dissplot

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Dissimilarity Plot

Visualizes a dissimilarity matrix using seriation and matrix shading using the method developed by Hahsler and Hornik (2011). Entries with lower dissimilarities (higher similarity) are plotted darker. Such a plot can be used to uncover hidden structure in the data.

The plot can also be used to visualize cluster quality (see Ling 1973). Objects belonging to the same cluster are displayed in consecutive order. The placement of clusters and the within cluster order is obtained by a seriation algorithm which tries to place large similarities/small dissimilarities close to the diagonal. Compact clusters are visible as dark squares (low dissimilarity) on the diagonal of the plot. Additionally, a Silhouette plot (Rousseeuw 1987) is added. This visualization is similar to CLUSION (see Strehl and Ghosh 2002), however, allows for using arbitrary seriating algorithms.

Keywords
hplot, cluster
Usage
dissplot(x, labels = NULL, method = "Spectral",
  control = NULL, options = NULL, …)
Arguments
x
an object of class dist.
labels
NULL or an integer vector of the same length as rows/columns in x indicating the cluster membership for each object in x as consecutive integers starting with one. The labels are used to reorder the matrix.
method
a list with up to three elements or a single character string. Use a single character string to apply the same algorithm to reorder the clusters (inter cluster seriation) as well as the objects within each cluster (intra cluster seriation).

If separate algorithms for inter and intra cluster seriation are required, method can be a list of two named elements (inter_cluster and intra_cluster each containing the name of the respective seriation method. See seriate.dist for available algorithms.

Set method to NA to plot the matrix as is (no or only coarse seriation). For intra cluster reordering the special method "silhouette width" is available. Objects in clusters are then ordered by silhouette width (from silhouette plots). If no method is given, the default method of seriate.dist is used.

The third list element (named aggregation) controls how inter cluster dissimilarities are computed from from the given dissimilarity matrix. The choices are "avg" (average pairwise dissimilarities; average-link), "min" (minimal pairwise dissimilarities; single-link), "max" (maximal pairwise dissimilarities; complete-link), and "Hausdorff" (pairs up each point from one cluster with the most similar point from the other cluster and then uses the largest dissimilarity of paired up points).

control
a list of control options passed on to the seriation algorithm. In case of two different seriation algorithms, control can contain a list of two named elements (inter_cluster and intra_cluster) containing each a list with the control options for the respective algorithm.
options
a list with options for plotting the matrix. The list can contain the following elements:

plot
a logical indicating if a plot should be produced. if FALSE, the returned object can be plotted later using the function plot which takes as the second argument a list of plotting options (see options below).
cluster_labels
a logical indicating whether to display cluster labels in the plot.
averages
a logical vector of length two. The first element controls the upper triangle and the second element the lower triangle of the plot. FALSE displays the original dissimilarity between objects, TRUE displays cluster-wise average dissimilarities, and NA leaves the triangle white (default: c(FALSE, TRUE), i.e., the lower triangle displays averages)
lines
a logical indicating whether to draw lines to separate clusters.
flip
a logical indicating if the clusters are displayed on the diagonal from north-west to south-east (FALSE; default) or from north-east to south-west (TRUE).
silhouettes
a logical indicating whether to include a silhouette plot (see Rousseeuw, 1987).
threshold
a numeric. If used, only plot distances below the threshold are displayed. Consider also using zlim for this purpose.
col
colors used for the image plot.
key
a logical indicating whether to place a color key below the plot.
zlim
range of values to display (defaults to range x).
axes
"auto" (default; enabled for less than 25 objects), "y" or "none".
main
title for the plot.
newpage
a logical indicating whether to start plot on a new page (see grid.newpage in package grid).
pop
a logical indicating whether to pop the created viewports (see package grid)?
gp, gp_lines, gp_labels
objects of class gpar containing graphical parameters (see gpar in package grid).

further arguments are added to options.
Value

An invisible object of class cluster_proximity_matrix with the following elements:

order
NULL or integer vector giving the order used to plot x.
cluster_order
NULL or integer vector giving the order of the clusters as plotted.
method
vector of character strings indicating the seriation methods used for plotting x.
k
NULL or integer scalar giving the number of clusters generated.
description
a data.frame containing information (label, size, average intra-cluster dissimilarity and the average silhouette) for the clusters as displayed in the plot (from top/left to bottom/right).

This object can be used for plotting via plot(x, options = NULL, ...), where x is the object and options contains a list with plotting options (see above).

References

Hahsler, M. and Hornik, K. (2011): Dissimilarity plots: A visual exploration tool for partitional clustering. Journal of Computational and Graphical Statistics, 10(2):335--354.

Ling, R.F. (1973): A computer generated aid for cluster analysis. Communications of the ACM, 16(6), 355--361.

Rousseeuw, P.J. (1987): Silhouettes: A graphical aid to the interpretation and validation of cluster analysis. Journal of Computational and Applied Mathematics, 20(1), 53--65.

Strehl, A. and Ghosh, J. (2003): Relationship-based clustering and visualization for high-dimensional data mining. INFORMS Journal on Computing, 15(2), 208--230.

See Also

dist, seriate, pimage and hmap.

Aliases
  • dissplot
  • plot.reordered_cluster_dissimilarity_matrix
  • print.reordered_cluster_dissimilarity_matrix
Examples
data("iris")
d <- dist(iris[-5])

## plot original matrix
res <- dissplot(d, method = NA)

## plot reordered matrix using the nearest insertion algorithm (from tsp)
res <- dissplot(d, method = "TSP",
    options = list(main = "Seriation (TSP)"))

## cluster with pam (we know iris has 3 clusters)
library("cluster")
l <- pam(d, 3, cluster.only = TRUE)

## we use a grid layout to place several plots on a page
library("grid")
grid.newpage()
pushViewport(viewport(layout=grid.layout(nrow = 2, ncol = 2),
    gp = gpar(fontsize = 8)))
pushViewport(viewport(layout.pos.row = 1, layout.pos.col = 1))

## visualize the clustering (using Spectral between clusters and MDS within)
res <- dissplot(d, l, method = list(inter = "Spectral", intra = "MDS"),
    options = list(main = "PAM + Seriation - standard",
    newpage = FALSE))

popViewport()
pushViewport(viewport(layout.pos.row = 1, layout.pos.col = 2))

## more visualization options. Note that we reuse the reordered object res!
## color: use 10 shades red-blue
plot(res, options = list(main = "PAM + Seriation",
    col= bluered(10, bias=.5), newpage = FALSE))

popViewport()
pushViewport(viewport(layout.pos.row = 2, layout.pos.col = 1))

## threshold (using zlim) and cubic scale to highlight differences
plot(res, options = list(main = "PAM + Seriation - threshold",
    zlim = c(0, 1.5), col = greys(100, power = 2), newpage = FALSE))

popViewport()
pushViewport(viewport(layout.pos.row = 2, layout.pos.col = 2))

## use custom (logistic) scale
plot(res, options = list(main = "PAM + Seriation - logistic scale",
    col= hcl(c = 0, l = (plogis(seq(10, 0, length=100),
	location = 2, scale = 1/2, log = FALSE))*100),
	newpage = FALSE))

popViewport(2)

## the reordered_cluster_dissimilarity_matrix object
res
names(res)
Documentation reproduced from package seriation, version 1.2-2, License: GPL-3

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