detector instrument
| Definition | A scorer that calls a row an outlier, of four families reading distance from the mean, distance to neighbours, density relative to neighbours, or cluster membership. Chapter 10 section 10.1. |
|---|---|
| Example | A row 3.6 spreads from the mean is an outlier to the statistical detector and may be ordinary to the density detector. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id detector, kind instrument. |
| Status | no ledger row names this entry. Corrections: none recorded. |
| Defining equation | none |
| Assumptions and scope |
|
| Prior art | none recorded |
| Evidence | lean/DataMiningAsObservation/Outlier.lean, lean/DataMiningAsObservation/Mahalanobis.lean, lean/DataMiningAsObservation/Dbscan.lean |
| Reviewed | not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
none
Conditions
- A scorer that calls a row an outlier, of four families. The statistical detector reads distance from the mean in units of spread, the proximity detector reads distance to neighbours, the density detector reads density relative to neighbours, and the clustering detector reads membership. Each reads a coordinate the others discard.
- No detector of the data alone sees the observer’s outliers, the anti-hubs, because they are a property of the queries, and a detector’s positives are few by Chebyshev’s arithmetic.
Conditions are curated in entries.toml rather than read
from a record.
Ledger
none
First stated
Chapter 10 section 10.1 of Data Mining as Observation, after
TSK chapter 9, with the hierarchical typing in
turboquant-pro/turboquant_pro/anatomy.py:98-170.
Measurements
| Where the book states it | Numbers, as the book’s sources table records them | Source |
|---|---|---|
| chapter 10 section 10.1 | the four detector families | TSK 2e chapter 9 |
Failures and corrections
none
Invariance envelope
none declared
Machine checked
lean/DataMiningAsObservation/Outlier.lean,
theorems zscore_mean, zscore_affine,
outlier_iff, zscore_reflect,
chebyshev, at observation-data-mining f3914f0; what the
check covers is stated in the book’s appendix
C.
lean/DataMiningAsObservation/Mahalanobis.lean,
theorems dM2_nonneg, dM2_mean,
dM2_scale, dM2_eq_whitened,
dM2_antitone_in_variance, at observation-data-mining
f3914f0; what the check covers is stated in the book’s appendix
C.
lean/DataMiningAsObservation/Dbscan.lean,
theorems ball_mono, core_mono,
core_anti, reach_from_core,
noise_unreachable, at observation-data-mining f3914f0; what
the check covers is stated in the book’s appendix
C.
Used in
Data Mining as Observation chapters 3, 8, 10, 13.
Related
outlier; Mahalanobis distance; density; DBSCAN; anti-hub.
See also
Book equations stated beside the entry’s terms, not defining it: 0.33, 10.3, 9.1.
Ledger rows that cite the entry’s records without naming it: NEG-14.
Sources-table rows that share a record with the entry without naming it: chapter 10 section 10.3.
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.