Triple
T4110981
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Albert W. Tucker |
E88569
|
entity |
| Predicate | knownFor |
P22
|
FINISHED |
| Object |
Tucker decomposition in multilinear algebra
Tucker decomposition in multilinear algebra is a form of higher-order principal component analysis that factorizes a tensor into a core tensor multiplied by factor matrices along each mode, enabling dimensionality reduction and structure discovery in multiway data.
|
E413306
|
NE FINISHED |
How this triple was built (4 steps)
Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.
NER
Named-entity recognition
gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Tucker decomposition in multilinear algebra | Statement: [Albert W. Tucker, knownFor, Tucker decomposition in multilinear algebra]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Tucker decomposition in multilinear algebra Context triple: [Albert W. Tucker, knownFor, Tucker decomposition in multilinear algebra]
-
A.
Kailath factorization in linear systems
Kailath factorization in linear systems is a matrix factorization technique used in control and signal processing to efficiently analyze and solve linear dynamical systems.
-
B.
Schmidt decomposition
The Schmidt decomposition is a mathematical technique in functional analysis and quantum information theory that expresses a bipartite vector (such as a quantum state) as a sum of orthogonal product states with nonnegative coefficients, revealing its entanglement structure.
-
C.
Clebsch–Aronhold invariants
The Clebsch–Aronhold invariants are classical algebraic invariants associated with binary forms, particularly quartic forms, that play a key role in invariant theory and the classification of algebraic curves.
-
D.
SVD
SVD is the abbreviation for the Special Victims Division, a specialized police unit that investigates sensitive crimes such as sexual offenses and crimes against vulnerable victims.
-
E.
Kronecker product
The Kronecker product is a matrix operation that forms a large block matrix from two smaller matrices and is widely used in linear algebra, quantum computing, and signal processing.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg
Description generation
gpt-5.1
Instruction
Generate a one-sentence description of the target entity. You are given a context triple in the form (subject, predicate, object), where the object is the target entity. # Instructions Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. Avoid repeating the information from the triple, unless really essential. # Response Format Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Tucker decomposition in multilinear algebra Triple: [Albert W. Tucker, knownFor, Tucker decomposition in multilinear algebra]
Generated description
Tucker decomposition in multilinear algebra is a form of higher-order principal component analysis that factorizes a tensor into a core tensor multiplied by factor matrices along each mode, enabling dimensionality reduction and structure discovery in multiway data.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Tucker decomposition in multilinear algebra Target entity description: Tucker decomposition in multilinear algebra is a form of higher-order principal component analysis that factorizes a tensor into a core tensor multiplied by factor matrices along each mode, enabling dimensionality reduction and structure discovery in multiway data.
-
A.
Kailath factorization in linear systems
Kailath factorization in linear systems is a matrix factorization technique used in control and signal processing to efficiently analyze and solve linear dynamical systems.
-
B.
Schmidt decomposition
The Schmidt decomposition is a mathematical technique in functional analysis and quantum information theory that expresses a bipartite vector (such as a quantum state) as a sum of orthogonal product states with nonnegative coefficients, revealing its entanglement structure.
-
C.
Clebsch–Aronhold invariants
The Clebsch–Aronhold invariants are classical algebraic invariants associated with binary forms, particularly quartic forms, that play a key role in invariant theory and the classification of algebraic curves.
-
D.
SVD
SVD is the abbreviation for the Special Victims Division, a specialized police unit that investigates sensitive crimes such as sexual offenses and crimes against vulnerable victims.
-
E.
Kronecker product
The Kronecker product is a matrix operation that forms a large block matrix from two smaller matrices and is widely used in linear algebra, quantum computing, and signal processing.
- F. None of above. chosen
Provenance (5 batches)
The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.
| Step | Stage | Batch ID | Status | When |
|---|---|---|---|---|
| creating | Elicitation | batch_69aed9484fb881909146f4c772ad277c |
completed | March 9, 2026, 2:29 p.m. |
| NER | Named-entity recognition | batch_69af01dd7140819093d3332eb94a357c |
completed | March 9, 2026, 5:22 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69b56b88228c8190ae971b54148e38a9 |
completed | March 14, 2026, 2:07 p.m. |
| NEDg | Description generation | batch_69b56cbfbe608190a65bfe1efee2317a |
completed | March 14, 2026, 2:12 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69b56d12caa88190a766ceccc5d158c4 |
completed | March 14, 2026, 2:13 p.m. |
Created at: March 9, 2026, 3:41 p.m.