Description
Return derivative=-intersection/union² for nonnegative intersection within a positive union.
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 derivative=-intersection/union² for nonnegative intersection within a positive union.
When to use this tool
Use Jaccard Single False Positive Sensitivity 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. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read derivative. Use the output convention below.
Return derivative=-intersection/union² for nonnegative intersection within a positive union.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| intersection | Intersection | Required. Finite number; minimum 0. |
| union | Union | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| derivative | Derivative | Required. Finite number. |
{
"input": {
"intersection": 3,
"union": 5
},
"output": {
"derivative": -0.12
}
}Limitations and assumptions
- This holds intersection fixed while varying the denominator continuously. It is not the exact finite score change from one added item or a data-derived estimate of false-positive sensitivity.
- 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
- Similarity: Dice Jaccard Scalar Crosswalk
Crosswalk compatible set Dice and Jaccard scalar scores using their exact algebraic relation, preserving which score is the target.
- Similarity: Jaccard Empty Pair Policy
Compute cardinality-based Jaccard similarity with explicit zero/one empty-union convention and a retained defined flag.