tensor-clustering-CONSTANT-vignette

library(tip)

# ################## NOTE ##################
# Order 3 Tensor dimension: c(d1,d2,d3)
# d1: number of rows
# d2: number of columns
# d3: number of slices 
############################################

# Set a random seed for reproducibility 
set.seed(007)

# A function to generate an order-3 tensor
generate_gaussian_tensor <- function(.tensor_dimension, .mean = 0, .sd = 1){
  array(data = c(rnorm(n = prod(.tensor_dimension), 
                       mean = .mean, 
                       sd = .sd)), 
        dim = .tensor_dimension)
} 

# Define the tensor dimension
tensor_dimension <- c(256,256,3)

# Generate clusters of tensors
c1 <- lapply(1:10, function(x) generate_gaussian_tensor(.tensor_dimension = tensor_dimension,
                                                        .mean = 0,
                                                        .sd = 1))


# Generate clusters of tensors
c2 <- lapply(1:10, function(x) generate_gaussian_tensor(.tensor_dimension = tensor_dimension,
                                                        .mean = 5,
                                                        .sd = 1))


# Generate clusters of tensors
c3 <- lapply(1:10, function(x) generate_gaussian_tensor(.tensor_dimension = tensor_dimension,
                                                        .mean = -5,
                                                        .sd = 1))

# Make a list of tensors 
X <- c(c1, c2, c3)

# Compute the number of subjects for each cluster 
n1 <- length(c1)
n2 <- length(c2)
n3 <- length(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", n1),
                 rep("Cluster 2", n2),
                 rep("Cluster 3", n3))

# Compute the total number of subjects 
n <- length(X)

# Construct the distance matrix 
distance_matrix <- matrix(data = NA, nrow = n, ncol = n) 
for(i in 1:n){
  for(j in i:n){
    distance_matrix[i,j] <- sqrt(sum((X[[i]] - X[[j]])^2))
    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 <- 1000

