Description
Return before=intersection/union and after=(intersection+1 when common, otherwise intersection)/(union+1), plus delta=after-before.
A similarity term depends on the comparison universe, missing-value policy, treatment of repeated features, and normalization. A score can also have a caller-selected value when its mathematical denominator vanishes. Those conventions matter before interpreting a threshold or comparing methods.
Return before=intersection/union and after=(intersection+1 when common, otherwise intersection)/(union+1), plus delta=after-before.
When to use this tool
Use Jaccard Union One Item Delta when you need this particular comparison term, normalization, domain condition, or empty-result policy in a larger matching workflow.
How to use the tool and how it works
- Enter intersection, union, common. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read before, after, delta. Use the output convention below.
Return before=intersection/union and after=(intersection+1 when common, otherwise intersection)/(union+1), plus delta=after-before. Require positive integer union and feasible intersection.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| intersection | Intersection | Required. Safe integer; minimum 0. |
| union | Union | Required. Safe integer; minimum 1. |
| common | Common | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| before | Before | Required. Finite number. |
| after | After | Required. Finite number. |
| delta | Delta | Required. Finite number. |
{
"input": {
"intersection": 1,
"union": 2,
"common": false
},
"output": {
"before": 0.5,
"after": 0.3333333333333333,
"delta": -0.16666666666666669
}
}Limitations and assumptions
- The operation models one new union item with supplied common-membership status. It does not verify novelty, edit actual sets, or estimate real false-positive rates.
- The field tables state structural bounds; the mechanics also specify cross-field constraints. Malformed inputs and unsupported domains cause errors. A successful false flag, empty branch value, or zero placeholder has the meaning stated above and is distinct from an input error.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Signed zero is exported as zero.
Alternative or Complementary methods
Compare methods only after aligning feature definitions, missingness, empty policies, multiplicities, and normalizers. Use a complete comparison when the tool returns only one contribution or count check.
References
Similar or alternative tools
- Weighted Jaccard Zero Union Policy
Return score=intersection/union when union is positive or supplied emptyScore when zero, and return empty.
- Similarity: Dice Jaccard Scalar Crosswalk
Crosswalk compatible set Dice and Jaccard scalar scores using their exact algebraic relation, preserving which score is the target.