Description
Return normalizer=sqrt(firstSize*secondSize) and score=intersection/normalizer.
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 normalizer=sqrt(firstSize*secondSize) and score=intersection/normalizer.
When to use this tool
Use Ochiai Binary Count Normalizer 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, firstSize, secondSize. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read normalizer, score. Use the output convention below.
Return normalizer=sqrt(firstSize*secondSize) and score=intersection/normalizer. Require positive integer sizes and feasible intersection count.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| intersection | Intersection | Required. Safe integer; minimum 0. |
| firstSize | First Size | Required. Safe integer; minimum 1. |
| secondSize | Second Size | Required. Safe integer; minimum 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| normalizer | Normalizer | Required. Finite number. |
| score | Score | Required. Finite number. |
{
"input": {
"intersection": 3,
"firstSize": 4,
"secondSize": 9
},
"output": {
"normalizer": 6,
"score": 0.5
}
}Limitations and assumptions
- This is the binary-count Ochiai normalizer, not a general real-vector cosine. Actual set membership, feature weighting, and empty-support conventions are not inferred.
- 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
- Dice Count Feasibility Residual
Return excess=max(0,intersection-min(leftSize,rightSize)), feasible when that is zero, and denominator=leftSize+rightSize.
- Dice Overlap Count Contribution
Return exact decimal numerator twice overlap and denominator firstSize+secondSize using BigInt, plus numeric dice.