latent semantic analysis instrument
| Definition | The truncated singular value decomposition of the term-document matrix, ordinarily uncentred, which coincides with principal components on documents only after centring. Chapter 12. Also latent semantic. |
|---|---|
| Example | A term-document matrix of 20000 terms by 5000 documents reduced to 100 singular components gives each document 100 coordinates. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id latent-semantic-analysis, kind instrument. |
| Status | no ledger row names this entry. Corrections: none recorded. |
| Defining equation | none |
| Assumptions and scope |
|
| Prior art | none recorded |
| Evidence | geometric-observation/chapters/ch10_the_blind_probe.md:100-118, geometric-observation/claims/LEDGER.md, lean/DataMiningAsObservation/PCA.lean, lean/DataMiningAsObservation/ExplainedVariance.lean, lean/DataMiningAsObservation/TFIDF.lean |
| Reviewed | semantic review 2026-09-06; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
none
Conditions
- The truncated singular value decomposition of the term-document matrix, ordinarily uncentred, with the top components kept. It coincides with principal components on documents only after the matrix is centred, or under an explicitly uncentred convention, and the fraction of squared singular values kept grows with the components kept and reaches one at full rank.
- It is the identity reader on term-document variance, and the components it keeps are the directions of largest variance whether or not the consumer reads them. The non-oracle test fit a frozen embedding of 100 components on the training split only and recovered the reader blind.
Conditions are curated in entries.toml rather than read
from a record.
Ledger
none
First stated
Deerwester, Dumais, Furnas, Landauer, and Harshman, indexing by
latent semantic analysis, 1990, as chapter 12 section 12.1 of Data
Mining as Observation reads it, with the program’s frozen embedding
in
geometric-observation/chapters/ch10_the_blind_probe.md:100-118.
Measurements
| Where the book states it | Numbers, as the book’s sources table records them | Source |
|---|---|---|
| chapter 12 section 12.3 | 041 non-oracle, frozen LSA TF-IDF to SVD 100 train-only, AUROC 0.975 vs 0.910, flip tied, magnitude overshot, partial | geometric-observation/chapters/ch10_the_blind_probe.md:100-118;
geometric-observation/claims/LEDGER.md
row GO-B-blind 041 |
Failures and corrections
none
Invariance envelope
none declared
Machine checked
lean/DataMiningAsObservation/PCA.lean,
theorems varAlong_basis, varAlong_le,
varAlong_ge, dropped_eq,
dropped_nonneg, at observation-data-mining f3914f0; what
the check covers is stated in the book’s appendix
C.
lean/DataMiningAsObservation/ExplainedVariance.lean,
theorems explained_mem_unit, explained_mono,
explained_full, retained_identity,
retained_example, at observation-data-mining f3914f0; what
the check covers is stated in the book’s appendix
C.
lean/DataMiningAsObservation/TFIDF.lean,
theorems weight_everywhere, weight_nonneg,
weight_antitone, tf_mem_unit, at
observation-data-mining f3914f0; what the check covers is stated in the
book’s appendix
C.
Used in
Data Mining as Observation primer L, chapters 0, 12.
Related
TF-IDF; principal component analysis; explained variance; bag of words; blind probe.
See also
Book equations stated beside the entry’s terms, not defining it: 0.36, 0.5, 4.2.
Ledger rows that cite the entry’s records without naming it: GO-B-legal (035→036).
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.