Association rules and clustering

Updated 11 Oct 2026

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Measures
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  For rule $A\to B$ :
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    Support -> fraction of all transactions containing both $A$ and $B$ .
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    Confidence -> $P(B\mid A)$ .
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    Lift -> confidence divided by the overall frequency of $B$ .
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  Lift $>1$ -> co-occurrence exceeds the independence baseline in the data.
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  Lift $<1$ -> co-occurrence is below that baseline.
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  Caution -> high confidence alone can mislead when the consequent is already common.
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Algorithms
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  Apriori -> grows frequent itemsets; prunes candidates when a subset is infrequent.
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    Repeated database scans can be costly.
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  ECLAT -> intersects vertical transaction-ID sets.
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  FP-Growth -> mines a compressed FP-tree without the same candidate-generation process.
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Worked bread-and-milk example
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  Transactions -> 5 total; bread appears in 4; milk appears in 4; both appear in 3.
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  Support -> $3/5=0.60$ .
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  Confidence -> $3/4=0.75$ in either direction.
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  Baseline frequency of consequent -> $4/5=0.80$ .
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  Lift -> $0.75/0.80=0.9375$ .
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  Confidence of $75\%$ alone does not show positive association against the baseline.
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  Use rules to suggest patterns; placement or promotion needs business context and testing.
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Task
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  Clustering -> groups observations by similarity without pre-existing class labels or target categories.
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K-means
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  Procedure
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    choose $K$ initial centroids.
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    assign each point to its nearest centroid.
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    recompute each centroid as the mean of its assigned points.
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    repeat until assignments or centroid movement stabilizes.
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  Euclidean distance -> common for numeric features.
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  Sensitivity -> initial centroids, outliers, feature scale.
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    standardize features when their units or ranges differ.
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  Typical shape -> favors compact, roughly spherical clusters.
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    inspect clusters before assigning business meaning.
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Practicum interpretation
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  Features -> purchase frequency and profit per sale; used to inform stock decisions.
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  Low frequency, high margin -> may call for a different stock policy.
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  High frequency, near-zero margin -> may call for another policy.
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  Caution -> cluster averages describe profiles; they do not justify the same action for every member.
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  11-point example centroids -> approximately $(15.283,2.083)$ , $(4.733,48.4)$ , and $(1.5,342.15)$ for low, medium, and high profit.
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  Coordinate meaning -> first is purchase frequency; second is profit per sale.
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  feature scales differ greatly and strongly affect Euclidean distance.

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Association rules and clustering

Measures

Algorithms

Worked bread-and-milk example

Task

K-means

Practicum interpretation

Linked references 1