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

Table of Contents

Overview

  • Models subject-relation-object triples joulin17_fast_linear_model_knowl_graph_embed_29e692067ce712b91a2a8e0e47f896ae9311f0d5.png
  • Can be used for the following problems:
    • joulin17_fast_linear_model_knowl_graph_embed_f7288078595113f97985f3a16e7312fb5cfe808d.png, i.e. predicting object from subject-relation pair which uses scoring function:

      joulin17_fast_linear_model_knowl_graph_embed_632b10e52a76dcdd5fb2c1b6f26819b6197e663f.png

    • joulin17_fast_linear_model_knowl_graph_embed_c2667c86ab1c9d8a358bdf5dfbc38a151623469b.png, i.e. predicting relation between two entities, which uses scoring function:

      joulin17_fast_linear_model_knowl_graph_embed_7e47522b380fcc52af03b949ac3a594c9f294b4e.png

  • 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 joulin17_fast_linear_model_knowl_graph_embed_b4bc85fbe6b1085924f1ba268e01893b52ddad89.png between joulin17_fast_linear_model_knowl_graph_embed_eaac7646cb022aa963b396c0e936a271d8f5e34f.png and joulin17_fast_linear_model_knowl_graph_embed_fefe9e556d399665a26a37824ec578cbffb0cabe.png depends on a path between joulin17_fast_linear_model_knowl_graph_embed_eaac7646cb022aa963b396c0e936a271d8f5e34f.png and joulin17_fast_linear_model_knowl_graph_embed_fefe9e556d399665a26a37824ec578cbffb0cabe.png which is longer than just one edge)
    • Might still provide useful representation of joulin17_fast_linear_model_knowl_graph_embed_29e692067ce712b91a2a8e0e47f896ae9311f0d5.png triplets as input to other predictive algorithms

Notation

  • joulin17_fast_linear_model_knowl_graph_embed_fefe9e556d399665a26a37824ec578cbffb0cabe.png denotes object / entity
  • joulin17_fast_linear_model_knowl_graph_embed_b4bc85fbe6b1085924f1ba268e01893b52ddad89.png denotes relation
  • joulin17_fast_linear_model_knowl_graph_embed_eaac7646cb022aa963b396c0e936a271d8f5e34f.png denotes subject (which also is in entity)
  • joulin17_fast_linear_model_knowl_graph_embed_ebac26f7eba81eb516f423f028596d8e6018aa7a.png denotes vector for an input
  • joulin17_fast_linear_model_knowl_graph_embed_fe480f547555026d210b55b5d4ef758235f32832.png denotes the vector representation for the output