# Notes on: Joulin, A., Grave, E., Bojanowski, P., Nickel, M., & Mikolov, T. (2017): Fast linear model for knowledge graph embeddings

## Overview

- Models subject-relation-object triples
- Can be used for the following problems:
, i.e. predicting object from subject-relation pair which uses scoring function:

, i.e. predicting relation between two entities, which uses scoring function:

- Only captures co-occurence between entities and relations
- NOT suitable for "implicit" relations, i.e. relations can occur from multiple edges (i.e. the existence of some relation between and depends on a path between and which is longer than just one edge)
- Might still provide useful representation of triplets as input to other predictive algorithms

## Notation

- denotes object / entity
- denotes relation
- denotes subject (which also is in entity)
- denotes vector for an
*input* - denotes the vector representation for the
*output*