Which graphical approach helps determine the optimal number of clusters by identifying an elbow in the plotted metric?

Which graphical approach helps determine the optimal number of clusters by identifying an elbow in the plotted metric?

• A. Scree Plots (Elbow Method)
• B. Dendrogram
• C. Silhouette Score Plot
• D. WCSS Histogram

Answer: (A)

In clustering, you want a number of clusters that captures structure without adding unnecessary complexity. The elbow method does this by plotting the within-cluster dispersion (WCSS) as you increase the number of clusters. Since WCSS always drops as you add more clusters, the curve falls steeply at first and then slows down; the point where the rate of decrease sharply changes—the elbow—indicates a good balance between fit and simplicity for the number of clusters. This is typically shown as a Scree Plot or Elbow Plot, hence it’s the go-to graphical approach for identifying the optimal k. Dendrograms come from hierarchical clustering and help decide where to cut the tree, but they aren’t about spotting an elbow in a WCSS-like metric. A Silhouette Score Plot assesses cluster separation and cohesion, often guiding the choice of k by maximizing the score, rather than looking for a bend in the curve. A WCSS histogram isn’t a standard method for determining the elbow.

In clustering, you want a number of clusters that captures structure without adding unnecessary complexity. The elbow method does this by plotting the within-cluster dispersion (WCSS) as you increase the number of clusters. Since WCSS always drops as you add more clusters, the curve falls steeply at first and then slows down; the point where the rate of decrease sharply changes—the elbow—indicates a good balance between fit and simplicity for the number of clusters. This is typically shown as a Scree Plot or Elbow Plot, hence it’s the go-to graphical approach for identifying the optimal k.

Dendrograms come from hierarchical clustering and help decide where to cut the tree, but they aren’t about spotting an elbow in a WCSS-like metric. A Silhouette Score Plot assesses cluster separation and cohesion, often guiding the choice of k by maximizing the score, rather than looking for a bend in the curve. A WCSS histogram isn’t a standard method for determining the elbow.