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

# Set the subject names
names_subjects <- paste(1:n)

# Run TIP clustering using only the prior
# --> That is, the likelihood function is constant
tip1 <- tip(.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)
#> Bayesian Clustering: Table Invitation Prior Gibbs Sampler
#> burn-in: 1000
#> samples: 1000
#> Likelihood Model: CONSTANT
#> 
  |                                                                            
  |                                                                      |   0%
  |                                                                            
  |                                                                      |   1%
  |                                                                            
  |=                                                                     |   1%
  |                                                                            
  |=                                                                     |   2%
  |                                                                            
  |==                                                                    |   2%
  |                                                                            
  |==                                                                    |   3%
  |                                                                            
  |==                                                                    |   4%
  |                                                                            
  |===                                                                   |   4%
  |                                                                            
  |===                                                                   |   5%
  |                                                                            
  |====                                                                  |   5%
  |                                                                            
  |====                                                                  |   6%
  |                                                                            
  |=====                                                                 |   6%
  |                                                                            
  |=====                                                                 |   7%
  |                                                                            
  |=====                                                                 |   8%
  |                                                                            
  |======                                                                |   8%
  |                                                                            
  |======                                                                |   9%
  |                                                                            
  |=======                                                               |   9%
  |                                                                            
  |=======                                                               |  10%
  |                                                                            
  |=======                                                               |  11%
  |                                                                            
  |========                                                              |  11%
  |                                                                            
  |========                                                              |  12%
  |                                                                            
  |=========                                                             |  12%
  |                                                                            
  |=========                                                             |  13%
  |                                                                            
  |=========                                                             |  14%
  |                                                                            
  |==========                                                            |  14%
  |                                                                            
  |==========                                                            |  15%
  |                                                                            
  |===========                                                           |  15%
  |                                                                            
  |===========                                                           |  16%
  |                                                                            
  |============                                                          |  16%
  |                                                                            
  |============                                                          |  17%
  |                                                                            
  |============                                                          |  18%
  |                                                                            
  |=============                                                         |  18%
  |                                                                            
  |=============                                                         |  19%
  |                                                                            
  |==============                                                        |  19%
  |                                                                            
  |==============                                                        |  20%
  |                                                                            
  |==============                                                        |  21%
  |                                                                            
  |===============                                                       |  21%
  |                                                                            
  |===============                                                       |  22%
  |                                                                            
  |================                                                      |  22%
  |                                                                            
  |================                                                      |  23%
  |                                                                            
  |================                                                      |  24%
  |                                                                            
  |=================                                                     |  24%
  |                                                                            
  |=================                                                     |  25%
  |                                                                            
  |==================                                                    |  25%
  |                                                                            
  |==================                                                    |  26%
  |                                                                            
  |===================                                                   |  26%
  |                                                                            
  |===================                                                   |  27%
  |                                                                            
  |===================                                                   |  28%
  |                                                                            
  |====================                                                  |  28%
  |                                                                            
  |====================                                                  |  29%
  |                                                                            
  |=====================                                                 |  29%
  |                                                                            
  |=====================                                                 |  30%
  |                                                                            
  |=====================                                                 |  31%
  |                                                                            
  |======================                                                |  31%
  |                                                                            
  |======================                                                |  32%
  |                                                                            
  |=======================                                               |  32%
  |                                                                            
  |=======================                                               |  33%
  |                                                                            
  |=======================                                               |  34%
  |                                                                            
  |========================                                              |  34%
  |                                                                            
  |========================                                              |  35%
  |                                                                            
  |=========================                                             |  35%
  |                                                                            
  |=========================                                             |  36%
  |                                                                            
  |==========================                                            |  36%
  |                                                                            
  |==========================                                            |  37%
  |                                                                            
  |==========================                                            |  38%
  |                                                                            
  |===========================                                           |  38%
  |                                                                            
  |===========================                                           |  39%
  |                                                                            
  |============================                                          |  39%
  |                                                                            
  |============================                                          |  40%
  |                                                                            
  |============================                                          |  41%
  |                                                                            
  |=============================                                         |  41%
  |                                                                            
  |=============================                                         |  42%
  |                                                                            
  |==============================                                        |  42%
  |                                                                            
  |==============================                                        |  43%
  |                                                                            
  |==============================                                        |  44%
  |                                                                            
  |===============================                                       |  44%
  |                                                                            
  |===============================                                       |  45%
  |                                                                            
  |================================                                      |  45%
  |                                                                            
  |================================                                      |  46%
  |                                                                            
  |=================================                                     |  46%
  |                                                                            
  |=================================                                     |  47%
  |                                                                            
  |=================================                                     |  48%
  |                                                                            
  |==================================                                    |  48%
  |                                                                            
  |==================================                                    |  49%
  |                                                                            
  |===================================                                   |  49%
  |                                                                            
  |===================================                                   |  50%
  |                                                                            
  |===================================                                   |  51%
  |                                                                            
  |====================================                                  |  51%
  |                                                                            
  |====================================                                  |  52%
  |                                                                            
  |=====================================                                 |  52%
  |                                                                            
  |=====================================                                 |  53%
  |                                                                            
  |=====================================                                 |  54%
  |                                                                            
  |======================================                                |  54%
  |                                                                            
  |======================================                                |  55%
  |                                                                            
  |=======================================                               |  55%
  |                                                                            
  |=======================================                               |  56%
  |                                                                            
  |========================================                              |  56%
  |                                                                            
  |========================================                              |  57%
  |                                                                            
  |========================================                              |  58%
  |                                                                            
  |=========================================                             |  58%
  |                                                                            
  |=========================================                             |  59%
  |                                                                            
  |==========================================                            |  59%
  |                                                                            
  |==========================================                            |  60%
  |                                                                            
  |==========================================                            |  61%
  |                                                                            
  |===========================================                           |  61%
  |                                                                            
  |===========================================                           |  62%
  |                                                                            
  |============================================                          |  62%
  |                                                                            
  |============================================                          |  63%
  |                                                                            
  |============================================                          |  64%
  |                                                                            
  |=============================================                         |  64%
  |                                                                            
  |=============================================                         |  65%
  |                                                                            
  |==============================================                        |  65%
  |                                                                            
  |==============================================                        |  66%
  |                                                                            
  |===============================================                       |  66%
  |                                                                            
  |===============================================                       |  67%
  |                                                                            
  |===============================================                       |  68%
  |                                                                            
  |================================================                      |  68%
  |                                                                            
  |================================================                      |  69%
  |                                                                            
  |=================================================                     |  69%
  |                                                                            
  |=================================================                     |  70%
  |                                                                            
  |=================================================                     |  71%
  |                                                                            
  |==================================================                    |  71%
  |                                                                            
  |==================================================                    |  72%
  |                                                                            
  |===================================================                   |  72%
  |                                                                            
  |===================================================                   |  73%
  |                                                                            
  |===================================================                   |  74%
  |                                                                            
  |====================================================                  |  74%
  |                                                                            
  |====================================================                  |  75%
  |                                                                            
  |=====================================================                 |  75%
  |                                                                            
  |=====================================================                 |  76%
  |                                                                            
  |======================================================                |  76%
  |                                                                            
  |======================================================                |  77%
  |                                                                            
  |======================================================                |  78%
  |                                                                            
  |=======================================================               |  78%
  |                                                                            
  |=======================================================               |  79%
  |                                                                            
  |========================================================              |  79%
  |                                                                            
  |========================================================              |  80%
  |                                                                            
  |========================================================              |  81%
  |                                                                            
  |=========================================================             |  81%
  |                                                                            
  |=========================================================             |  82%
  |                                                                            
  |==========================================================            |  82%
  |                                                                            
  |==========================================================            |  83%
  |                                                                            
  |==========================================================            |  84%
  |                                                                            
  |===========================================================           |  84%
  |                                                                            
  |===========================================================           |  85%
  |                                                                            
  |============================================================          |  85%
  |                                                                            
  |============================================================          |  86%
  |                                                                            
  |=============================================================         |  86%
  |                                                                            
  |=============================================================         |  87%
  |                                                                            
  |=============================================================         |  88%
  |                                                                            
  |==============================================================        |  88%
  |                                                                            
  |==============================================================        |  89%
  |                                                                            
  |===============================================================       |  89%
  |                                                                            
  |===============================================================       |  90%
  |                                                                            
  |===============================================================       |  91%
  |                                                                            
  |================================================================      |  91%
  |                                                                            
  |================================================================      |  92%
  |                                                                            
  |=================================================================     |  92%
  |                                                                            
  |=================================================================     |  93%
  |                                                                            
  |=================================================================     |  94%
  |                                                                            
  |==================================================================    |  94%
  |                                                                            
  |==================================================================    |  95%
  |                                                                            
  |===================================================================   |  95%
  |                                                                            
  |===================================================================   |  96%
  |                                                                            
  |====================================================================  |  96%
  |                                                                            
  |====================================================================  |  97%
  |                                                                            
  |====================================================================  |  98%
  |                                                                            
  |===================================================================== |  98%
  |                                                                            
  |===================================================================== |  99%
  |                                                                            
  |======================================================================|  99%
  |                                                                            
  |======================================================================| 100%
# 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))
#>            cluster_assignment
#> true_label   1  2  3  4
#>   Cluster 1  7  3  0  0
#>   Cluster 2  0  0 10  0
#>   Cluster 3  0  0  0 10
# 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)
#> Warning: Duplicated override.aes is ignored.

# 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)