classifier concept

Definition	A consumer that produces a score per row and turns it into a decision with a threshold. Chapter 6.
Example	A score of 0.7 against a threshold of 0.5 is a positive decision, and raising the threshold to 0.8 flips it.
Book	Data Mining as Observation, draft 0.2, commit `f3914f0`; entry id `classifier`, kind concept.
Status	measures [predicted]. Corrections: none recorded.
Defining equation	Book equation 6.1.
Assumptions and scope	A consumer that produces a score per row and turns it into a decision with a threshold. For a linear classifier the sensitivity is the link’s slope times the weight direction, so the read operator is the workload mean of the squared slope times the outer product of the weights, sends every vector to a multiple of the weights, and reads nothing orthogonal to them. The score is affine, so chapter 0’s exact quotient applies before the link. The whale clan classifier is the flip’s classifier case, held-out AUROC 0.934 against 0.883 for a code that reconstructs twice as well.
Prior art	none recorded
Evidence	`geometric-observation/claims/LEDGER.md:120`, `lean/DataMiningAsObservation/Classifier.lean`
Reviewed	not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page.

A score per row and a threshold that turns it into a decision.

Equation

Book equation 6.1.

\[s(x)=w\cdot x+b,\qquad P_C=\mathbb E\big[\sigma'(s)^{2}\big]\,w\,w^{\top},\qquad \operatorname{rank}P_C=1.\]

Conditions

A consumer that produces a score per row and turns it into a decision with a threshold. For a linear classifier the sensitivity is the link’s slope times the weight direction, so the read operator is the workload mean of the squared slope times the outer product of the weights, sends every vector to a multiple of the weights, and reads nothing orthogonal to them.
The score is affine, so chapter 0’s exact quotient applies before the link. The whale clan classifier is the flip’s classifier case, held-out AUROC 0.934 against 0.883 for a code that reconstructs twice as well.

Conditions are curated in entries.toml rather than read from a record.

Ledger

measures. GO-B-whale (038) [predicted]. Sperm-whale coda dialect (DSWP/Sharma 2024), Clan classifier — cetacean communication; promotes the exploratory (A2) verdict to a sealed flip geometric-observation/claims/LEDGER.md:120.

First stated

Chapter 6 section 6.1 of Data Mining as Observation, with the classifier row of Volume 14’s consumer table and the whale clan classifier of ledger row GO-B-whale.

Measurements

none

Failures and corrections

none

Invariance envelope

none declared

Machine checked

lean/DataMiningAsObservation/Classifier.lean, theorems readOp_classifier, readOp_classifier_mulVec, readOp_classifier_orth, score_orth, at observation-data-mining f3914f0; what the check covers is stated in the book’s appendix C.

Used in

Data Mining as Observation primers L and S, chapters 0, 1, 2, 4, 5, 6, 7, 8, 10, 11, 12, 14.

consumer; read operator; threshold; decision boundary; margin.

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.

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