Database Marketing

N. Kumar, Asst. Professor of Marketing

Database Marketing

Cluster Analysis


2

AgendaDiscussion of the first Assignment

Motivation for conducting Cluster AnalysisBenefit Segmentation

Cluster AnalysisBasic ConceptsHierarchical/Non- Hierarchical Clustering

Implementation in SAS and interpreting the output


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

What should I say?


Ad CampaignHow many customer segments are there?

How many do I want to target?

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


Promotional StrategiesCoupon 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?


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


DataConsumer Income ($ 1000s) Education (years)

1 5 5

2 6 6

3 15 14

4 16 15

5 25 19

6 30 20


Geometrical View of Cluster Analysis Education

Income


Similarity MeasuresWhy 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


Similarity MatrixC1 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


Clustering Techniques

Hierarchical Clustering

Non-Hierarchical Clustering


Hierarchical ClusteringDistance(1,2) = 2 = Distance(3,4)Say, we group 1 and 2 together and leave the others as isHow do we compute the distance between a group that has two (or more) members and the others?


Hierarchical Clustering Algorithms

Centroid MethodNearest-Neighbor or Single-LinkageFarthest-Neighbor or Complete-LinkageAverage-LinkageWard’s Method


Centroid MethodEach group is replaced by an average consumerCluster 1 – average income = 5.5 and average education = 5.5


Data for Five ClustersCluster 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


Similarity MatrixC1&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


Data for Four ClustersCluster 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


Similarity MatrixC1&C2 C3&C4 C5 C6

C1&C2 0

C3&C4 181 0

C5 590 120.5 0

C6 782.5 230.5 26 0


Data for Three ClustersCluster Members Income Education

1 C1&C2 5.5 5.5

2 C3&C4 15.5 14.5

3 C5&C6 27.5 19.5


Similarity MatrixC1&C2 C3&C4 C5&C6

C1&C2 0

C3&C4 181 0

C5&C6 680 169 0


Dendogram for the Data

C1 C2 C3 C4 C5 C6


Single LinkageFirst Cluster is formed in the same fashionDistance 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



C1&C2 0

C3 145 0

C4 181 2 0

C5 557 136 106 0

C6 745 250 212 26 0


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



C1&C2 0

C3 181 0

C4 221 2 0

C5 625 136 106 0

C6 821 250 212 26 0


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



C1&C2 0

C3 163 0

C4 201 2 0

C5 591 136 106 0

C6 783 250 212 26 0


Ward’s MethodDoes not compute distance between clustersForms 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


Ward’s MethodCL1 CL2 CL3 CL4 CL5 ESS

1 C1,C2 C3 C4 C5 C6 12 C1,C3 C2 C4 C5 C6 90.53 C1,C4 C2 C3 C5 C6 110.54 C1,C5 C2 C3 C4 C6 312.55 C1,C6 C2 C3 C4 C5 410.56 C2,C3 C1 C4 C5 C6 72.57 C2,C4 C1 C3 C5 C6 90.5


Non-Hierarchical ClusteringData are grouped into K clusters

Requires a priori knowledge of K


Basic Steps in Non-Hierarchical Clustering

Select K initial cluster centroidsAssign each observation to the cluster to which it is closestReassign or reallocate each observation to one of the K clusters according to a pre-determined stopping ruleStop if there is no reallocationApproaches differ in Step 1 and/or step 3


Algorithm ISelects first K observations as cluster centers


Initial Cluster CentroidsVariable CL1 CL2 CL3

Income 5 6 15

Education 5 6 14


Initial AssignmentDistance 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


New Cluster CentroidsVariable CL1 CL2 CL3

Income 5 6 21.5

Education 5 6 17


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


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


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


Initial AssignmentDistance 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


New Cluster CentroidsVariable CL1 CL2 CL3

Income 5.5 15.5 27.5

Education 5.5 14.5 19.5


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


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


Voter ProfilingSurvey 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


Ad CampaignUse attitudinal data to segment customers

Target message appropriately


Promotional StrategiesUse 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

Database Marketing

Documents

professor of marketingwhat

professor of marketingdatan

specifyeach group

customer segments

average income

average consumercluster

average education

minimum of distance1