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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. Dissimilarity plots can be used to uncover hidden structure in the data and judge cluster quality.
dissplot(
x,
labels = NULL,
method = "Spectral",
control = NULL,
lower_tri = TRUE,
upper_tri = "average",
diag = TRUE,
cluster_labels = TRUE,
cluster_lines = TRUE,
reverse_columns = FALSE,
options = NULL,
...
)# S3 method for reordered_cluster_dissimilarity_matrix
plot(
x,
lower_tri = TRUE,
upper_tri = "average",
diag = TRUE,
options = NULL,
...
)
# S3 method for reordered_cluster_dissimilarity_matrix
print(x, ...)
ggdissplot(
x,
labels = NULL,
method = "Spectral",
control = NULL,
lower_tri = TRUE,
upper_tri = "average",
diag = TRUE,
cluster_labels = TRUE,
cluster_lines = TRUE,
reverse_columns = FALSE,
...
)
dissplot() returns an invisible object of class
cluster_proximity_matrix with the following elements:
NULL or integer vector giving the order used to plot x.
NULL or integer vector giving the order of the
clusters as plotted.
vector of character strings indicating
the seriation methods used for plotting x.
NULL or integer scalar giving the number of clusters generated.
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).
ggdissplot() returns a ggplot2 object representing the plot.
The plot description as an object of class reordered_cluster_dissimilarity_matrix.
an object of class dist.
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.
A single character string indicating the seriation method used
to reorder the clusters (inter cluster seriation) as well as the objects
within each cluster (intra cluster seriation). If different 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. Use list_seriation_methods() with kind = "dist" to find available algorithms.
Set method to NA to plot the matrix as is (no or, if cluster labels
are supplied, only coarse seriation). For intra cluster reordering with the
special method "silhouette width" is available (for dissplot()
only). 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.
A third list element (named aggregation) can be added to control 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).
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.
a logical indicating whether to show the upper triangle, the lower triangle or the diagonal of the distance matrix. The string "average" can also be used to display within and between cluster averages in the two triangles.
a logical indicating whether to display cluster labels in the plot.
a logical indicating whether to draw lines to separate clusters.
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).
a list with options for plotting the matrix (dissplot
only).
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).
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().
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 for the plot
lines and labels (see gpar().
dissplot(): further arguments are added to options.
ggdissplot() further arguments are passed on to ggpimage().
Michael Hahsler
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.
Note: Since pimage() uses grid, it should not be mixed
with base R primitive plotting functions.
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. tools:::Rd_expr_doi("10.1198/jcgs.2010.09139")
Ling, R.F. (1973): A computer generated aid for cluster analysis. Communications of the ACM, 16(6), 355--361. tools:::Rd_expr_doi("10.1145/362248.362263")
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. tools:::Rd_expr_doi("10.1016/0377-0427(87)90125-7")
Strehl, A. and Ghosh, J. (2003): Relationship-based clustering and visualization for high-dimensional data mining. INFORMS Journal on Computing, 15(2), 208--230. tools:::Rd_expr_doi("10.1287/ijoc.15.2.208.14448")
Other plots:
VAT(),
bertinplot(),
hmap(),
palette(),
pimage()
data("iris")
# shuffle rows
x_iris <- iris[sample(seq(nrow(iris))), -5]
d <- dist(x_iris)
# Plot original matrix
dissplot(d, method = NA)
# Plot reordered matrix using the nearest insertion algorithm (from tsp)
dissplot(d, method = "TSP", main = "Seriation (TSP)")
# Cluster iris with k-means and 3 clusters and reorder the dissimality matrix
l <- kmeans(x_iris, centers = 3)$cluster
dissplot(d, labels = l, main = "k-means")
# show only distances as lower triangle
dissplot(d, labels = l, main = "k-means", lower_tri = TRUE, upper_tri = FALSE)
# Use a grid layout to place several plots on a page
library("grid")
grid.newpage()
pushViewport(viewport(layout=grid.layout(nrow = 2, ncol = 2),
gp = gpar(fontsize = 8)))
pushViewport(viewport(layout.pos.row = 1, layout.pos.col = 1))
# Visualize the clustering (using Spectral between clusters and MDS within)
res <- dissplot(d, l, method = list(inter = "Spectral", intra = "MDS"),
main = "K-Means + Seriation", newpage = FALSE)
popViewport()
pushViewport(viewport(layout.pos.row = 1, layout.pos.col = 2))
