Description
Inspect a supplied normalized dot product’s deviation from orthogonality; no vectors are inferred.
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.
Inspect a supplied normalized dot product’s deviation from orthogonality; no vectors are inferred.
When to use this tool
Use Cosine Orthogonal Residual 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 cosine. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read absoluteCosine, squaredProjectionFraction, orthogonal. Inspect orthogonal before interpreting the associated values.
Return absoluteCosine, squaredProjectionFraction=cosine², and orthogonal only for exact zero, requiring cosine within minus one through one.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| cosine | Cosine | Required. Finite number; minimum -1; maximum 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| absoluteCosine | Absolute Cosine | Required. Finite number. |
| squaredProjectionFraction | Squared Projection Fraction | Required. Finite number. |
| orthogonal | Orthogonal | Required. Boolean. |
{
"input": {
"cosine": 0.6
},
"output": {
"absoluteCosine": 0.6,
"squaredProjectionFraction": 0.36,
"orthogonal": false
}
}Limitations and assumptions
- No tolerance or underlying-vector validation is applied. The projection interpretation assumes a genuine normalized vector angle, not an arbitrary score with similar range.
- 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.
- Cosine Antiparallel Negative Score Label
Return negative for score<0 and antiparallel when abs(score+1)<=tolerance.