N. Kumar, Asst. Professor of Marketing

Database Marketing

Cluster Analysis

N. Kumar, Asst. Professor of Marketing

2

Agenda

Discussion of the first Assignment

Motivation for conducting Cluster AnalysisBenefit Segmentation

Cluster AnalysisBasic ConceptsHierarchical/Non- Hierarchical Clustering

Implementation in SAS and interpreting the output

N. Kumar, Asst. Professor of Marketing

Voter Profiling

What are the different voting segments out there? What do they want to hear i.e. issues they care about?

What should I say?

N. Kumar, Asst. Professor of Marketing

Ad Campaign

How many customer segments are there?

How many do I want to target?

How should I target – what message should I communicate to each segment?

N. Kumar, Asst. Professor of Marketing

Promotional Strategies

Coupon Drops – who should they be targeted at?

Catalog Example – should the catalog be accompanied with a $5 coupon or a $10 coupon or no coupon?

N. Kumar, Asst. Professor of Marketing

What is Cluster Analysis?

Cluster Analysis is a technique for combining observations into groups or clusters such that:

Each group is homogenous with respect to certain characteristics (that you specify)

Each group is different from the other groups with respect to the same characteristics

N. Kumar, Asst. Professor of Marketing

DataConsumer Income ($ 1000s) Education (years)

1 5 5

2 6 6

3 15 14

4 16 15

5 25 19

6 30 20

N. Kumar, Asst. Professor of Marketing

Geometrical View of Cluster Analysis Education

Income

N. Kumar, Asst. Professor of Marketing

Similarity Measures

Why are consumers 1 and 2 similar? Distance(1,2) = (5-6)2 + (5-6)2

More generally, if there are p variables: Distance(i,j) = (xik - xjk)2

N. Kumar, Asst. Professor of Marketing

Similarity Matrix

C1 C2 C3 C4 C5 C6

C1 0 2 181 221 625 821

C2 2 0 145 181 557 745

C3 181 145 0 2 136 250

C4 221 181 2 0 106 212

C5 625 557 136 106 0 26

C6 821 745 250 212 26 0

N. Kumar, Asst. Professor of Marketing

Clustering Techniques

Hierarchical Clustering

Non-Hierarchical Clustering

N. Kumar, Asst. Professor of Marketing

Hierarchical Clustering

Distance(1,2) = 2 = Distance(3,4)

Say, we group 1 and 2 together and leave the others as is

How do we compute the distance between a group that has two (or more) members and the others?

N. Kumar, Asst. Professor of Marketing

Hierarchical Clustering Algorithms

Centroid Method

Nearest-Neighbor or Single-Linkage

Farthest-Neighbor or Complete-Linkage

Average-Linkage

Ward’s Method

N. Kumar, Asst. Professor of Marketing

Centroid Method

Each group is replaced by an average consumer

Cluster 1 – average income = 5.5 and average education = 5.5

N. Kumar, Asst. Professor of Marketing

Data for Five Clusters

Cluster Members Income Education

1 C1&C2 5.5 5.5

2 C3 15 14

3 C4 16 15

4 C5 25 20

5 C6 30 19

N. Kumar, Asst. Professor of Marketing

Similarity Matrix

C1&C2 C3 C4 C5 C6

C1&C2 0

C3 162.5 0

C4 200.5 2 0

C5 590.5 135.96 106 0

C6 782.5 250 212 26 0

N. Kumar, Asst. Professor of Marketing

Data for Four Clusters

Cluster Members Income Education

1 C1&C2 5.5 5.5

2 C3&C4 15.5 14.5

3 C5 25 20

4 C6 30 19

N. Kumar, Asst. Professor of Marketing

Similarity Matrix

C1&C2 C3&C4 C5 C6

C1&C2 0

C3&C4 181 0

C5 590 120.5 0

C6 782.5 230.5 26 0

N. Kumar, Asst. Professor of Marketing

Data for Three Clusters

Cluster Members Income Education

1 C1&C2 5.5 5.5

2 C3&C4 15.5 14.5

3 C5&C6 27.5 19.5

N. Kumar, Asst. Professor of Marketing

Similarity Matrix

C1&C2 C3&C4 C5&C6

C1&C2 0

C3&C4 181 0

C5&C6 680 169 0

N. Kumar, Asst. Professor of Marketing

Dendogram for the Data

C1 C2 C3 C4 C5 C6

N. Kumar, Asst. Professor of Marketing

Single Linkage

First Cluster is formed in the same fashion

Distance between Cluster 1 comprising of customers 1 and 2 and customer 3 is the minimum of Distance(1,3) = 181 and Distance(2,3) = 145

N. Kumar, Asst. Professor of Marketing

Similarity Matrix

C1&C2 C3 C4 C5 C6

C1&C2 0

C3 145 0

C4 181 2 0

C5 557 136 106 0

C6 745 250 212 26 0

N. Kumar, Asst. Professor of Marketing

Complete Linkage

Distance between Cluster 1 comprising of customers 1 and 2 and customer 3 is the maximum of Distance(1,3) = 181 and Distance(2,3) = 145

N. Kumar, Asst. Professor of Marketing

Similarity Matrix

C1&C2 C3 C4 C5 C6

C1&C2 0

C3 181 0

C4 221 2 0

C5 625 136 106 0

C6 821 250 212 26 0

N. Kumar, Asst. Professor of Marketing

Average Linkage

Distance between Cluster 1 comprising of customers 1 and 2 and customer 3 is the average of Distance(1,3) = 181 and Distance(2,3) = 145

