Plot Within-Cluster Sum of Distances

Plot the within-cluster sum of distances from the corresponding cluster consensus for different number of clusters. This function is useful for selecting the number of mixture.

Usage

plot_elbow(...)

Arguments

...

One or more objects returned from compute_mallows(), separated by comma, or a list of such objects. Typically, each object has been run with a different number of mixtures, as specified in the n_clusters argument to compute_mallows(). Alternatively an object returned from compute_mallows_mixtures().

Value

A boxplot with the number of clusters on the horizontal axis and the with-cluster sum of distances on the vertical axis.

See also

Other posterior quantities: assign_cluster(), compute_consensus(), compute_posterior_intervals(), get_acceptance_ratios(), heat_plot(), plot.BayesMallows(), plot.SMCMallows(), plot_top_k(), predict_top_k(), print.BayesMallows()

Examples

# SIMULATED CLUSTER DATA
set.seed(1)
n_clusters <- seq(from = 1, to = 5)
models <- compute_mallows_mixtures(
  n_clusters = n_clusters, data = setup_rank_data(cluster_data),
  compute_options = set_compute_options(nmc = 2000, include_wcd = TRUE))

# There is good convergence for 1, 2, and 3 cluster, but not for 5.
# Also note that there seems to be label switching around the 7000th iteration
# for the 2-cluster solution.
assess_convergence(models)

# We can create an elbow plot, suggesting that there are three clusters, exactly
# as simulated.
burnin(models) <- 1000
plot_elbow(models)


# We now fit a model with three clusters
mixture_model <- compute_mallows(
  data = setup_rank_data(cluster_data),
  model_options = set_model_options(n_clusters = 3),
  compute_options = set_compute_options(nmc = 2000))

# The trace plot for this model looks good. It seems to converge quickly.
assess_convergence(mixture_model)

# We set the burnin to 500
burnin(mixture_model) <- 500

# We can now look at posterior quantities
# Posterior of scale parameter alpha
plot(mixture_model)

plot(mixture_model, parameter = "rho", items = 4:5)

# There is around 33 % probability of being in each cluster, in agreemeent
# with the data simulating mechanism
plot(mixture_model, parameter = "cluster_probs")

# We can also look at a cluster assignment plot
plot(mixture_model, parameter = "cluster_assignment")


# DETERMINING THE NUMBER OF CLUSTERS IN THE SUSHI EXAMPLE DATA
if (FALSE) { # \dontrun{
  # Let us look at any number of clusters from 1 to 10
  # We use the convenience function compute_mallows_mixtures
  n_clusters <- seq(from = 1, to = 10)
  models <- compute_mallows_mixtures(
    n_clusters = n_clusters, data = setup_rank_data(sushi_rankings),
    compute_options = set_compute_options(include_wcd = TRUE))
  # models is a list in which each element is an object of class BayesMallows,
  # returned from compute_mallows
  # We can create an elbow plot
  burnin(models) <- 1000
  plot_elbow(models)
  # We then select the number of cluster at a point where this plot has
  # an "elbow", e.g., n_clusters = 5.

  # Having chosen the number of clusters, we can now study the final model
  # Rerun with 5 clusters
  mixture_model <- compute_mallows(
    rankings = sushi_rankings,
    model_options = set_model_options(n_clusters = 5),
    compute_options = set_compute_options(include_wcd = TRUE))
  # Delete the models object to free some memory
  rm(models)
  # Set the burnin
  burnin(mixture_model) <- 1000
  # Plot the posterior distributions of alpha per cluster
  plot(mixture_model)
  # Compute the posterior interval of alpha per cluster
  compute_posterior_intervals(mixture_model, parameter = "alpha")
  # Plot the posterior distributions of cluster probabilities
  plot(mixture_model, parameter = "cluster_probs")
  # Plot the posterior probability of cluster assignment
  plot(mixture_model, parameter = "cluster_assignment")
  # Plot the posterior distribution of "tuna roll" in each cluster
  plot(mixture_model, parameter = "rho", items = "tuna roll")
  # Compute the cluster-wise CP consensus, and show one column per cluster
  cp <- compute_consensus(mixture_model, type = "CP")
  cp$cumprob <- NULL
  stats::reshape(cp, direction = "wide", idvar = "ranking",
                 timevar = "cluster", varying = list(as.character(unique(cp$cluster))))

  # Compute the MAP consensus, and show one column per cluster
  map <- compute_consensus(mixture_model, type = "MAP")
  map$probability <- NULL
  stats::reshape(map, direction = "wide", idvar = "map_ranking",
                 timevar = "cluster", varying = list(as.character(unique(map$cluster))))

  # RUNNING IN PARALLEL
  # Computing Mallows models with different number of mixtures in parallel leads to
  # considerably speedup
  library(parallel)
  cl <- makeCluster(detectCores() - 1)
  n_clusters <- seq(from = 1, to = 10)
  models <- compute_mallows_mixtures(
    n_clusters = n_clusters,
    rankings = sushi_rankings,
    compute_options = set_compute_options(include_wcd = TRUE),
    cl = cl)
  stopCluster(cl)
} # }