Knowledge Graph Embedding

These models interpret relations as geometric translations in the embedding space. For a true triple (head, relation, tail), the embedding of the head entity plus the relation vector should approximately equal the tail entity embedding.

• TransE: The foundational model where h + r ≈ t. Highly efficient but struggles with complex 1-to-N relations.
• TransR: Projects entities into a relation-specific space before translation, capturing diverse relational patterns.
• RotatE: Models relations as rotations in complex space, naturally capturing symmetry, inversion, and composition patterns common in biological pathways.

These models use bilinear tensor products to measure the compatibility of entity-relation-entity triples, capturing richer latent semantics than purely translational approaches.

• RESCAL: A bilinear model where each relation is a full matrix capturing pairwise interactions between all latent dimensions. Powerful but parameter-heavy.
• DistMult: A diagonalized simplification of RESCAL, reducing parameters but limiting to symmetric relations only.
• ComplEx: Extends DistMult into complex-valued space, enabling the modeling of asymmetric relations (e.g., treats vs treated_by) critical for drug-target interactions.

Modern approaches use message-passing neural networks to generate embeddings by aggregating information from a node's multi-hop neighborhood, capturing the full graph topology.

• R-GCN (Relational Graph Convolutional Network): Applies relation-specific weight matrices during neighbor aggregation, distinguishing between different edge types like binds_to and catalyzes.
• CompGCN: A compositional operator that jointly embeds entities and relations, reducing parameter explosion while maintaining expressivity.
• These encoders are inductive, meaning they can generate embeddings for previously unseen entities (e.g., a newly discovered gene) without retraining.

Training knowledge graph embeddings requires contrasting true triples against synthetically generated false triples. The sampling strategy critically impacts embedding quality.

• Uniform Negative Sampling: Randomly corrupts the head or tail entity. Fast but generates many trivial negatives that don't help the model learn.
• Bernoulli Sampling: Adjusts corruption probability based on relation cardinality to avoid generating false negatives in 1-to-many relations.
• Adversarial Sampling: Dynamically selects high-scoring false triples that the current model finds plausible, focusing learning on hard negatives near the decision boundary.

The primary downstream task: predicting missing edges in a biomedical knowledge graph to generate mechanistic hypotheses.

• Drug Repurposing: Predicts novel treats edges between existing drugs and diseases by scoring all drug-disease pairs.
• Target Discovery: Identifies unlinked proteins that are likely associated_with a disease pathway based on their embedding proximity.
• Polypharmacy Side Effects: Predicts adverse causes edges for drug combinations by modeling the joint embedding of two drug entities and their shared protein targets.

Knowledge graph embeddings serve as a structured prior that regularizes and enriches purely data-driven multi-omics models.

• Embedding Concatenation: The KG embedding of a gene is concatenated with its expression vector before input to a classifier, providing network context.
• Graph-Regularized Autoencoders: The autoencoder's latent space is constrained so that genes with similar KG embeddings (e.g., same pathway) have similar latent representations.
• Attention-Based Fusion: Cross-modal attention layers use KG-derived entity embeddings as a key-value context when processing transcriptomic or proteomic data, allowing the model to attend to functionally related molecules.

A foundational class of embedding methods that model relations as vector translations in the latent space. The core assumption is that for a valid triple (head, relation, tail), the embedding of the tail entity should lie close to the head entity embedding plus the relation vector.

• TransE: The seminal model where h + r ≈ t, optimized using a margin-based ranking loss
• TransH: Projects entities onto a relation-specific hyperplane before translation, better handling complex relation patterns
• TransR: Maps entities into a distinct relation space via a projection matrix, capturing diverse relational semantics
• RotatE: Models relations as rotations in complex space, naturally capturing symmetry, antisymmetry, and composition patterns

These models are computationally efficient and particularly effective for one-to-one relations in biomedical graphs, such as gene-disease associations.

