如何生成预定义簇的树状图并对比其与层次聚类结果？

Hey there! Let's work through how to compare your predefined clusters with the agnes hierarchical clustering results—including creating a dendrogram for your manual groups and other handy comparison methods. First, let's fix a small issue in your original code: your c1 and c2 columns are stored as characters, so we'll convert them to numeric first for valid distance calculations.

Required Packages #

Make sure you have these packages loaded to run all the code below:

library(dplyr)
library(factoextra)
library(clValid)
library(dendextend)
library(aricode)
library(ggplot2)
library(FactoMineR)

Fix Your Data Type #

set.seed(73) 
great <- data.frame(
  c0=c("r1","r2","r3","r4","r5","r6"),
  c1=c("0.89","46","0","0.56","12","0"),
  c2=c("0","0.45","45","79","0.45","4.4")
) %>%
  mutate(across(c(c1, c2), as.numeric)) # Convert to numeric for distance calculations

1. Create a Dendrogram for Predefined Clusters #

To use tanglegram(), we need an hclust object for your manual clusters. Since your groups are already fixed (cl1: r1/r2/r4; cl2: r3/r5/r6), we'll manually build a hierarchy that reflects this grouping.

# Define predefined cluster labels as a numeric vector
predefined_clusters <- rep(2, nrow(great))  # Default to cl2
predefined_clusters[c(1,2,4)] <- 1          # Set cl1 for r1, r2, r4

# Build a manual hclust object
pre_hclust <- list(
  # Merge matrix: negatives = individual samples, positives = merged clusters
  merge = matrix(
    c(-1, -2,  # Merge r1 & r2 first
      -4, 1,   # Merge r4 with the r1-r2 cluster (now cluster 1)
      -3, -5,  # Merge r3 & r5 first
      -6, 3,   # Merge r6 with the r3-r5 cluster (now cluster 3)
      2, 4),   # Merge the two final clusters (cluster 2 & 4)
    ncol = 2, byrow = TRUE
  ),
  # Heights: arbitrary values to represent hierarchy levels
  height = c(0.1, 0.2, 0.1, 0.2, 1),
  # Order of samples in the dendrogram
  order = c(1,2,4,3,5,6),
  # Sample labels
  labels = great$c0
)
class(pre_hclust) <- "hclust" # Assign hclust class to the object

Generate the Tanglegram #

Now compare your agnes result with the predefined clusters using tanglegram():

# Convert your agnes result to hclust format
agnes_hclust <- as.hclust(agnes(great, method = "ward"))

# Create the tanglegram
tanglegram(
  agnes_hclust, pre_hclust,
  main_left = "Agnes (Ward's Method)",
  main_right = "Predefined Clusters",
  cex = 0.7,
  common_subtrees_color_lines = TRUE,
  highlight_distinct_edges = TRUE
)

This plot will align the two dendrograms and visually highlight where sample groupings differ or match between the two clusterings.

2. Other Cluster Comparison Methods #

Beyond tanglegrams, here are practical ways to quantify and visualize differences between your clusterings:

Adjusted Rand Index (ARI) #

A normalized measure of similarity between two clusterings, ranging from -1 (complete disagreement) to 1 (perfect agreement). It accounts for chance, making it more reliable than raw counts.

ari_score <- ARI(predefined_clusters, cutree(agnes_hclust, k=2))
cat("Adjusted Rand Index:", round(ari_score, 3), "\n")

Contingency Table #

A simple way to see how samples map between the two clusterings:

cluster_table <- table(
  Predefined = factor(predefined_clusters, labels = c("cl1", "cl2")),
  Agnes = factor(cutree(agnes_hclust, k=2), labels = c("Cluster 1", "Cluster 2"))
)
print(cluster_table)

Silhouette Analysis #

Compare how well each clustering separates samples. Higher average silhouette scores indicate better cluster structure:

great_dist <- dist(great[, -1])

# Silhouette for agnes clusters
sil_agnes <- silhouette(cutree(agnes_hclust, k=2), great_dist)
fviz_silhouette(sil_agnes, main = "Silhouette Plot: Agnes Ward Clustering")

# Silhouette for predefined clusters
sil_pre <- silhouette(predefined_clusters, great_dist)
fviz_silhouette(sil_pre, main = "Silhouette Plot: Predefined Clusters")

PCA Visualization #

Plot your data in 2D using PCA, then color points by both clusterings to visually compare groupings:

# Run PCA (exclude the ID column)
pca_res <- PCA(great[, -1], graph = FALSE)
pca_data <- cbind(great[, 1], as.data.frame(pca_res$ind$coord))
colnames(pca_data)[1] <- "ID"
pca_data$Predefined <- factor(predefined_clusters, labels = c("cl1", "cl2"))
pca_data$Agnes <- factor(cutree(agnes_hclust, k=2), labels = c("Cluster 1", "Cluster 2"))

# Plot with predefined clusters
ggplot(pca_data, aes(PC1, PC2, color = Predefined, label = ID)) +
  geom_point(size = 4) + geom_text(nudge_y = 0.1) +
  labs(title = "PCA Plot: Predefined Clusters") + theme_minimal()

# Plot with agnes clusters
ggplot(pca_data, aes(PC1, PC2, color = Agnes, label = ID)) +
  geom_point(size = 4) + geom_text(nudge_y = 0.1) +
  labs(title = "PCA Plot: Agnes Ward Clustering") + theme_minimal()

内容的提问来源于stack exchange，提问作者takeITeasy