MétaCan
Menu
Back to cohort
Record W2003787220 · doi:10.1002/cem.665

An index formalism that generalizes the capabilities of matrix notation and algebra to n‐way arrays

2001· article· en· W2003787220 on OpenAlexafffund
Richard A. Harshman

Bibliographic record

VenueJournal of Chemometrics · 2001
Typearticle
Languageen
FieldMathematics
TopicTensor decomposition and applications
Canadian institutionsWestern University
FundersNatural Sciences and Engineering Research Council of CanadaKorea Institute of Energy Research
KeywordsNotationFormalism (music)Algebra over a fieldComputer scienceMatrix (chemical analysis)Context (archaeology)Matrix algebraTheoretical computer scienceMathematicsArithmeticPure mathematicsPhysics

Abstract

fetched live from OpenAlex

Abstract The capabilities of matrix notation and algebra are generalized to n‐way arrays. The resulting language seems easy to use; all the capabilities of matrix notation are retained and most carry over naturally to the n‐way context. For example, one can multiply a three‐way array times a four‐way array to obtain a three‐way product. Many of the language's key characteristics are based on the rules of tensor notation and algebra. The most important example of this is probably the incorporation of subscript/index‐related information into both the names of array objects and the rules used to operate on them. Some topics that emerge are relatively unexplored, such as inverses of n‐way arrays; these might prove interesting for future theoretical study. Copyright © 2001 John Wiley & Sons, Ltd.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

How this classification was reachedexpand

Full frame machine prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.

metaresearch head score (Codex)0.003
metaresearch head score (Gemma)0.004
Version: metacan-v3-hybrid-931329e0061cValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Methods · Consensus signal: Methods
Teacher disagreement score0.005
Threshold uncertainty score0.016

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0030.004
Meta-epidemiology (narrow)0.0010.000
Meta-epidemiology (broad)0.0010.002
Bibliometrics0.0020.002
Science and technology studies0.0010.003
Scholarly communication0.0040.008
Open science0.0020.003
Research integrity0.0010.002
Insufficient payload (model declined to judge)0.0050.002

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.046
GPT teacher head0.337
Teacher spread0.292 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it

Classification

machine, unvalidated

Machine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.

The models applied no category: nothing in the taxonomy fit this work.
Study designTheoretical or conceptual
Domainnot available
GenreMethods

How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".

Quick stats

Citations38
Published2001
Admission routes2
Has abstractyes

Explore more

Same venueJournal of ChemometricsSame topicTensor decomposition and applicationsFrench-language works237,207