BUSINFO700 Chap.8 Cluster Analysis for Customer Segmentation
Cluster Analysis for Customer Segmentation
This chapter shows how k-means cluster analysis turns a varied customer base into a few segments a business can act on. It contrasts segmentation by one or two manager-chosen cut-offs with data-driven segmentation across several variables, and explains why the method counts as unsupervised machine learning.
The core mechanics are Euclidean distance, nearest-centre assignment and the need to standardise variables so that the widest-ranging one does not dominate. A worked example shows a distance changing completely once two variables are scaled. You will choose the number of clusters with average silhouette scores and the course's quality bands, then apply analyst judgement on statistical, visual and business grounds.
The chapter ends with profiling: frequencies for cluster sizes, chi-square for categorical traits, ANOVA with Levene and post-hoc tests for metric ones, and naming each segment from its profile. Cluster analysis is taught in Week 7, after the November test, so this chapter is not part of the test scope.
What this chapter covers
- 01
Cut-off segmentation versus data-driven segments
- 02
Euclidean distance and nearest-centre assignment
- 03
Standardising variables with scale()
- 04
Choosing k with silhouette scores
- 05
Analyst judgement on statistical, visual and business grounds
- 06
Profiling and naming clusters
Worked example · free
Assign a new member to the nearest cluster centre
- 1Distance to regulars = √((0.5 − 1.2)² + (−0.8 + 0.9)²) = √(0.49 + 0.01) = √0.50 = 0.71.
- 1Distance to treat seekers = √((0.5 + 1.0)² + (−0.8 − 1.3)²) = √(2.25 + 4.41) = √6.66 = 2.58.
- 1Distance to drifters = √((0.5 + 0.4)² + (−0.8 + 0.6)²) = √(0.81 + 0.04) = √0.85 = 0.92.
- 1The smallest distance is 0.71, so the new member joins the regulars cluster: more visits than average and below-average spend per visit.
Key terms
- Market segmentation
- Dividing a varied market into smaller groups of customers with similar needs so that each group can be served differently.
- Euclidean distance
- The straight-line gap between two observations, found as the square root of their summed squared differences across variables.
- Cluster centre
- The average position of a cluster's members on every clustering variable, recalculated as k-means reassigns observations.
- Silhouette score
- A value up to 1 comparing how close an observation is to its own cluster against the nearest other cluster.
- Cluster profiling
- Describing each segment after clustering by comparing its size and characteristics with frequencies, chi-square and ANOVA.
Cluster Analysis for Customer Segmentation FAQ
Why must variables be standardised before k-means?
k-means compares customers by Euclidean distance, so a variable measured on a wide range, such as annual spend in dollars, would swamp one on a narrow range, such as visits per month. Converting each variable to z-scores with scale() gives every variable an equal say in the distance.
How do I pick the number of clusters?
Run k-means for k from 2 to 8, average the silhouette scores for each solution and start from the highest. Then apply judgement: treat differences of about 0.01 as negligible and prefer fewer clusters, check the scatter plot for overlap, and confirm that every cluster is big enough to target.
What do the silhouette quality bands mean?
The course grades an average score of 0.71 to 1.00 as strong, 0.51 to 0.70 as reasonable, 0.26 to 0.50 as weak with some overlap, and anything below 0.25 as showing no meaningful structure. Weak solutions are common with real customer data and may still be useful if they make business sense.
What are the main limitations of k-means?
The number of clusters has to be fixed before running it, and the algorithm gives no guarantee of the best possible solution. Categorical variables need dummy coding or other distance measures, and every observation is forced into a cluster, so extreme outliers can distort the centres.
How are clusters profiled once they are found?
Treat cluster membership as a categorical variable. Report each cluster's share of customers with a frequency table, compare categorical traits across clusters with a cross-table and chi-square, and compare metric traits with ANOVA, a Levene test and the matching post-hoc procedure, wrapping cluster membership in factor().
Assessment move
Draw a small scatter plot by hand with eight or nine invented customers on two standardised variables, mark three centres and assign each point to its nearest centre by computing the distances. Then repeat one distance calculation on raw values with very different ranges to see why scaling matters. Write the k-means call from memory, including the seed and the number of random starts, and explain each argument in a sentence.
Practise reading a silhouette chart: name the peak, its quality band and whether a neighbouring k is close enough to prefer a simpler solution. Finally, take a cluster profile table you have built yourself and write one short paragraph per segment, giving it a name, its size and the two variables that most clearly separate it, and say which bivariate test supports each claim.
Close by explaining to an imaginary manager why one segment deserves its own campaign and another does not.
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