Description
Calculate union=firstOnes+secondOnes-dot and score=dot/union after feasible nonnegative integer binary-count checks and 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.
Calculate union=firstOnes+secondOnes-dot and score=dot/union after feasible nonnegative integer binary-count checks and a positive union.
When to use this tool
Use Tanimoto Binary Dot Norm Identity 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 dot, firstOnes, secondOnes. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read union, score. Use the output convention below.
Calculate union=firstOnes+secondOnes-dot and score=dot/union after feasible nonnegative integer binary-count checks and a positive union.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| dot | Dot | Required. Safe integer; minimum 0. |
| firstOnes | First Ones | Required. Safe integer; minimum 0. |
| secondOnes | Second Ones | Required. Safe integer; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| union | Union | Required. Safe integer. |
| score | Score | Required. Finite number. |
{
"input": {
"dot": 3,
"firstOnes": 4,
"secondOnes": 5
},
"output": {
"union": 6,
"score": 0.5
}
}Limitations and assumptions
- Both-zero support is rejected. The supplied dot must represent joint ones; no binary vectors, weighting convention, or semantic relationship is verified.
- 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
- Cosine Dot Product Roundoff Clamp
Clamp cosine to minus one through one when it is within the supplied tolerance outside that interval.
- Cosine Norm Rescale Invariance Residual
Return cosine=dot/(firstNorm*secondNorm), scaledCosine=sign(firstScale*secondScale)*cosine, and their residual.