In an agglomerative hierarchical clustering dendrogram, how do you determine the number of clusters by "cutting" the tree?

Question

BlackTom AI · Accepted Answer

Drawing a horizontal cut at a chosen height on the dendrogram produces clusters: each vertical branch that the horizontal line crosses corresponds to one cluster.

Relevant knowledge points and concepts:
- Agglomerative hierarchical clustering starts with each observation as its own cluster and successively merges the two closest clusters; the dendrogram records these merges as vertical joins at heights representing linkage distances.
- A cut across the dendrogram at a particular height selects all clusters whose internal linkage distances are below that height; equivalently, each branch that extends above the cut remains separate below the cut.
- The number of clusters equals the number of disconnected branches (vertical lines) intersected by that horizontal cut.

Step-by-step reasoning with an example:
1. Suppose five observations A, B, C, D, E. The algorithm produces merges at heights: h1 = 0.2 (merge A+B), h2 = 0.4 (merge C+D), h3 = 0.9 (merge (A+B) with E), h4 = 1.5 (merge ((A+B)+E) with (C+D)). These heights are plotted on the vertical axis of the dendrogram.
2. If you draw a horizontal line at height 0.3, it intersects the vertical branches corresponding to clusters: (A+B), C, D, E — giving 4 clusters (because the merge at h1 is below the cut while h2 and higher are above).
3. If you draw the line at 1.0, it intersects just two vertical branches: ((A+B)+E) and (C+D) — giving 2 clusters.
4. If you draw the line above the highest merge (e.g., 2.0), it intersects one branch (all data merged) — giving 1 cluster.

Why the correct answer is correct:
- The horizontal cut selects clusters at a chosen dissimilarity threshold; counting vertical branches intersected by that cut directly counts the clusters that remain separate below that threshold.

Why other options are incorrect:
- Counting leaves at the bottom gives the number of original observations, not the number of clusters after cutting.
- Counting the number of times the algorithm merged two points yields the total number of merges (n−1 for n observations), not the current cluster count at a chosen cut.
- Identifying the single highest point on the vertical axis corresponds to the final merge (one cluster) or the maximum linkage distance, which does not tell you how many clusters you want at an intermediate cut.

Conclusion: Cutting the dendrogram by drawing a horizontal line and counting the vertical lines it intersects gives the number of clusters, which matches the provided correct answer.

In an agglomerative hierarchical clustering dendrogram, how do you determine the number of clusters by "cutting" the tree?单项选择题

类似问题

What is the main concept behind hierarchical clustering?

Which of the following is an advantage of hierarchical clustering over k-Means clustering?

What is a dendrogram?

If a dendrogram shows two main branches that merge at a very high distance (height) on the vertical axis, what does this suggest?

Which rule defines the "Complete Linkage" method in Hierarchical clustering?

Which of the following is finally produced by hierarchical clustering?

Hierarchical clustering differs from K-means clustering in that:

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单