Jaccard Distance One Intersection Update Tool

Description

Update Jaccard distance using supplied intersection and union changes.

Discrete distances depend on the representation of symbols, sets and counts. A local mismatch or count update assumes the surrounding sequence or set bookkeeping is already correct.

Update Jaccard distance using supplied intersection and union changes.

When to use this tool

Use Jaccard Distance One Intersection Update when checking a supplied discrete-distance contribution or update.

How to use the tool and how it works

Enter intersection, union, intersectionDelta, unionDelta. 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.

Update Jaccard distance using supplied intersection and union changes. Require initial and updated whole counts with union >= 1 and intersection in [0,union]; distance = 1-updatedIntersection/updatedUnion.^[1]

Input field	Meaning and units	Accepted input
intersection	Intersection	Required. Safe integer; minimum 0.
union	Union	Required. Safe integer; minimum 1.
intersectionDelta	Intersection Delta	Required. Safe integer.
unionDelta	Union Delta	Required. Safe integer.

Output field	Interpretation	Returned shape
distance	Distance	Required. Finite number.

json

{
  "input": {
    "intersection": 2,
    "union": 5,
    "intersectionDelta": 1,
    "unionDelta": 0
  },
  "output": {
    "distance": 0.4
  }
}

Limitations and assumptions

The deltas do not prove that any actual set operation produced those counts.
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

Use the full sequences or sets to establish the original distance and actual operation before applying a local update.

References

Calculation and input contract: distance/jaccard-distance-one-intersection-update — tool.io

Similar or alternative tools

Hamming Distance Single Symbol Update
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Distance: Discrete Symbol Mismatch Cost
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