support concept

Definition	Of an itemset, the fraction of transactions that contain it. Chapter 5.
Example	An itemset in 30 of 200 baskets has support 0.15.
Book	Data Mining as Observation, draft 0.2, commit `f3914f0`; entry id `support`, kind concept.
Status	no ledger row names this entry. Corrections: none recorded.
Defining equation	Book equation 5.1.
Assumptions and scope	The fraction of transactions that contain an itemset. Support cannot increase when an itemset grows, so an infrequent itemset has only infrequent supersets and every subset of a frequent itemset is frequent, which is the license to prune the lattice. The count of candidates rather than the count of transactions decides whether a run finishes, and a rare consequent lets lift reach the transaction count on a single co-occurrence.
Prior art	none recorded
Evidence	`lean/DataMiningAsObservation/SafePruning.lean`
Reviewed	not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page.

The fraction of transactions that contain the itemset.

Equation

Book equation 5.1.

\[s(X)=\frac{\sigma(X)}{N},\qquad c(X\to Y)=\frac{\sigma(X\cup Y)}{\sigma(X)}=\frac{s(X\cup Y)}{s(X)}.\]

Book equation 5.3.

\[X\subseteq Y\ \Longrightarrow\ s(X)\ge s(Y).\]

Conditions

The fraction of transactions that contain an itemset. Support cannot increase when an itemset grows, so an infrequent itemset has only infrequent supersets and every subset of a frequent itemset is frequent, which is the license to prune the lattice.
The count of candidates rather than the count of transactions decides whether a run finishes, and a rare consequent lets lift reach the transaction count on a single co-occurrence.

Conditions are curated in entries.toml rather than read from a record.

Ledger

none

First stated

TSK chapter 5, as chapter 5 section 5.1 of Data Mining as Observation states it, with anti-monotonicity as the Apriori license.

Measurements

Where the book states it	Numbers, as the book’s sources table records them	Source
chapter 5 section 5.1 to 5.3, 5.5	support, confidence, lift, the Apriori principle, FP-growth, closed and maximal itemsets, objective measures, Simpson’s paradox, cross-support	TSK 2e chapter 5

Failures and corrections

none

Invariance envelope

none declared

Machine checked

lean/DataMiningAsObservation/SafePruning.lean, theorems support_anti, apriori, subset_of_frequent, at observation-data-mining f3914f0; what the check covers is stated in the book’s appendix C.

Used in

Data Mining as Observation chapters 2, 5, 6, 7, 8.

itemset; Apriori principle; lift; cross-support ratio.

Status

Generated 2026-09-10 by encyclopedia/generate.py; book at observation-data-mining f3914f0; the commit of every record is listed in the encyclopedia’s provenance.

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