---
title: "usarrests-NIW-vignette"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{usarrests-NIW-vignette}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```

```{r setup}
# Import the TIP library 
library(tip)

# Import the US Arrests dataset
data(USArrests)

# Convert the data to a matrix 
X <- data.matrix(USArrests)

# Compute the distance matrix
distance_matrix <- data.matrix(dist(X))

# 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
# RECOMENDATION: *** burn >= 1000 ***
burn <- 10

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

# Extract the state names 
names_subjects <- rownames(USArrests)

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

```{r}
# Produce plots for the Bayesian Clustering Model
tip_plots <- plot(tip1)
```

```{r}
# View the posterior distribution of the number of clusters
tip_plots$trace_plot_posterior_number_of_clusters
```

```{r}
# View the trace plot with respect to the posterior number of clusters
tip_plots$trace_plot_posterior_number_of_clusters
```

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

# Create a list where each element stores the cluster assignments
cluster_assignment_list <- list()
for(k in 1:length(unique(cluster_assignments))){
  cluster_assignment_list[[k]] <- names_subjects[which(cluster_assignments == k)]
}
cluster_assignment_list
```

```{r}
# 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)
```

```{r}
# View the state names
# names_subjects

# Create a vector of true region labels to see if there is a pattern
true_region <- c("Southeast", "West", "Southwest", "Southeast", "West", "West",
                 "Northeast", "Northeast", "Southeast", "Southeast", "West", "West",
                 "Midwest", "Midwest", "Midwest", "Midwest", "Southeast", "Southeast",
                 "Northeast", "Northeast", "Northeast", "Midwest", "Midwest", "Southeast",
                 "Midwest", "West", "Midwest", "West", "Northeast", "Northeast",
                 "Southwest", "Northeast", "Southeast", "Midwest", "Midwest", "Southwest",
                 "West", "Northeast", "Northeast", "Southeast", "Midwest", "Southeast",
                 "Southwest", "West", "Northeast", "Southeast", "West", "Southeast",
                 "Midwest", "West")

names_subjects

# Associate class labels and colors for the plot
class_palette_colors <- c("Northeast" = "blue",
                          "Southeast" = "red",
                          "Midwest" = "purple",
                          "Southwest" = "orange",
                          "West" = "green")

# Associate class labels and shapes for the plot
class_palette_shapes <- c("Northeast" = 15,
                          "Southeast" = 16,
                          "Midwest" = 17,
                          "Southwest" = 18,
                          "West" = 19)

# 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$partitioned_graph_matrix,
                .subject_names = names_subjects,
                .subject_class_names = true_region,
                .class_colors = class_palette_colors,
                .class_shapes = class_palette_shapes,
                .node_size = 2,
                .add_node_labels = TRUE)
```
```{r}
# Visualize the posterior similarity matrix by constructing a graph plot of 
# the one-cluster graph. The true labels are used here (below they are not).
# Remove the subject names with .add_node_labels = FALSE
ggnet2_network_plot(.matrix_graph = partition_list$partitioned_graph_matrix,
                .subject_names = names_subjects,
                .subject_class_names = true_region,
                .class_colors = class_palette_colors,
                .class_shapes = class_palette_shapes,
                .node_size = 2,
                .add_node_labels = FALSE)
```

```{r}
# Construct a network plot without 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)

```