Tensor Factorization for Multi-relational Learning

Nickel, Maximilian; Tresp, Volker

doi:10.1007/978-3-642-40994-3_40

Cited by 128 publications

(129 citation statements)

References 9 publications

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“…From [4], we get idea from the relation network learning that tensor are applying for provide a way to represent multiple relations between the nodes. We expand the adjacent matrix A that stores the links information to an graph information tensor that stores how many links between the nodes.…”

Section: Graph Information Tensormentioning

confidence: 99%

Metric learning with graph information

Pan¹

2017

AIP Conference Proceedings

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Abstract. The vast majority of metric learning approaches are dedicated to be applied on data described by feature vectors, with some notable exceptions such as times series and trees or graphs. Many real-world networks are described by both connectivity information and features for every node. The objective of this paper is to propose better model and understand these networks. We present metric learning with Graph Information (MLGI), an algorithm for learning a Mahalanobis distance metric with the connectivity structure information of the links between nodes.

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Section: Graph Information Tensormentioning

confidence: 99%

Metric learning with graph information

Pan¹

2017

AIP Conference Proceedings

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“…As in [27] we can exploit the following property of the singular value decomposition (SVD) regarding the Kronecker product of two matrices [28]…”

Section: Collective Factorization Of Type-constrained Relationsmentioning

confidence: 99%

“…The use of factorization approaches to predict ground atoms was pioneered in [17]; [1], [18], [19], and [20] applied tensor models for this task, where [1] introduced the RESCAL model. This model was the basis of many recent published works: [21] introduced non-negative constraints, [22] presented a logistic factorization and [20] explicitly models the 2nd and 3rd order interactions. [23] introduced neural tensor networks that includes a RESCAL factorization and [2] used a neural tensor decomposition for defining graph-based priors during construction of the Google Knowledge Vault.…”

Section: Introductionmentioning

confidence: 99%

Large-scale factorization of type-constrained multi-relational data

Krompaß

Nickel

Tresp

2014

2014 International Conference on Data Science and Advanced Analytics (DSAA)

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Abstract-The statistical modeling of large multi-relational datasets has increasingly gained attention in recent years. Typical applications involve large knowledge bases like DBpedia, Freebase, YAGO and the recently introduced Google Knowledge Graph that contain millions of entities, hundreds and thousands of relations, and billions of relational tuples. Collective factorization methods have been shown to scale up to these large multirelational datasets, in particular in form of tensor approaches that can exploit the highly scalable alternating least squares (ALS) algorithms for calculating the factors. In this paper we extend the recently proposed state-of-the-art RESCAL tensor factorization to consider relational type-constraints. Relational type-constraints explicitly define the logic of relations by excluding entities from the subject or object role. In addition we will show that in absence of prior knowledge about type-constraints, local closedworld assumptions can be approximated for each relation by ignoring unobserved subject or object entities in a relation. In our experiments on representative large datasets (Cora, DBpedia), that contain up to millions of entities and hundreds of typeconstrained relations, we show that the proposed approach is scalable. It further significantly outperforms RESCAL without type-constraints in both, runtime and prediction quality.

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“…The big advantage of the proposed method is that R ( * ) can now be derived by simply projecting X ( * ) into the latent space that is spanned by the RESCAL factor matrix A. This can be done very efficiently: Consider the ALS updates derived in [17]. Essentially what is needed is to calculate the latent matrix for the materialized view, i.e., R ( * ) as…”

Section: Querying Factorized Probabilistic Databasesmentioning

confidence: 99%

“…T explicitly, what is both slow and impractical [18] and pattern-based approaches (such as stochastic gradient descent) have not proven to be effective with a Bernoulli cost function.…”

Section: Cost Functionsmentioning

confidence: 99%

Querying Factorized Probabilistic Triple Databases

Krompaβ

Nickel

Tresp

2014

Lecture Notes in Computer Science

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Abstract. An increasing amount of data is becoming available in the form of large triple stores, with the Semantic Web's linked open data cloud (LOD) as one of the most prominent examples. Data quality and completeness are key issues in many community-generated data stores, like LOD, which motivates probabilistic and statistical approaches to data representation, reasoning and querying. In this paper we address the issue from the perspective of probabilistic databases, which account for uncertainty in the data via a probability distribution over all database instances. We obtain a highly compressed representation using the recently developed RESCAL approach and demonstrate experimentally that efficient querying can be obtained by exploiting inherent features of RESCAL via sub-query approximations of deterministic views.

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Tensor Factorization for Multi-relational Learning

Cited by 128 publications

References 9 publications

Metric learning with graph information

Metric learning with graph information

Large-scale factorization of type-constrained multi-relational data

Querying Factorized Probabilistic Triple Databases

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