Let us step through the merging process using different similarity measures.
The pairs of data points that are connected with a black line in the figure above have been clustered together at the current stage.
In the next stage, the two clusters that have the smallest dissimilarity will be merged together.
Complete the next 4 merges using single linkage, complete linkage, and average linkage. Identify the resulting clusters for each.
Single linkage: Complete linkage: Average linkage:
(Choose one per column.)
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Without the figure or any specific data, it is not possible to complete the merges and identify the resulting clusters. Please provide the necessary information for further assistance.
To complete the next 4 merges using single linkage, complete linkage, and average linkage, we need to know the dissimilarity values between clusters at the current stage. Can you please provide the dissimilarity values?
To complete the merges using different similarity measures, we need to understand how each similarity measure works and then apply them to the given data points.
1. Single linkage: In single linkage, the similarity between two clusters is defined as the minimum distance between any two data points in the two clusters. To find the two clusters with the smallest dissimilarity, we look for the pair of clusters with the shortest distance between any two data points.
2. Complete linkage: In complete linkage, the similarity between two clusters is defined as the maximum distance between any two data points in the two clusters. To find the two clusters with the smallest dissimilarity, we look for the pair of clusters with the largest distance between any two data points.
3. Average linkage: In average linkage, the similarity between two clusters is defined as the average distance between all pairs of data points, where one point is from each cluster. To find the two clusters with the smallest dissimilarity, we calculate the average distance for each pair of clusters and choose the pair with the smallest average distance.
Now, let's go through the merges and identify the resulting clusters for each similarity measure:
Single linkage: Choose the pair of clusters with the shortest distance between any two data points and merge them. Repeat this process until all data points are clustered together.
Complete linkage: Choose the pair of clusters with the largest distance between any two data points and merge them. Repeat this process until all data points are clustered together.
Average linkage: Calculate the average distance for each pair of clusters and choose the pair with the smallest average distance. Merge these clusters, and repeat the process until all data points are clustered together.
Unfortunately, without the specific data points and distances given, it is not possible to provide the resulting clusters for each similarity measure. You would need to have the actual data points and their distances to perform the merges and determine the resulting clusters.