N. Kumar, Asst. Professor of Marketing

Similarity Matrix

C1&C2 C3 C4 C5 C6

C1&C2 0

C3 163 0

C4 201 2 0

C5 591 136 106 0

C6 783 250 212 26 0

N. Kumar, Asst. Professor of Marketing

Ward’s Method

Does not compute distance between clusters

Forms clusters by maximizing within-cluster homogeneity or minimizing error sum of squares (ESS)

ESS for cluster with two observations (say, C1 and C2) = (5-5.5)2 + (6-5.5)2 + (5-5.5)2 + (6-5.5)2

N. Kumar, Asst. Professor of Marketing

Ward’s Method

CL1 CL2 CL3 CL4 CL5 ESS

1 C1,C2 C3 C4 C5 C6 1

2 C1,C3 C2 C4 C5 C6 90.5

3 C1,C4 C2 C3 C5 C6 110.5

4 C1,C5 C2 C3 C4 C6 312.5

5 C1,C6 C2 C3 C4 C5 410.5

6 C2,C3 C1 C4 C5 C6 72.5

7 C2,C4 C1 C3 C5 C6 90.5

N. Kumar, Asst. Professor of Marketing

Non-Hierarchical Clustering

Data are grouped into K clusters

Requires a priori knowledge of K

N. Kumar, Asst. Professor of Marketing

Basic Steps in Non-Hierarchical Clustering

Select K initial cluster centroids

Assign each observation to the cluster to which it is closest

Reassign or reallocate each observation to one of the K clusters according to a pre-determined stopping rule

Stop if there is no reallocation

Approaches differ in Step 1 and/or step 3

N. Kumar, Asst. Professor of Marketing

Algorithm I

Selects first K observations as cluster centers

N. Kumar, Asst. Professor of Marketing

Initial Cluster Centroids

Variable CL1 CL2 CL3

Income 5 6 15

Education 5 6 14

N. Kumar, Asst. Professor of Marketing

Initial Assignment

Distance from C1

Distance from C2

Distance from C3

Assigned to CL

C1 0 2 181 1

C2 2 0 145 2

C3 181 145 0 3

C4 221 181 2 3

C5 625 557 136 3

C6 821 745 250 3

N. Kumar, Asst. Professor of Marketing

New Cluster Centroids

Variable CL1 CL2 CL3

Income 5 6 21.5

Education 5 6 17

N. Kumar, Asst. Professor of Marketing

Distance MatrixDistance from CL1

Distance from CL2

Distance from CL3

Previous Assignment

Current Assignment

C1 0 2 416.15 1 1

C2 2 0 316.25 2 2

C3 181 145 51.25 3 3

C4 221 181 34.25 3 3

C5 625 557 21.25 3 3

C6 821 990 76.25 3 3

N. Kumar, Asst. Professor of Marketing

Algorithm IIDiffers from Algorithm I in how the initial seeds are modifiedAs before first K observations are selected as the initial cluster seedsA seed that is a candidate for replacement is from one of the two seeds that are closest to each otherAn observation qualifies to replace one of the two candidates if the distance between the seeds is less than the distance between the observation and the closest seed

N. Kumar, Asst. Professor of Marketing

Algorithm II …contd.C1, C2 and C3 are the initial seedsThe smallest distance between the seeds is between C1 and C2Observation C4 does not qualify as a replacement as Distance(C1,C2) > Distance(C4 and the nearest seed C3)Observation C5 does qualify as a replacement as Distance(C1,C2) < Distance(C5 and the nearest seed C3): replace C2 with C5

N. Kumar, Asst. Professor of Marketing

Initial Assignment

Distance from C1

Distance from C2

Distance from C3

Assigned to CL

C1 0 181 625 1

C2 2 145 557 1

C3 181 0 136 2

C4 221 2 106 2

C5 625 136 0 3

C6 821 250 26 3

N. Kumar, Asst. Professor of Marketing

New Cluster Centroids

Variable CL1 CL2 CL3

Income 5.5 15.5 27.5

Education 5.5 14.5 19.5

N. Kumar, Asst. Professor of Marketing

Distance MatrixDistance from CL1

Distance from CL2

Distance from CL3

Previous Assignment

Current Assignment

C1 0.5 200.5 716.5 1 1

C2 0.5 162.5 644.5 1 1

C3 162.5 0.5 186.5 2 2

C4 200.5 0.5 152.5 2 2

C5 590.5 120.5 6.5 3 3

C6 600.50 230.5 6.5 3 3

N. Kumar, Asst. Professor of Marketing

Hierarchical vs. Non-Hierarchical Clustering

Hierarchical clustering does not require a priori knowledge of the number of clustersAssignments are staticUse hierarchical clustering for exploratory purposesNon-Hierarchical Methods can be viewed as a complementary rather than a competing method

N. Kumar, Asst. Professor of Marketing

Voter Profiling

Survey of voters concerns may help us group customers with similar concerns – perhaps they all live in a certain area?

Target ads/mailings with customized messages

N. Kumar, Asst. Professor of Marketing

Ad Campaign

Use attitudinal data to segment customers

Target message appropriately

N. Kumar, Asst. Professor of Marketing

Promotional Strategies

Use transaction data to group customers into those that are more prone to purchasing the product on deal

Give a stronger incentive to the price sensitive segment