# More visualization options. Note that we reuse the reordered object res!
# color: use 10 shades red-blue, biased towards small distances
plot(res, main = "K-Means + Seriation (red-blue + biased)",
col= bluered(10, bias = .5), newpage = FALSE)
popViewport()
pushViewport(viewport(layout.pos.row = 2, layout.pos.col = 1))
# Threshold (using zlim) and cubic scale to highlight differences
plot(res, main = "K-Means + Seriation (cubic + threshold)",
zlim = c(0, 2), col = grays(100, power = 3), newpage = FALSE)
popViewport()
pushViewport(viewport(layout.pos.row = 2, layout.pos.col = 2))
# Use gray scale with logistic transformation
plot(res, main = "K-Means + Seriation (logistic scale)",
col = gray(
plogis(seq(max(res$x_reordered), min(res$x_reordered), length.out = 100),
location = 2, scale = 1/2, log = FALSE)
),
newpage = FALSE)
popViewport(2)
# The reordered_cluster_dissimilarity_matrix object
res
names(res)
## --------------------------------------------------------------------
## ggplot-based dissplot
if (require("ggplot2")) {
library("ggplot2")
# Plot original matrix
ggdissplot(d, method = NA)
# Plot seriated matrix
ggdissplot(d, method = "TSP") +
labs(title = "Seriation (TSP)")
# Cluster iris with k-means and 3 clusters
l <- kmeans(x_iris, centers = 3)$cluster
ggdissplot(d, labels = l) +
labs(title = "K-means + Seriation")
# show only lower triangle
ggdissplot(d, labels = l, lower_tri = TRUE, upper_tri = FALSE) +
labs(title = "K-means + Seriation")
# No lines or cluster labels and add a label for the color key (fill)
ggdissplot(d, labels = l, cluster_lines = FALSE, cluster_labels = FALSE) +
labs(title = "K-means + Seriation", fill = "Distances\n(Euclidean)")
# Diverging color palette with manual set midpoint and different seriation methods
ggdissplot(d, l, method = list(inter = "Spectral", intra = "MDS")) +
labs(title = "K-Means + Seriation", subtitle = "biased color scale") +
scale_fill_gradient2(midpoint = median(d))
# Use manipulate scale using package scales
library("scales")
# Threshold (using limit and na.value) and cubic scale to highlight differences
cubic_dist_trans <- trans_new(
name = "cubic",
# note that we have to do the inverse transformation for distances
trans = function(x) x^(1/3),
inverse = function(x) x^3
)
ggdissplot(d, l, method = list(inter = "Spectral", intra = "MDS")) +
labs(title = "K-Means + Seriation", subtitle = "cubic + biased color scale") +
scale_fill_gradient(low = "black", high = "white",
limit = c(0,2), na.value = "white",
trans = cubic_dist_trans)
# Use gray scale with logistic transformation
logis_2_.5_dist_trans <- trans_new(
name = "Logistic transform (location, scale)",
# note that we have to do the inverse transformation for distances
trans = function(x) plogis(x, location = 2, scale = .5, log = FALSE),
inverse = function(x) qlogis(x, location = 2, scale = .5, log = FALSE),
)
ggdissplot(d, l, method = list(inter = "Spectral", intra = "MDS")) +
labs(title = "K-Means + Seriation", subtitle = "logistic color scale") +
scale_fill_gradient(low = "black", high = "white",
trans = logis_2_.5_dist_trans,
breaks = c(0, 1, 2, 3, 4))
}
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