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
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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)