matrix-clustering-CONSTANT-vignette"
In tip: Bayesian Clustering Using the Table Invitation Prior (TIP)

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

library(tip)

# A function to generate random matrices from a matrix normal distribution 
random_mat_normal <- function(mu, num_rows, num_cols){
  LaplacesDemon::rmatrixnorm(M = matrix(mu, 
                                      nrow = num_rows, 
                                      ncol = num_cols), 
                           U = diag(num_rows), 
                           V = diag(num_cols))
}

# Generate 3 clusters of matrices 
p <- 5
m <- 3
c1 <- lapply(1:10, function(x) random_mat_normal(mu = 0, num_rows = m, num_cols = p))
c2 <- lapply(1:10, function(x) random_mat_normal(mu = 5, num_rows = m, num_cols = p))
c3 <- lapply(1:10, function(x) random_mat_normal(mu = -5, num_rows = m, num_cols = p))

# Put all the data into a list
data_list <- c(c1,c2,c3)

# Create a vector of true labels. True labels are only necessary 
# for constructing network graphs that incorporate the true labels;
# this is often useful for research. 
true_labels <- c(rep("Cluster 1", length(c1)),
                 rep("Cluster 2", length(c2)),
                 rep("Cluster 3", length(c3)))

distance_matrix <- matrix(NA, 
                          nrow = length(true_labels),
                          ncol = length(true_labels))
# Distance matrix 
for(i in 1:length(true_labels)){
  for(j in i:length(true_labels)){
    distance_matrix[i,j] <- SMFilter::FDist2(mX = data_list[[i]],
                                             mY = data_list[[j]])
    distance_matrix[j,i] <- distance_matrix[i,j]
  }
}

# Compute the temperature parameter estiamte
temperature <- 1/median(distance_matrix[upper.tri(distance_matrix)])

# For each subject, compute the point estimate for the number of similar 
# subjects using  univariate multiple change point detection (i.e.)
init_num_neighbors = get_cpt_neighbors(.distance_matrix = distance_matrix)

# Set the number of burn-in iterations in the Gibbs samlper
# RECOMMENDATION: burn >= 1000
burn <- 10

# Set the number of sampling iterations in the Gibbs sampler
# RECOMMENDATION: samples >= 1000
samples <- 10

# Set the subject names
names_subjects <- paste(1:dim(distance_matrix)[1])

# Run TIP clustering using only the prior
# --> That is, the likelihood function is constant
tip1 <- tip(.data = data_list,
            .burn = burn,
            .samples = samples,
            .similarity_matrix = exp(-1.0*temperature*distance_matrix),
            .init_num_neighbors = init_num_neighbors,
            .likelihood_model = "CONSTANT",
            .subject_names = names_subjects,
            .num_cores = 1)

# Produce plots for the Bayesian Clustering Model
tip_plots <- plot(tip1)

# View the posterior distribution of the number of clusters
tip_plots$histogram_posterior_number_of_clusters

# View the trace plot with respect to the posterior number of clusters
tip_plots$trace_plot_posterior_number_of_clusters

# Extract posterior cluster assignments using the Posterior Expected Adjusted Rand (PEAR) index
cluster_assignments <- mcclust::maxpear(psm = tip1@posterior_similarity_matrix)$cl

# If the true labels are available, then show the cluster result via a contigency table
table(data.frame(true_label = true_labels,
                 cluster_assignment = cluster_assignments))

# Create the one component graph with minimum entropy
partition_list <- partition_undirected_graph(.graph_matrix = tip1@posterior_similarity_matrix,
                                             .num_components = 1,
                                             .step_size = 0.001)

# Associate class labels and colors for the plot
class_palette_colors <- c("Cluster 1" = "blue",
                          "Cluster 2" = 'green',
                          "Cluster 3" = "red")

# Associate class labels and shapes for the plot
class_palette_shapes <- c("Cluster 1" = 19,
                          "Cluster 2" = 18,
                          "Cluster 3" = 17)

# Visualize the posterior similarity matrix by constructing a graph plot of 
# the one-cluster graph. The true labels are used here (below they are not).
ggnet2_network_plot(.matrix_graph = partition_list$partitioned_graph_matrix,
                .subject_names = NA,
                .subject_class_names = true_labels,
                .class_colors = class_palette_colors,
                .class_shapes = class_palette_shapes,
                .node_size = 2,
                .add_node_labels = FALSE)

# If true labels are not available, then construct a network plot
# of the one-cluster graph without any class labels.
# Note: Subject labels may be suppressed using .add_node_labels = FALSE.  
ggnet2_network_plot(.matrix_graph = partition_list$partitioned_graph_matrix,
                .subject_names = names_subjects,
                .node_size = 2,
                .add_node_labels = TRUE)