Knowledge Graph Embedding

These models interpret relations as geometric translations in the embedding space. The core hypothesis is that for a valid triple (head, relation, tail), the embedding of the head plus the relation should approximate the embedding of the tail.

• 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 distinct aspects of entities for different relations.
• RotatE: Models relations as rotations in complex vector space, naturally capturing symmetry, inversion, and composition patterns.

These models measure the plausibility of facts by matching the latent semantics of entities and relations using multiplicative or neural operations, rather than distance-based translations.

• RESCAL: Captures pairwise interactions via a bilinear product using a full-rank relation matrix. Highly expressive but prone to overfitting due to quadratic parameter growth.
• DistMult: A simplified bilinear model restricting relation matrices to diagonals. Computationally efficient but limited to symmetric relations only.
• ComplEx: Extends DistMult into the complex domain, using complex-valued embeddings to elegantly model asymmetric and antisymmetric relations via the Hermitian dot product.

These architectures employ deep neural layers to learn non-linear feature interactions from entity and relation embeddings, offering high expressivity at the cost of increased computational demand.

• ConvE: Uses 2D convolutions over reshaped embedding matrices to capture deep feature interactions. Excels at modeling complex relational patterns with fewer parameters than fully connected layers.
• ConvKB: Applies a convolutional layer to the concatenation of head, relation, and tail embeddings to capture global relationships and transitional characteristics.
• R-GCN: A graph neural network that acts as an encoder, generating entity embeddings by aggregating messages from neighbors based on distinct relation types.

Training knowledge graph embeddings requires contrasting true triples against false ones. The strategy for generating these negative samples critically impacts model quality and convergence speed.

• Uniform Negative Sampling: Randomly corrupts the head or tail of a true triple. Simple but generates many trivial negatives that provide little learning signal.
• Bernoulli Sampling: Replaces entities with probabilities inversely proportional to relation cardinality, reducing false negatives in 1-to-many relations.
• Adversarial Sampling: Dynamically selects high-scoring negative triples during training using the current model state, focusing learning on the most informative decision boundaries.

The primary downstream task for evaluating embedding quality is predicting missing links. Standard metrics measure how well the model ranks true entities against all possible corruptions.

• Mean Reciprocal Rank (MRR): The average inverse rank of the first correct entity across all test triples. Sensitive to top-ranked results.
• Hits@K: The proportion of test triples where the correct entity appears in the top K predictions (typically K=1, 3, 10).
• Filtered Setting: Removes all other known valid triples from the ranking before evaluation, preventing penalization for predicting other correct answers.

Standard embeddings assume static facts. Temporal extensions incorporate timestamps to model the evolution of facts, enabling reasoning over time-sensitive supply chain events.

• Time-Aware Representation: Entities and relations are modeled as functions of time, e.g., h(t) + r(t) ≈ t(t).
• HyTE: Projects entities onto a time-specific hyperplane before applying translational scoring.
• TComplEx: Extends ComplEx into a fourth-order tensor factorization, adding a temporal dimension to the complex-valued embeddings for modeling recurring event patterns.