Dr. Michael R. Hyman

• 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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• 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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• 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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• Theory and practice
• Distance that clusters combine
• Within/between group variance
• Relative sizes of clusters
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• Single (nearest neighbor)
• Makes long, thin clusters
• Complete (maximum distance to farthest neighbor)
• Sensitive to outliers
• Average distance between objects
• Variance methods (minimum withincluster 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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• 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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• 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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