The Observation Theory EncyclopediaFrom TSKAboutBy kindBy chapterBy Lean fileLedgerProvenance

cross-support ratio concept

DefinitionThe smallest item support in an itemset over the largest, with a threshold below which the itemset is discarded. Chapter 5. Also cross-support.
ExampleAn item in 2 percent of baskets paired with one in 40 percent has cross-support ratio 0.05.
BookData Mining as Observation, draft 0.2, commit f3914f0; entry id cross-support-ratio, kind concept.
Statusno ledger row names this entry. Corrections: none recorded.
Defining equationnone
Assumptions and scope
  • The smallest item support in an itemset over the largest. It lies in the unit interval, is one exactly when every item has the same support, and adding an item can only lower it, so a threshold on it prunes supersets safely in chapter 5’s sense.
  • It is a property of the item supports alone and says nothing about the itemset’s own support, so it discards an itemset for pairing a common item with a rare one, not for being rare.
Prior artnone recorded
Evidencelean/DataMiningAsObservation/CrossSupport.lean
Reviewednot yet reviewed; generated 2026-09-10 from records at the commits on the provenance page.
common itemrare itemcommon item ∩ rare item
The support of the rarer item over the support of the commoner one.

Equation

none

Conditions

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

Ledger

none

First stated

TSK chapter 5 on cross-support patterns, as chapter 5 section 5.5 of Data Mining as Observation states it.

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/CrossSupport.lean, theorems ratio_mem_unit, ratio_eq_one_iff, ratio_anti, at observation-data-mining f3914f0; what the check covers is stated in the book’s appendix C.

Used in

Data Mining as Observation chapters 5.

Related

Apriori principle; safe pruning; lift; multiple comparisons.

See also

Book equations stated beside the entry’s terms, not defining it: 5.3, 5.1.

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.

← cross-entropycross-validation →