Cluster Analysis

1
Cluster Analysis

• Objectives
• ADDRESS HETEROGENEITY
• Combine observations into groups or clusters such
  that groups formed are homogeneous (similar)
  within the group and heterogeneous (different)
  from other groups on some variables (?).
• When we dont have some variables, we can still
  form groups using Multidimensional Scaling (MDS)
  Techniques.
• MDS - continuous Space
• Cluster - discrete groups
• Main Application in Marketing Market
  Segmentation
• Data requirement generally interval or ratio
  (ordinal and nominal ??)
• Steps
• Decide on measures of distance (similarity or
  dissimilarity)
• Hierarchical Cluster decide on how to combine
  observations
• Non-hierarchical cluster (K-means or quick
  cluster)
• Interpretation of clusters
• How many clusters
• Cluster validation

2
Cluster AnalysisMeasures of Distance
Similarity or Dissimilarity

• Two types of measures of distance ( or proximity,
  similarity)
• Direct we shall use in MDS
• Indirect
• Derived from original variables or factor scores
• Indirect Measures of distance
• Non-metric we shall use in MDS
• Metric Data
• Euclidean Distance
• Minkowski Distance
• Mahalanobis Distance
• Distance between BMW and Ford

iBMW jFord k nos. variables
Euclidean
Minkowski
v2
Mahalanobis
ED
v1
3
Cluster AnalysisHierarchical Clustering

• Methods to combine observations
• Centroid
• Nearest Neighbor or single linkage
• Farthest-neighbor or complete linkage
• Average linkage
• Wards
• Centriod Method

Dendogram
distance
Data should be scaled?
s1
s2
s3
s4
s5
s6
Nearest neighbor
4
Cluster AnalysisNon-Hierarchical Clustering

• K-Means Cluster/ Quick Cluster
• The data are divided into k-groups each group
  representing a cluster
• STEPS
• Select k initial cluster centroids, the number of
  cluster desired
• Assign each observation to the cluster to which
  it is closest
• Reassign or relocate each observation to one of
  the k clusters according to predetermined
  stopping rule

Say we want 3 clusters and first 3 observations
are centroids
Change criterion Continue if gt 2
Which Clustering Method is Best? 1. Hierarchical
Which one to use? Advantage no prior
knowledge of nos. of clusters, Disadvantage
Once assigned, no reassignment 2. K-Means / Quick
Cluster require prior knowledge, how many
clusters? Complementary Run Hierarchical,
decide on no of clusters, Run K -Means
5
Interpretation of Clusters

• .

• Pseudo F

6
Cluster AnalysisValidation
Cross-validation

• .

S1 assignment based on cluster on 1-14 cases S2
assignment based on separate cluster
Example from Text
Hit rate 112/151 74
7

• Latent Segments Model to Incorporate
  Heterogeneity

8
Introduction

• Customer segmentation - partition consumers into
  homogeneous groups that differ in purchasing
  behavior
• It provides information about consumer
  preferences and market structure at segment level
• Consumers with similar socio-demographics have
  different purchasing behavior
• Brand choice probabilities can be used to define
  both market segment and market structure
• Theoretical model Multinomial logit
• Conceptual appeal being grounded in economic
  theory
• Analytical tractability and ease of econometric
  estimation
• Excellent Empirical performance

9

• Kamakura and Russell (1989) propose and test
  latent segmentation.
• Number of applications and numerous citation,
  200
• Discrete interpretation of continuous
  distribution.
• Number of useful applications in Marketing and
  other areas.
• In our own work used to determine size of price
  sensitive segment (25 to 35).