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")

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.

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".

Author

Christian Hennig christian.hennig@unibo.it https://www.unibo.it/sitoweb/christian.hennig/en/

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

Run this code

  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.

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