SPSS tutorial on cluster analysis (.pdf), Lecture notes of Marketing

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SPSS TutorialSPSS Tutorial

AEB 37 / AE 802

Marketing Research Methods

Week 7

Cluster analysisCluster analysis

Lecture / Tutorial outline

• Cluster analysis
• Example of cluster analysis
• Work on the assignment

Cluster AnalysisCluster Analysis andand

marketing research marketing research

• Market segmentation. E.g. clustering of

consumers according to their attribute

preferences

• Understanding buyers behaviours.

Consumers with similar

behaviours/characteristics are clustered

• Identifying new product opportunities.

Clusters of similar brands/products can help

identifying competitors / market opportunities

• Reducing data. E.g. in preference mapping

Steps to conduct aSteps to conduct a Cluster Analysis Cluster Analysis

1. Select a distance measure

2. Select a clustering algorithm

3. Determine the number of clusters

4. Validate the analysis

Defining distance: theDefining distance: the

Euclidean distance Euclidean distance

D

ij

distance between cases i and j

x

ki

value of variable X

k

for case j

Problems:

• Different measures = different weights

• Correlation between variables (double

counting)

Solution: Principal component analysis

n

ij ki kj

k

D x x

Clustering proceduresClustering procedures

• Hierarchical procedures
  • Agglomerative (start from n clusters,

to get to 1 cluster)

• Divisive (start from 1 cluster, to get to

n cluster)

• Non hierarchical procedures
  • K-means clustering

AgglomerativeAgglomerative

clustering clustering

• Linkage methods
  • Single linkage (minimum distance)
  • Complete linkage (maximum distance)
  • Average linkage
• Ward’s method
  1. Compute sum of squared distances within clusters
  2. Aggregate clusters with the minimum increase in the overall sum of squares
• Centroid method
  • The distance between two clusters is defined as the difference between the centroids (cluster averages)

KK--means clusteringmeans clustering

1. The number k of cluster is fixed
2. An initial set of k “seeds” (aggregation centres) is provided

• First k elements
• Other seeds

3. Given a certain treshold, all units are assigned to the nearest cluster seed
4. New seeds are computed
5. Go back to step 3 until no reclassification is necessary Units can be reassigned in successive steps ( optimising partioning )

Suggested approachSuggested approach

1. First perform a hierarchical

method to define the number of

clusters

2. Then use the k - means procedure

to actually form the clusters

Defining the number ofDefining the number of clusters: elbow rule (1) clusters: elbow rule (1) Agglomeration Schedule 4 7 .015 0 0 4 6 10 .708 0 0 5 8 9 .974 0 0 4 4 8 1.042 1 3 6 1 6 1.100 0 2 7 4 5 3.680 4 0 7 1 4 3.492 5 6 8 1 11 6.744 7 0 9 1 2 8.276 8 0 10 1 12 8.787 9 0 11 1 3 11.403 10 0 0 Stage 1 2 3 4 5 6 7 8 9 10 11 Cluster 1 Cluster 2 Cluster Combined CoefficientsCluster 1 Cluster 2 Stage Cluster First Appears Next Stage Stage Number of clusters 0 12 1 11 2 10 3 9 4 8 5 7 6 6 7 5 8 4 9 3 10 2 11 1

n

Validating theValidating the

analysis analysis

• Impact of initial seeds / order of

cases

• Impact of the selected method
• Consider the relevance of the

chosen set of variables

SPSS ExampleSPSS Example

Agglomeration Schedule 3 6 .026 0 0 8 2 5 .078 0 0 7 4 9 .224 0 0 5 1 7 .409 0 0 6 4 10 .849 3 0 8 1 8 1.456 4 0 7 1 2 4.503 6 2 9 3 4 9.878 1 5 9 1 3 18.000 7 8 0 Stage 1 2 3 4 5 6 7 8 9 Cluster 1 Cluster 2 Cluster Combined Coefficients Cluster 1 Cluster 2 Stage Cluster First Appears Next Stage

Number of clusters: 10 – 6 = 4

Component

-1.5 -1.0 -.5 0.0 .5 1.0 1.5 2.

Component

.

-. -1. -1. -2.

Cluster Number of Ca

4 3 2 1 LUCY JULIA FRED ARTHUR JENNIFER THOMAS MATTHEW NICOLE PAMELA JOHN