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.