cross-support ratio concept
| Definition | The smallest item support in an itemset over the largest, with a threshold below which the itemset is discarded. Chapter 5. Also cross-support. |
|---|---|
| Example | An item in 2 percent of baskets paired with one in 40 percent has cross-support ratio 0.05. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id cross-support-ratio, kind concept. |
| Status | no ledger row names this entry. Corrections: none recorded. |
| Defining equation | none |
| Assumptions and scope |
|
| Prior art | none recorded |
| Evidence | lean/DataMiningAsObservation/CrossSupport.lean |
| Reviewed | not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
none
Conditions
- 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.
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.