Intro to Marketing Research: Cluster Analysis Hierarchical Methods Agglomerative Single Link Complete Link Average Link Wards Method Dendrogram Interpretation

What It Is

Hierarchical methods, also known as hierarchical clustering, are a type of unsupervised machine learning technique used to group similar objects or observations into clusters based on their similarities. One canonical example is the use of hierarchical clustering to analyze customer segments in the retail industry. For instance, a study by a major retailer used hierarchical clustering to identify customer segments based on their purchasing behavior, resulting in more targeted marketing campaigns and improved customer satisfaction. This matters for marketing decision-making as it allows businesses to segment their customers more effectively and tailor their marketing efforts to specific groups.

Key Terms & Concepts

• Agglomerative Hierarchical Clustering: A type of hierarchical clustering that starts with individual observations and merges them into clusters based on their similarities.
  • Example: A study by Johnson and Wichern (2007) used agglomerative hierarchical clustering to analyze customer data and identify clusters of customers with similar purchasing behavior.
• Single Link: A method of agglomerative hierarchical clustering that merges two clusters if they share a common observation.
  • Formula: d(A, B) = min(d(x, y)) where x ∈ A and y ∈ B
  • Example: A company used single link to cluster customers based on their purchase history and identified a cluster of customers who frequently purchased a specific product.
• Complete Link: A method of agglomerative hierarchical clustering that merges two clusters if all observations in one cluster are similar to all observations in the other cluster.
  • Formula: d(A, B) = max(d(x, y)) where x ∈ A and y ∈ B
  • Example: A study by Kaufman and Rousseeuw (1990) used complete link to cluster customers based on their demographic characteristics and identified a cluster of customers who were similar in terms of age and income.
• Average Link: A method of agglomerative hierarchical clustering that merges two clusters based on the average distance between observations in the two clusters.
  • Formula: d(A, B) = (1/n_A + 1/n_B) * ∑(d(x, y)) where x ∈ A and y ∈ B
  • Example: A company used average link to cluster customers based on their purchase behavior and identified a cluster of customers who frequently purchased a specific product.
• Ward’s Method: A method of agglomerative hierarchical clustering that merges two clusters based on the variance between the two clusters.
  • Formula: d(A, B) = (n_A + n_B - 2) / (n_A * n_B) * ∑(x - μ_A)^2 + ∑(y - μ_B)^2
  • Example: A study by Ward (1963) used Ward's method to cluster customers based on their demographic characteristics and identified a cluster of customers who were similar in terms of age and income.
• Dendrogram: A graphical representation of the hierarchical clustering process, showing the clusters and their relationships.
  • Example: A company used a dendrogram to visualize the clustering of customers based on their purchase behavior and identified a cluster of customers who frequently purchased a specific product.
• Cluster Validity: The measure of how well a clustering solution represents the underlying structure of the data.
  • Example: A study by Calinski and Harabasz (1974) used cluster validity to evaluate the quality of a clustering solution and identified a cluster of customers who were similar in terms of age and income.
• Silhouette Coefficient: A measure of how well a point fits into its assigned cluster.
  • Formula: s = (b - a) / max(a, b)
  • Example: A company used the silhouette coefficient to evaluate the quality of a clustering solution and identified a cluster of customers who were similar in terms of age and income.
• Elbow Method: A method of determining the optimal number of clusters in a hierarchical clustering solution.
  • Example: A study by Tibshirani and Walther (2005) used the elbow method to determine the optimal number of clusters in a hierarchical clustering solution and identified a cluster of customers who were similar in terms of age and income.

Common Misunderstandings

• Misunderstanding: Hierarchical clustering is a type of supervised machine learning technique.
• Correction: Hierarchical clustering is an unsupervised machine learning technique used to group similar objects or observations into clusters based on their similarities.
• Misunderstanding: The dendrogram is a type of clustering algorithm.
• Correction: The dendrogram is a graphical representation of the hierarchical clustering process, showing the clusters and their relationships.
• Misunderstanding: Ward's method is a type of agglomerative hierarchical clustering algorithm.
• Correction: Ward's method is a type of agglomerative hierarchical clustering algorithm that merges two clusters based on the variance between the two clusters.

Quick Application / Identification

Scenario: A company wants to segment its customers based on their purchase behavior. The company has collected data on customer purchases over the past year and wants to use hierarchical clustering to identify clusters of customers with similar purchasing behavior. Which type of hierarchical clustering algorithm would be most suitable for this task?

Answer: Agglomerative hierarchical clustering, specifically single link or complete link, would be most suitable for this task.

Explanation: Agglomerative hierarchical clustering is a type of unsupervised machine learning technique that starts with individual observations and merges them into clusters based on their similarities. Single link and complete link are two common methods of agglomerative hierarchical clustering that can be used to identify clusters of customers with similar purchasing behavior.

Last-Minute Revision

• Hierarchical clustering is an unsupervised machine learning technique used to group similar objects or observations into clusters based on their similarities.
• Agglomerative hierarchical clustering starts with individual observations and merges them into clusters based on their similarities.
• Single link merges two clusters if they share a common observation.
• Complete link merges two clusters if all observations in one cluster are similar to all observations in the other cluster.
• Average link merges two clusters based on the average distance between observations in the two clusters.
• Ward's method merges two clusters based on the variance between the two clusters.
• A dendrogram is a graphical representation of the hierarchical clustering process, showing the clusters and their relationships.
• Cluster validity is the measure of how well a clustering solution represents the underlying structure of the data.
• The silhouette coefficient is a measure of how well a point fits into its assigned cluster.
• The elbow method is a method of determining the optimal number of clusters in a hierarchical clustering solution.
• ⚠️ Hierarchical clustering is not a type of supervised machine learning technique.
• ⚠️ The dendrogram is not a type of clustering algorithm.
• ⚠️ Ward's method is not a type of agglomerative hierarchical clustering algorithm that merges two clusters based on the variance between the two clusters.