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.
ncoord(xd, clvecd, nn=50, weighted=FALSE,
sphere="mcd", orderall=TRUE, countmode=1000, ...)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 data matrix; a numerical object which can be coerced to a matrix.
integer vector of class numbers; length must equal
nrow(xd).
integer. Number of points which belong to the neighborhood of each point (including the point itself).
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).
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.
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.
optional positive integer. Every countmode
algorithm runs ncoord shows a message.
no effect
Christian Hennig christian.hennig@unibo.it https://www.unibo.it/sitoweb/christian.hennig/en/
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.
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.
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