A class of embedding techniques that measure the semantic similarity of entities and relations using multiplicative or neural operations, rather than simple vector translation. These models excel at capturing complex relational patterns like symmetry and antisymmetry.

• RESCAL: Factorizes a three-way tensor where each relation is a full matrix capturing pairwise interactions between latent factors
• DistMult: A simplified bilinear diagonal model that is highly efficient but restricted to symmetric relations only
• ComplEx: Extends DistMult into complex-valued space, using the imaginary component to model antisymmetric relations crucial for biomedical hierarchies
• TuckER: Applies Tucker decomposition to the knowledge graph tensor, enabling multi-task learning across relations

Semantic matching models are preferred when modeling drug-drug interactions or protein-protein interaction networks where symmetry is biologically meaningful.

Modern approaches that leverage message-passing neural networks to generate entity embeddings by aggregating information from local graph neighborhoods. Unlike translational or factorization methods, GNNs naturally incorporate the structural topology of the knowledge graph.

• R-GCN (Relational Graph Convolutional Network): Extends GCNs to handle multiple edge types by applying relation-specific weight matrices during neighborhood aggregation
• CompGCN: A composition-based GCN that jointly embeds entities and relations using vector operations (subtraction, multiplication, circular correlation) before message passing
• HGT (Heterogeneous Graph Transformer): Applies self-attention over node and edge types, dynamically weighting the importance of different biomedical relations

GNN encoders are particularly powerful for inductive link prediction—predicting links for entities unseen during training, such as newly discovered genes or drugs.

A geometric approach that embeds hierarchical biomedical knowledge into hyperbolic space rather than Euclidean space. Hyperbolic geometry has negative curvature, causing volume to grow exponentially with radius—perfectly mirroring the tree-like branching structure of biological ontologies.

• Poincaré Embeddings: Map entities into the Poincaré ball model where distances reflect semantic similarity and hierarchy depth
• MuRP (Multi-Relational Poincaré): Extends hyperbolic embeddings to multi-relational knowledge graphs using Möbius transformations
• AttH (Attentive Hyperbolic): Incorporates attention mechanisms to weigh the importance of different hierarchical levels during embedding

Hyperbolic embeddings achieve lower distortion when representing the Gene Ontology (GO), Disease Ontology (DO), or anatomical hierarchies where tree depth is significant. They require fewer dimensions than Euclidean models to achieve equivalent fidelity.

A family of methods that generate embeddings by encoding the explicit relational paths between entities, rather than relying solely on direct triples. These approaches capture higher-order reasoning chains essential for biomedical discovery.

• PTransE: Extends TransE by composing relation embeddings along multi-hop paths using addition, multiplication, or recurrent neural networks
• OPTransE: Optimizes path reliability by learning attention weights over different paths connecting the same entity pair
• RGHAT (Relational Graph Hierarchical Attention): Uses hierarchical attention to aggregate information from both direct neighbors and multi-hop paths

Path encoding is critical for drug repurposing tasks, where the mechanistic link between a drug and a disease may involve multiple intermediate genes, pathways, and phenotypes. The path Drug → inhibits → Protein → participates_in → Pathway → implicated_in → Disease provides mechanistic explainability.

Architectural strategies that co-embed knowledge graph triples alongside experimental omics data into a shared latent space, enabling the graph structure to regularize and enrich purely data-driven molecular representations.

• Multi-Modal VAE with KG Prior: Uses a variational autoencoder where the prior distribution is informed by knowledge graph embeddings, guiding the latent space toward biologically plausible configurations
• KG-Augmented GCN: Initializes patient similarity graph nodes with knowledge graph embeddings before propagating omics-derived features
• Contrastive KG-Omics Learning: Trains encoders to maximize mutual information between a sample's omics profile and its corresponding knowledge graph neighborhood

This fusion approach directly addresses the small-n, large-p problem in genomics, where the number of features vastly exceeds the number of samples. The structured prior from the knowledge graph acts as a powerful regularizer, improving generalization in biomarker discovery models.