Description
Return squaredNormTerm=weight*coordinate² with nonnegative weight.
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 squaredNormTerm=weight*coordinate² with nonnegative weight.
When to use this tool
Use Weighted Cosine Single Norm Term 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 coordinate, weight. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read squaredNormTerm. Use the output convention below.
Return squaredNormTerm=weight*coordinate² with nonnegative weight.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| coordinate | Coordinate | Required. Finite number. |
| weight | Supplied weight; interpretation follows the stated model rather than an inferred probability. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| squaredNormTerm | Squared Norm Term | Required. Finite number. |
{
"input": {
"coordinate": -3,
"weight": 2
},
"output": {
"squaredNormTerm": 18
}
}Limitations and assumptions
- This is one weighted squared-norm contribution, not a complete cosine similarity. Coordinate units and weight convention must match the eventual norm and dot-product calculation.
- 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 Norm Rescale Invariance Residual
Return cosine=dot/(firstNorm*secondNorm), scaledCosine=sign(firstScale*secondScale)*cosine, and their residual.
- Similarity: Cosine Zero Norm Policy
Compute cosine similarity with an explicit reject/zero undefined-norm policy and a retained defined flag; zero is not silently treated as a measured cosine.