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# Towards Understanding the Geometry of Knowledge Graph Embeddings
This is the code for generating the results in the paper "[Towards Understanding the Geometry of Knowledge Graph Embeddings](https://www.aclweb.org/anthology/P18-1012/)" to be presented at the 56th Annual Meeting of the Association for Computational Linguistics at Melbourne, July 15 to July 20, 2018.

## Required data format
The analysis requires pre-trained KG embeddings along with the KG triples data.
The KG triples data should be a pickle (python2.7) file named `"<dataset>.<method>.bin"`. It should contain the following key values:
  1.  `'train_subs'`: list of KG triples used for training, in (head_entity_index, tail_entity_index, relation_index) format.
  2.  `'valid_subs'`: list of KG triples used for validation, in (head_entity_index, tail_entity_index, relation_index) format.
  3.  `'test_subs'`: list of KG triples used for testing, in (head_entity_index, tail_entity_index, relation_index) format.
  4.  `'relations'`: list of KG relations.
  5.  `'entities'`: list of KG entities.
  
The KG embeddings should be stored as pickle (python2.7) file named `"<dataset>.<method>.n<no-of-negatives>.d<dimension>.p"`. It should contain following key values:
  1.  `'rNames'` : list of KG relations.
  2.  `'eNames'` : list of KG entities.
  3.  `'E'` : numpy array of size (numEntities X dimension) containing entity embeddings.
  4.  `'R'` : numpy array of size (numRelations X dimension) containing relation embeddings.
  5.  `'model'` : model name.
  6.  `'fpos test'` : ranks of head and tail entities obtained during link prediction. It is required for performance analysis. It should be a dictionary with relation index as keys, e.g. `{rel_id1 :{'head':[head_rank_1, head_rank_2, ...], 'tail':[tail_rank_1, tail_rank_2, ...]}}`.
  
  ## Running type analysis
  For running type analysis (Section 5.1 in the paper), please run the following command:
  1.  `python typeAnalysis.py -m <data-directory> -d <dataset-name> -g <conicity/length> --opdir <output-directory> --type <ent/rel>`
  2.  `python typeAnalysis.py -m <data-directory> -d <dataset-name> -g <conicity/length> --opdir <output-directory> --type <ent/rel> --result` (for generating the plots)
  
  ## Running negative analysis
  For running negative analysis (Section 5.2 in the paper), please run the following command:
  1.  `python negativeAnalysis.py -m <data-directory> -d <dataset-name> -g <conicity/length> --opdir <output-directory> --type <ent/rel>`
  2.  `python negativeAnalysis.py -m <data-directory> -d <dataset-name> -g <conicity/length> --opdir <output-directory> --type <ent/rel> --result` (for generating the plots)
  
  ## Running dimension analysis
  For running dimension analysis (Section 5.3 in the paper), please run the following command:
  1.  `python dimensionAnalysis.py -m <data-directory> -d <dataset-name> -g <conicity/length> --opdir <output-directory> --type <ent/rel>`
  2.  `python dimensionAnalysis.py -m <data-directory> -d <dataset-name> -g <conicity/length> --opdir <output-directory> --type <ent/rel> --result` (for generating the plots)
  
  ## Running performance analysis
  For running performance analysis (Section 5.4 in the paper), please run the following command:
  1.  `python perfAnalysis.py -m <data-directory> -d <dataset-name> -g <conicity/length> --opdir <output-directory> --type <ent/rel> -p <performance-file>`
  2.  `python perfAnalysis.py -m <data-directory> -d <dataset-name> -g <conicity/length> --opdir <output-directory> --type <ent/rel> --result -p <performance-file>` (for generating the plots)
  
      Here the `<performance-file>` is a pickled file containing performance of different models. It is a nested dictionary and `perf['<method>'][<dimension>][<numNegatives>]` should contain performance `{'MRR':<MRR-value>, 'MR':<MR-value>, 'Hits@10':<Hits@10-value>}` for `<method>` with vector size `<dimension>` and `<numNegatives>` number of negative samples.
  
  ## Citation
  If you find our work or this codebase useful, please cite us:
  ```
  @inproceedings{chandrahas-etal-2018-towards,
    title = "Towards Understanding the Geometry of Knowledge Graph Embeddings",
    author = "{Chandrahas}  and
      Sharma, Aditya  and
      Talukdar, Partha",
    booktitle = "Proceedings of the 56th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)",
    month = jul,
    year = "2018",
    address = "Melbourne, Australia",
    publisher = "Association for Computational Linguistics",
    url = "https://www.aclweb.org/anthology/P18-1012",
    pages = "122--131",
    }

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