Dissimilarity Plot

Description

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.

Usage

# grid-based dissimilarity plot
dissplot(x, labels = NULL, method = "Spectral", control = NULL,
  lower_tri = TRUE, upper_tri = "average",
  cluster_labels = TRUE, cluster_lines = TRUE,
  reverse_columns = FALSE, options = NULL, ...)

# ggplot2-based dissimilarity plot
ggdissplot(x, labels = NULL, method = "Spectral", control = NULL,
  lower_tri = TRUE, upper_tri = "average",
  cluster_labels = TRUE, cluster_lines = TRUE,
  reverse_columns = FALSE, ...)

Arguments

Details

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, but the appropriate functions in grid-package.

Value

dissplot() returns an invisible object of class cluster_proximity_matrix with the following elements:

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.

Author(s)

Michael Hahsler

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. 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. 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. 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. doi: 10.1287/ijoc.15.2.208.14448

See Also

grid-package, dist, seriate, pimage and hmap.

Examples

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))
}