Jaccard concept
| Definition | The size of the intersection of two sets over the size of their union, between zero and one, zero exactly when the sets are disjoint, which discards joint absence. Chapter 0 section 0.6 and chapter 3. |
|---|---|
| Example | Sets {a, b, c} and {b, c, d} share 2 of 4 elements, a Jaccard coefficient of 0.5. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id jaccard, kind concept. |
| Status | no ledger row names this entry. Corrections: none recorded. |
| Defining equation | none |
| Assumptions and scope |
|
| Prior art | none recorded |
| Evidence | lean/DataMiningAsObservation/Jaccard.lean |
| Reviewed | not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
none
Conditions
- The size of the intersection of two sets over the size of their union, between zero and one, one for a nonempty set against itself, symmetric, and zero exactly when the sets are disjoint. A subset’s coefficient is its share of the larger set.
- It reads nothing outside the union, so its distance lives on the quotient that discards joint absence, which is the right quotient for a consumer that reads presence and the wrong one for a consumer that reads counts.
Conditions are curated in entries.toml rather than read
from a record.
Ledger
none
First stated
Jaccard, the distribution of the flora in the alpine zone, 1912, as chapter 0 section 0.6 and chapter 3 section 3.1 of Data Mining as Observation read it.
Measurements
none
Failures and corrections
none
Invariance envelope
none declared
Machine checked
lean/DataMiningAsObservation/Jaccard.lean,
theorems jaccard_nonneg, jaccard_le_one,
jaccard_self, jaccard_comm,
jaccard_eq_zero_iff, jaccard_subset, at
observation-data-mining f3914f0; what the check covers is stated in the
book’s appendix
C.
Used in
Data Mining as Observation chapters 0, 3.
Related
cosine; quotient; bag of words; Euclidean distance; itemset.
See also
Book equations stated beside the entry’s terms, not defining it: 0.1, 3.1.
Sources-table rows that share a record with the entry without naming it: chapter 3 section 3.2.
Status
Generated 2026-09-10 by encyclopedia/generate.py; book
at observation-data-mining f3914f0; the commit of every record is listed
in the encyclopedia’s provenance.