14.3 Cluster analysis techniques

Cluster analysis is a powerful tool for market segmentation, grouping similar customers or products based on shared characteristics. It helps marketers identify distinct segments, develop targeted strategies, and uncover new opportunities in the market.

There are two main types of clustering: hierarchical and non-hierarchical. Each has its strengths, with hierarchical clustering providing visual representations and non-hierarchical methods being faster for large datasets. Marketers can apply various algorithms and evaluate results to find meaningful segments.

Cluster Analysis in Market Segmentation

Concept of cluster analysis

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• Groups similar objects or data points into clusters based on their characteristics or attributes
• Objects within a cluster are more similar to each other than to objects in other clusters (customers, products)
• Helps identify distinct customer segments with similar needs, preferences, or behaviors
• Enables development of targeted marketing strategies for each segment (personalized promotions, product recommendations)
• Discovers new market opportunities or niches (underserved segments, emerging trends)

Hierarchical vs non-hierarchical clustering

• Hierarchical clustering builds a hierarchy of clusters by merging smaller clusters into larger ones (agglomerative) or dividing larger clusters into smaller ones (divisive)
  • Does not require specifying the number of clusters in advance
  • Provides a visual representation of the clustering process through dendrograms (tree-like diagrams)
• Non-hierarchical clustering (partitional clustering) directly divides the data into a specified number of clusters without creating a hierarchical structure
  • Generally faster and more efficient than hierarchical clustering, especially for large datasets (customer transactions, social media interactions)
  • Allows for the reassignment of objects to different clusters during the clustering process

Application of clustering algorithms

• K-means clustering, a non-hierarchical clustering algorithm, partitions data into k clusters
  1. Specify the number of clusters (k) and randomly initialize k centroids (cluster centers)
  2. Assign each data point to the nearest centroid
  3. Recalculate the centroids based on the mean of the data points in each cluster
  4. Repeat steps 2 and 3 until the centroids no longer change or a maximum number of iterations is reached
• Agglomerative hierarchical clustering
  1. Start with each data point as a separate cluster
  2. Merge the two closest clusters based on a distance metric (Euclidean distance, Manhattan distance)
  3. Repeat step 2 until all data points are in a single cluster
• Linkage methods for determining the distance between clusters in hierarchical clustering
  • Single linkage: minimum distance between any two points in different clusters
  • Complete linkage: maximum distance between any two points in different clusters
  • Average linkage: average distance between all pairs of points in different clusters

Evaluation of cluster solutions

• Silhouette coefficient measures how well each object fits into its assigned cluster compared to other clusters
  • Calculated for each data point $i$ as: $s(i) = \frac{b(i) - a(i)}{max(a(i), b(i))}$
    • $a(i)$: average distance between $i$ and all other points in the same cluster
    • $b(i)$: minimum average distance between $i$ and all points in any other cluster
  • Ranges from -1 to 1, with higher values indicating better clustering (well-separated clusters, cohesive within clusters)
• Dendrograms visualize the hierarchical clustering process and help determine the optimal number of clusters
  • Identify the longest vertical lines that do not cross any horizontal lines (distinct clusters)
  • Assess the stability of clusters by examining how the dendrogram changes with different linkage methods or distance metrics (robust to variations)