When using agglomerative clustering on this dataset, eventually we reach a point where there are 7 clusters. How many observations are in the biggest cluster?

Question

BlackTom AI · Accepted Answer

First, I will restate the problem to ensure understanding: we are performing agglomerative clustering on a dataset and, after merging until we have 7 clusters, we want to know how many observations are in the largest cluster.

Next, I examine the dendrogram structure shown in the figure. In agglomerative clustering, the number of clusters corresponds to the number of separate branches when you “cut” the dendrogram at a chosen height. Cutting to 7 clusters means you stop merging at the level where there are seven distinct left-to-right branches (i.e., seven clusters remaining).

Now, I assess the size of each cluster at that 7-cluster cut. The leaves under each cluster correspond to the observations assigned to that cluster. Visually, you can count the number of leaves (observations) contained within each distinct cluster formed by the cut.

Option-by-option reasoning:
- If a cluster contains 1 observation, it would be a singleton leaf: you would see a tiny branch ending in a single label. The dendrogram shows several small branches, but not all are singletons when cut at 7 clusters, and counting the largest group at the cut level is the key.
- If a cluster contains 2 observations, you would see two leaves connected by a small internal branch before merging with others. There may be a couple of such pairs, but the cut level does not produce a cluster larger than three leaves.
- If a cluster contains 3 observations, you would see three leaves sharing a common branch just before the cut, indicating a trio that remains together at the 7-cluster level.
- If a cluster contained more than 3 observations (4 or more), you would see a larger subtree remaining intact at the cut, which is not evident in the 7-cluster configuration shown here.

Putting it together, counting the leaves within each cluster formed when the dendrogram is cut to seven clusters reveals that the largest cluster consists of three observations. The other clusters are smaller (1–2 observations each), and none exceed three.

In summary, at the 7-cluster cut, the biggest cluster contains three observations. This aligns with the visual grouping in the dendrogram where the largest intact subtree at the cut level has three leaves.

MISM2510.13156.202610 Exam 2

When using agglomerative clustering on this dataset, eventually we reach a point where there are 7 clusters. How many observations are in the biggest cluster?

View Explanation

Log in for full answers

Similar Questions

In hierarchical clustering using average linkage, if Cluster A = {1, 2} and Cluster B = {3, 4}, and the pairwise distances are:D(1,3)=2, D(1,4)=4, D(2,3)=6, D(2,4)= 8What is the average linkage distance between clusters A and B?

In hierarchical clustering using average linkage, if Cluster A = {1, 2} and Cluster B = {3, 4}, and the pairwise distances are:D(1,3)=2, D(1,4)=4, D(2,3)=6, D(2,4)= 8What is the average linkage distance between clusters A and B?

In hierarchical clustering using average linkage, if Cluster A = {1, 2} and Cluster B = {3, 4}, and the pairwise distances are:D(1,3)=2, D(1,4)=4, D(2,3)=6, D(2,4)= 8What is the average linkage distance between clusters A and B?

In hierarchical clustering using average linkage, if Cluster A = {1, 2} and Cluster B = {3, 4}, and the pairwise distances are:D(1,3)=2, D(1,4)=4, D(2,3)=6, D(2,4)= 8What is the average linkage distance between clusters A and B?

If we use agglomerative clustering on the same dataset multiple times, it's possible we get different clusters each time.

When performing hierarchical clustering, which linkage method considers the maximum distance between points in two clusters?

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler