Description
Require affinity in (0, 1] and return -ln(affinity) as distance.
Divergences and information densities compare probabilities on a common support. A weighted cell contribution and an unweighted logarithmic ratio differ, and zero-support cases require explicit limits.
Require affinity in (0, 1] and return -ln(affinity) as distance.
When to use this tool
Use Bhattacharyya Log Affinity Term when you need one precisely defined information-comparison term.
How to use the tool and how it works
- Enter affinity. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read distance. Use the output convention below.
Require affinity in (0, 1] and return -ln(affinity) as distance.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| affinity | Affinity | Required. Finite number; maximum 1; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| distance | Distance | Required. Finite number. |
{
"input": {
"affinity": 0.5
},
"output": {
"distance": 0.6931471805599453
}
}Limitations and assumptions
- This is the logarithm of a supplied complete Bhattacharyya affinity; a single symbol term is not automatically the full affinity and zero is rejected.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- 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. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Align and validate complete distributions before summing terms or interpreting a full divergence or dependence measure.
References
Similar or alternative tools
- Hellinger Affinity Symbol Term
Return sqrt(first × second) through separate square roots for affinity and half the squared difference of those roots for squaredDistanceTerm.
- Jensen Shannon One Bin Contribution
Validate first and second in [0, 1], use their mean as reference, and return half-weighted base-two relative-entropy terms, treating zero terms as zero.