order. |
units |
columns are coordinates of projection basis vectors.
New points |
proj |
projections of |
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.
set.seed(4634) face <- rFace(600,dMoNo=2,dNoEy=0) grface <- as.integer(attr(face,"grouping")) adcf <- adcoord(face,grface==2) adcf2 <- adcoord(face,grface==4) plot(adcf$proj,col=1+(grface==2)) plot(adcf2$proj,col=1+(grface==4)) # ...done in one step by function plotcluster.
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