From axioms over graphs to vectors, and back again: evaluating the properties of graph-based ontology embeddings

Abstract:

Several approaches have been developed that generate embeddings for Description Logic ontologies and use these embeddings in machine learning. One approach of generating ontologies embeddings is by first embedding the ontologies into a graph structure, i.e., introducing a set of nodes and edges for named entities and logical axioms, and then applying a graph embedding to embed the graph in R 𝑛 . Methods that embed ontologies in graphs (graph projections) have different formal properties related to the type of axioms they can utilize, whether the projections are invertible or not, and whether they can be applied to asserted axioms or their deductive closure. We analyze several graph projection methods that have been used to embed ontologies qualitatively and quantitatively, and we demonstrate the effect of the properties of graph projections on the performance of predicting axioms from ontology embeddings. We find that there are substantial differences between different projection methods, and both the projection of axioms into nodes and edges as well ontological choices in representing knowledge will impact the success of using ontology embeddings to predict axioms.

Method and results

The projections used in this analyses were:

• Onto2Graph projection
• Projection found in OWL2Vec*
• RDF rendering of OWL

The ontologies used were:

• Gene Ontology (GO)
• Food Ontology (FoodOn)

Repository overview

Provide an overview of the directory structure and files, for example:

├── README.md
├── environment.yml
├── src
│   ├── data
│   ├── projectors
└── use_cases
    ├── experiments
    ├── foodon
    │   ├── data
    │   └── models
    └── go
        ├── data
        └── models
 

Setting up

Dependencies

• Python 3.8
• Anaconda

Set up environment

git clone --recursive https://github.com/bio-ontology-research-group/ontology-graph-projections.git

cd ontology-graph-projections
conda env create -f environment.yml
conda activate projections

cd use_cases

Getting the data

The data is located in the use_cases directory. You will find the files use_cases/go/go_data.tar.gz for GO and use_cases/foodon/foodon_data.tar.gz for FoodOn. Uncompress the files with:

cd use_cases/go/
tar -xzvf go_data.tar.gz

and

cd use_cases/foodon/
tar -xzvf foodon_data.tar.gz

Running the model

To run the script, use the run_model.py script. The parameters are the following:

Parameter	Command line	Options
case	-case	go, foodon
graph	-g	taxonomy, owl2vec, onto2graph, rdf
kge model	-kge	transe, transr
root directory	-r	[case]/data
embedding dimension	-dim	64, 128, 256
margin	-margin	0.0, 0.2, 0.4
weight decay	-wd	0.0000, 0.0001, 0.0005
batch size	-bs	4096, 8192, 16834
learning rate	-lr	0.1, 0.01, 0.001
testing batch size	-tbs	8, 16
epochs	-e	1000, 2000, ...
device	-d	cpu, cuda
reduced subsumption	-rs	Train on ontology with some axioms $C \sqsubseteq D$ removed
reduced existential	-re	Train on ontology with some axioms $C \sqsubseteq \exists R.D$ removed
results file	-rd	name_of_results_csv_file.csv
testing file	-tf	name_of_testing_file.csv
test subsumption	-ts	Flag to test $C \sqsubseteq D$ axioms
test existential	-te	Flag to test $C \sqsubseteq \exists R.D$ axioms
test both quantifiers	-tbq	Flag to test axioms $C \sqsubseteq \exists R.D$ including $C \sqsubseteq \forall R.D$
only train	-otr	Flag to only perform training
only test	-ot	Flag to only perform testing

For example, to train the Gene Ontology reduced version with the taxonomy projection, we can run

python run_model.py -case go -g taxonomy -kge transe -r go/data -dim 64 -m 0.2 -wd 0.0001 -bs 4096 -lr 0.1 -tbs 8 -e 4000 -d cuda -rd results_tax_sub.csv -tf foodon/data/go_subsumption_closure_filtered.csv -ts -rs

The commands to run the experiments in the paper are located at use_cases/experiments