Dr. Michael R. Hyman

Cluster Analysis

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Introduction

• Also called classification analysis and numerical taxonomy

• Goal: assign objects to groups so that intra-group similarity and inter-group dissimilarity as maximized

• No (in)dependent variables

• Find naturally occurring groupings of objects

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Uses in Studying Consumers

• Benefit segmentation

• Finding market niches

• Finding homogeneous market segments for future study

• Data reduction

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Clusters Formed by Using Data on Two Characteristics

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Scatter Plot of Income and Education Data for PC Owners and Non-owners

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Procedure #1: Divisive (tear down)

• Start with profile data

• Find variable with highest variance

• Split objects above and below mean on this variable

• Find remaining high variance variable and split along mean

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Procedure #2: Agglomerative (build up)

• Select similarity measure– Distance (Euclidean, city block)– Correlation– Similarity

• Search similarity matrix for most similar cluster pair

• Repeat iteratively until only one cluster remains

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Commonly Used Similarity Coefficients

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Procedure #2: Agglomerative Stopping Rules

• Theory and practice

• Distance that clusters combine

• Within/between group variance

• Relative sizes of clusters

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Procedure #2: Agglomerative Linkage Methods

• Single (nearest neighbor)• Makes long, thin clusters

• Complete (maximum distance to farthest neighbor)

• Sensitive to outliers• Average distance between objects• Variance methods (minimum within-

cluster variance)• Nodal (begin with two least similar

objects as nodes)

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Procedure #2: Agglomerative Reliability and Validity Assessment

• Use different distance measures• Use different clustering methods• Split data, run both halves, and compare• Shuffle cases (objects)• Solve with subset of profile variables

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General Problems

• Early assignments treated as permanent

– Precludes later revision for improved fit

• Number of clusters

– More clusters means greater intra-group homogeneity but less descriptive power

• No good measure of cluster compactness

• Lack of statistical properties makes inference difficult

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General Problems (cont.)

• Coping with inter-correlated profile variables

• Must select profile variables that can discriminate among objects

• Sensitive to unit of measurement and outliers

– Fix: Standardize data and delete outliers

• Subjective interpretation of results (i.e., naming clusters)

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Steps for Conducting a Cluster Analysis: A Summary

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