ancoord: Asymmetric neighborhood based discriminant coordinates

In fpc: Flexible Procedures for Clustering

Asymmetric neighborhood based discriminant coordinates

Description

Asymmetric neighborhood based 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 covariance matrix, which is defined by averaging the between classes covariance matrices in the neighborhoods of the points of the homogeneous class and the projection of the covariance matrix within the homogeneous class.

Usage

ancoord(xd, clvecd, clnum=1, nn=50, method="mcd", 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).
clnum	integer. Number of the homogeneous class.
nn	integer. Number of points which belong to the neighborhood of each point (including the point itself).
method	one of "mve", "mcd" or "classical". Covariance matrix used within the homogeneous class. "mcd" and "mve" are robust covariance matrices as implemented in cov.rob. "classical" refers to the classical covariance matrix.
countmode	optional positive integer. Every countmode algorithm runs ancoord shows a message.
...	no effect

Details

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.

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.

Author(s)

Christian Hennig [e-mail] https://www.unibo.it/sitoweb/christian.hennig/en/

References

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.

See Also

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

Examples

  set.seed(4634)
  face <- rFace(600,dMoNo=2,dNoEy=0)
  grface <- as.integer(attr(face,"grouping"))
  ancf2 <- ancoord(face,grface==4)
  plot(ancf2$proj,col=1+(grface==4))
  # ...done in one step by function plotcluster.

fpc documentation built on Jan. 7, 2023, 1:13 a.m.