Entities and relations are represented in a real valued point -wise euclidean space . The various space for projection are shown in the figure

Point-Wise Space 

Entities and relations are represented in a complex space, $h, t, r \in \mathcal{C}^d$

Complex Vector Space

Uncertainties in entity and relations are modeled using gaussian distribution. Entities and relations are embedded into multi-dimensional gaussian distribution function ,$\mathcal{H} \sim \mathcal{N}(\mu_h,\Sigma_h)  and  \mathcal{T}(\mu_t,\Sigma_t)$

Mean vector u represents entities and relations position.

$\Sigma$ represents entities and relation’s (un)certainties.


Gaussian Distribution

Representation of knowledge in manifold space. Sphere as a manifold embedding is shown in figure.


Manifold and Group

The space where entities and relations are represented after analysis. Representation space is also called embedding space. The embedding space should satisfy three conditions differentiability, calculation possibility, and definability of a scoring function. The representation space can be categorized into

 - Point-Wise Space
 - Complex Vector Space
 - Gaussian Distribution
 - Manifold and Group:


San Jose State University

Knowledge representation learning(KRL) maps entities and relations onto a low dimensional vector space by capturing its semantic meaning. KRL is also called multi-relation learning or statistical relational learning. The recent advancement in distributed representation learning can be categorized into four scopes

 - Representation Space 
 - Scoring Function 
 - Encoding Models 
 - Embedding with Auxiliary Information


Knowledge Representation Learning /Knowledge Graph Embedding

A Survey on Knowledge Graphs: Representation, Acquisition and Applications

KRL model will answer the following four questions

1. ” Which representation space to choose?”
2. ”How to measure the plausibility of triplets in a specific space?”
3. “Which encoding model to use for modeling relational interaction ?”
4. ”Whether to utilize auxiliary information?”


KRL Model 

Representation Space 

Scoring function is used to measure the credibility of facts, it is also referred to as energy function There are two types of scoring functions to measure the plausibility of facts.

 - Distance-based Scoring Function
 - Semantic Matching


Scoring Function

Various architecture models are used to capture the interaction between entities and relations.

 - Linear/Bilinear Models
 - Factorization Models
 - Neural Networks
 - Convolutional Neural Networks
 - Recurrent Neural Networks
 - Transformers
 - Graph Neural Networks (GNNs)


Encoding Models

In this form of knowledge representation extra information like text descriptions, type constraints, visual information ,relational paths along with knowledge graphs are used to learn embeddings. The external information needed can be categorized into

 - Textual Description
 - Type Information
 - Visual Information
 - Uncertain Information


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