Cluster analysis Lecture / Tutorial outline
Cluster analysis
Example of cluster analysis
Work on the assignment

Cluster Analysis :

Cluster Analysis It is a class of techniques used to classify cases into groups that are relatively homogeneous within themselves and heterogeneous between each other, on the basis of a defined set of variables. These groups are called clusters.

Cluster Analysis and marketing research :

Cluster Analysis and 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 a Cluster Analysis :

Steps to conduct a Cluster Analysis Select a distance measure
Select a clustering algorithm
Determine the number of clusters
Validate the analysis

Defining distance: the Euclidean distance :

Defining distance: the Euclidean distance Dij distance between cases i and j
xki value of variable Xk for case j
Problems:
Different measures = different weights
Correlation between variables (double counting)
Solution: Principal component analysis

Clustering procedures :

Clustering 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

Agglomerative clustering :

Agglomerative clustering

Agglomerative clustering :

Agglomerative clustering Linkage methods
Single linkage (minimum distance)
Complete linkage (maximum distance)
Average linkage
Ward’s method
Compute sum of squared distances within clusters
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)

K-means clustering :

K-means clustering The number k of cluster is fixed
An initial set of k “seeds” (aggregation centres) is provided
First k elements
Other seeds
Given a certain treshold, all units are assigned to the nearest cluster seed
New seeds are computed
Go back to step 3 until no reclassification is necessary
Units can be reassigned in successive steps (optimising partioning)

Hierarchical vs Non hierarchical methods :

Hierarchical vs Non hierarchical methods Hierarchical clustering
No decision about the number of clusters
Problems when data contain a high level of error
Can be very slow
Initial decision are more influential (one-step only) Non hierarchical clustering
Faster, more reliable
Need to specify the number of clusters (arbitrary)
Need to set the initial seeds (arbitrary)

Suggested approach :

Suggested approach First perform a hierarchical method to define the number of clusters
Then use the k-means procedure to actually form the clusters

Defining the number of clusters: elbow rule (1) :

Defining the number of clusters: elbow rule (1) n

Elbow rule (2): the scree diagram :

Elbow rule (2): the scree diagram

Validating the analysis :

Validating the analysis Impact of initial seeds / order of cases
Impact of the selected method
Consider the relevance of the chosen set of variables

SPSS Example :

SPSS Example

Slide 19:

Number of clusters: 10 – 6 = 4

Open the dataset supermarkets.sav :

Open the dataset supermarkets.sav From your N: directory (if you saved it there last time
Or download it from: http://www.rdg.ac.uk/~aes02mm/supermarket.sav
Open it in SPSS

The supermarkets.sav dataset :

The supermarkets.sav dataset

Run Principal Components Analysis and save scores :

Run Principal Components Analysis and save scores Select the variables to perform the analysis
Set the rule to extract principal components
Give instruction to save the principal components as new variables

Cluster analysis: basic steps :

Cluster analysis: basic steps Apply Ward’s methods on the principal components score
Check the agglomeration schedule
Decide the number of clusters
Apply the k-means method

Analyse / Classify :

Analyse / Classify

Select the component scores :

Select the component scores Select from here Untick this

Select Ward’s algorithm :

Select Ward’s algorithm Click here first Select method here

Output: Agglomeration schedule :

Output: Agglomeration schedule

Number of clusters :

Number of clusters Identify the step where the “distance coefficients” makes a bigger jump

The scree diagram (Excel needed) :

The scree diagram (Excel needed)

Number of clusters :

Number of clusters Number of cases 150
Step of ‘elbow’ 144
__________________________________
Number of clusters 6

Now repeat the analysis :

Now repeat the analysis Choose the k-means technique
Set 6 as the number of clusters
Save cluster number for each case
Run the analysis

K-means :

K-means

K-means dialog box :

K-means dialog box Specify number of clusters

Save cluster membership :

Save cluster membership Click here first Thick here

Final output :

Final output

Cluster membership :

Cluster membership

Component meaning(tutorial week 5) :

Component meaning(tutorial week 5) 1. “Old Rich Big Spender” 3. Vegetarian TV lover 4. Organic radio listener 2. Family shopper 5. Vegetarian TV and web hater

Cluster interpretation through mean component values :

Cluster interpretation through mean component values Cluster 1 is very far from profile 1 (-1.34) and more similar to profile 2 (0.38)
Cluster 2 is very far from profile 5 (-0.93) and not particularly similar to any profile
Cluster 3 is extremely similar to profiles 3 and 5 and very far from profile 2
Cluster 4 is similar to profiles 2 and 4
Cluster 5 is very similar to profile 3 and very far from profile 4
Cluster 6 is very similar to profile 5 and very far from profile 3

Which cluster to target? :

Which cluster to target? Objective: target the organic consumer
Which is the cluster that looks more “organic”?
Compute the descriptive statistics on the original variables for that cluster

Representation of factors 1 and 4(and cluster membership) :

Representation of factors 1 and 4(and cluster membership)

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