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Example 10.3 Agglomerative versus divisive hierarchical clustering. Figure 10.6 shows the appli- cation of AGNES (AGglomerative NESting), an agglomerative hierarchical clustering method, and DIANA (DIvisive ANAlysis), a divisive hierarchical clustering method, on a data set of five objects, {a, b, c, d, e}. Initially, AGNES, the agglomerative method, places each object into a cluster of its own. The clusters are then merged step-by-step according to some criterion. For example, clusters C1 and C2 may be merged if an object in C1 and an object in C2 form the minimum Euclidean distance between any two objects from solve

Question

Example 10.3 Agglomerative versus divisive hierarchical clustering. Figure 10.6 shows the appli- cation of AGNES (AGglomerative NESting), an agglomerative hierarchical clustering method, and DIANA (DIvisive ANAlysis), a divisive hierarchical clustering method, on a data set of five objects, {a, b, c, d, e}. Initially, AGNES, the agglomerative method, places each object into a cluster of its own. The clusters are then merged step-by-step according to some criterion. For example, clusters C1 and C2 may be merged if an object in C1 and an object in C2 form the minimum Euclidean distance between any two objects from solve

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Solution

Sure, let's solve the problem step by step.

Step-by-Step Solution:

  1. Initial Setup:

    • We have a data set of five objects: {a, b, c, d, e}.
    • AGNES (Agglomerative Nesting) starts by placing each object in its own cluster.
    • DIANA (Divisive Analysis) starts with all objects in a single cluster and then splits them.

  2. AGNES (Agglomerative Method):

    • Step 1: Each object is its own cluster: {a}, {b}, {c}, {d}, {e}.
    • Step 2: Find the pair of clusters with the minimum Euclidean distance between any two objects. Suppose the minimum distance is between objects a and b.
    • Step 3: Merge clusters {a} and {b} into a new cluster {a, b}.
    • Step 4: Repeat the process of finding the next pair of clusters with the minimum distance. Suppose the next minimum distance is between clusters {a, b} and {c}.
    • Step 5: Merge clusters {a, b} and {c} into a new cluster {a, b, c}.
    • Step 6: Continue this process until all objects are merged into a single cluster. The final sequence of merges might look like: {a, b, c}, {d}, {e} -> {a, b, c, d}, {e} -> {a, b, c, d, e}.

  3. DIANA (Divisive Method):

    • Step 1: Start with all objects in a single cluster: {a, b, c, d, e}.
    • Step 2: Find the object that is most dissimilar to the rest and split it off into its own cluster. Suppose object e is the most dissimilar.
    • Step 3: Split the cluster into {a, b, c, d} and {e}.
    • Step 4: Repeat the process on the remaining cluster {a, b, c, d}. Find the next most dissimilar object. Suppose object d is the next most dissimilar.
    • Step 5: Split the cluster into {a, b, c} and {d}.
    • Step 6: Continue this process until each object is its own cluster. The final sequence of splits might look like: {a, b, c}, {d}, {e} -> {a, b}, {c}, {d}, {e} -> {a}, {b}, {c}, {d}, {e}.

Summary:

  • AGNES starts with individual objects and merges them step-by-step based on minimum distance.
  • DIANA starts with all objects in one cluster and splits them step-by-step based on maximum dissimilarity.

This step-by-step approach helps in understanding how agglomerative and divisive hierarchical clustering methods work.

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Similar Questions

In agglomerative hierarchical clustering, what does the algorithm begin with?1 pointEach data point in a separate clusterAll data points in one clusterA predefined number of clustersThe optimal number of clusters

Explain the concept of hierarchical clustering. Compare and contrastagglomerative and divisive hierarchical clustering. Discuss theapplications of hierarchical clustering in real-world situations.

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