correlation concept
| Definition | The cosine of two centred columns, between minus one and one, unchanged by shifting or rescaling either. Its distance lives on the quotient that discards shift and scale. Chapter 0 section 0.6. Also correlat. |
|---|---|
| Example | Columns (1, 2, 3) and (2, 4, 6) have correlation 1, and (1, 2, 3) and (3, 2, 1) have correlation minus 1. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id correlation, 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/Correlation.lean |
| Reviewed | not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
none
Conditions
- The cosine of two centred columns. It lies between minus one and one, is one for a column against itself, is symmetric, and is unchanged by shifting or positively rescaling either column, so correlation distance lives on the quotient that discards shift and scale.
- Rank correlations read the order and discard the values, and a read distortion that correlates with a downstream ranking at 0.80 is a control and not a complete rank statistic, NEG-9.
Conditions are curated in entries.toml rather than read
from a record.
Ledger
none
First stated
Pearson, 1895, as chapter 0 section 0.6 and chapter 3 section 3.1 of
Data Mining as Observation read it, with the
radius-against-degree correlation in
the-angular-observer/README.md:135-139.
Measurements
| Where the book states it | Numbers, as the book’s sources table records them | Source |
|---|---|---|
| chapter 3 section 3.3 | radius against degree correlation 0.92 to 0.99 | the-angular-observer/README.md:135-139 |
Failures and corrections
none
Invariance envelope
none declared
Machine checked
lean/DataMiningAsObservation/Correlation.lean,
theorems abs_corr_le_one, corr_self,
cosine_comm, corr_comm,
center_shift, center_smul,
corr_shift, corr_smul, at
observation-data-mining f3914f0; what the check covers is stated in the
book’s appendix
C.
Used in
Data Mining as Observation primer S, chapters 0, 1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14.
Related
cosine; Spearman correlation; Kendall correlation; covariance matrix; quotient.
See also
Book equations stated beside the entry’s terms, not defining it: 0.1, 3.1, 0.18.
Ledger rows that cite the entry’s records without naming it: NEG-9.
Sources-table rows that share a record with the entry without naming it: chapter 6 section 6.4, chapter 8 section 8.5.
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.