fpc (version 2.2-9)

# ridgeline.diagnosis: Ridgeline plots, ratios and unimodality

## Description

Computes ridgeline ratios and unimodality checks for pairs of components given the parameters of a Gaussian mixture. Produces ridgeline plots.

## Usage

ridgeline.diagnosis (propvector,muarray,Sigmaarray,
k=length(propvector),
ipairs="all", compute.ratio=TRUE,by=0.001,
ratiocutoff=NULL,ridgelineplot="matrix")

## Arguments

propvector

vector of component proportions. Length must be number of components, and must sum up to 1.

muarray

matrix of component means (different components are in different columns).

Sigmaarray

three dimensional array with component covariance matrices (the third dimension refers to components).

k

integer. Number of components.

ipairs

"all" or list of vectors of two integers. If ipairs="all", computations are carried out for all pairs of components. Otherwise, ipairs gives the pairs of components for which computations are carried out.

compute.ratio

logical. If TRUE, a matrix of ridgeline ratios is computed, see Hennig (2010a).

by

real between 0 and 1. Interval width for density computation along the ridgeline.

ratiocutoff

real between 0 and 1. If not NULL, the connection.matrix (see below) is computed by checking whether ridgeline ratios between components are below ratiocutoff.

ridgelineplot

one of "none", "matrix", "pairwise". If "matrix", a matrix of pairwise ridgeline plots (see Hennig 2010b) will be plotted. If "pairwise", pairwise ridgeline plots are plotted (you may want to set par(ask=TRUE) to see them all). No plotting if "none".

## Value

A list with components

merged.clusters

vector of integers, stating for every mixture component the number of the cluster of components that would be merged by merging connectivity components of the graph specified by connection.matrix.

connection.matrix

zero-one matrix, in which a one means that the mixture of the corresponding pair of components of the original mixture is either unimodel (if ratiocutoff=NULL) or that their ridgeline ratio is above ratiocutoff. If ipairs!="all", ignored pairs always have 0 in this matrix, same for ratio.matrix.

ratio.matrix

matrix with entries between 0 und 1, giving the ridgeline ratio, which is the density minimum of the mixture of the corresponding pair of components along the ridgeline divided by the minimum of the two maxima closest to the beginning and the end of the ridgeline.

## References

Hennig, C. (2010a) Methods for merging Gaussian mixture components, Advances in Data Analysis and Classification, 4, 3-34.

Hennig, C. (2010b) Ridgeline plot and clusterwise stability as tools for merging Gaussian mixture components. To appear in Classification as a Tool for Research, Proceedings of IFCS 2009.

Ray, S. and Lindsay, B. G. (2005) The Topography of Multivariate Normal Mixtures, Annals of Statistics, 33, 2042-2065.

## Examples

# NOT RUN {
muarray <- cbind(c(0,0),c(0,0.1),c(10,10))
sigmaarray <- array(c(diag(2),diag(2),diag(2)),dim=c(2,2,3))
rd <-
ridgeline.diagnosis(c(0.5,0.3,0.2),muarray,sigmaarray,ridgelineplot="matrix",by=0.1)
# Much slower but more precise with default by=0.001.
# }