## 4 Representation Learning Methods for Traffic Accident Knowledge Graphs  
### Translation-Based Embedding Methods  
Translation-based embedding methods for knowledge graphs map entities and relations into a continuous vector space by treating each relation as a translation operator. Specifically, for any valid triple (\(h\), \(r\), \(t\)), they enforce that the vector of the head entity plus the relation vector should lie close to the tail entity vector. During training, the distance induced by this translational mapping for positive triples is minimized, while negative samples are generated to maximize incorrect translation distances. This process effectively captures both semantic connections and relational structure, enabling the model to learn the latent semantics and logical patterns within the graph, and providing strong support for downstream tasks such as link prediction and entity classification. Common translation models in knowledge graph embedding include TransE [30,31], TransH [32], TransR [33], and TransD [34]. [PERSON] et al. [31] introduced the TransE model, which embeds entities and multi-relation data into a low-dimensional vector space. The core idea is to interpret a relation as a translation from the head entity embedding to the tail entity embedding. As illustrated in Figure 5, given a triple (\(h\), \(r\), \(t\)), the relation vector \(r\) represents the translation \(h+r\approx t\). In other words, if (\(h\), \(r\), \(t\)) holds in the knowledge graph, then the embeddings should satisfy \(h+r\approx t\). The TransE model is notable for its simplicity and intuitive design; however, its basic translational operation struggles to distinguish entities within one-to-many, many-to-one, or many-to-many relationships, leading to insufficient representational capacity. To address these shortcomings, subsequent models such as TransH, TransR, and TransD have been proposed to extend and refine TransE. TransH, in particular, assigns each relation a dedicated hyperplane and projects entity embeddings onto this hyperplane before applying the translation operation. Concretely, for a triple (\(h\), \(r\), \(t\)), the head and tail embeddings h and t are projected to \(h_{p}\) and \(t_{p}\) on the relation-specific hyperplane, and the model enforces \(h_{p}+r\approx t_{p}\). As illustrated in Figure 6, this mechanism allows entities to adopt distinct representations depending on the relation context, thereby better differentiating one-to-many and many-to-one mappings. Nonetheless, TransH still faces challenges in fully capturing very complex relations and introduces extra computational overhead due to the projection step. TransR further extends TransH's idea that entities and relationships should exist separately in different semantic spaces. As shown in Figure 7, each relationship \(r\) has an exclusive projection matrix \(\text{M}_{(t)}\) used to map entities from a unified entity space to a relationship-specific space, and then perform translation operations within that space. The optimization objective is \(\left\|M_{(r)}\cdot h+r-M_{(r)}\cdot t\right\|_{2}\). Here, \(\left\|\cdot\right\|_{2}\) notes the L2 norm, to measure the Euclidean distance in the embedding space. This approach separates entity and relation spaces, enabling the model to capture relation-specific characteristics at a finer granularity  
Figure 5: Schematic illustration of the TransE model. and thus better accommodate more complex mappings. However, it necessitates learning a distinct projection matrix for each relation, which significantly increases the number of parameters, raises computational complexity, and prolongs training time. TransD addresses the parameter redundancy of projection matrices in TransR--caused by the heterogeneous types of relations and entities--by dynamically generating mapping matrices.