C oncept2 B ox: Joint Geometric Embeddings for Learning Two-View Knowledge Graphs (2023)

Abstract: Knowledge graph embeddings (KGE) have been extensively studied to embed large-scale relational data for many real-world applications. Existing methods have long ignored the fact many KGs contain two fundamentally different views: high-level ontology-view concepts and fine-grained instance-view entities. They usually embed all nodes as vectors in one latent space. However, a single geometric representation fails to capture the structural differences between two views and lacks probabilistic semantics towards concepts’ granularity. We propose Concept2Box, a novel approach that jointly embeds the two views of a KG using dual geometric representations. We model concepts with box embeddings, which learn the hierarchy structure and complex relations such as overlap and disjoint among them. Box volumes can be interpreted as concepts’ granularity. Different from concepts, we model entities as vectors. To bridge the gap between concept box embeddings and entity vector embeddings, we propose a novel vector-to-box distance metric and learn both embeddings jointly. Experiments on both the public DBpedia KG and a newly-created industrial KG showed the effectiveness of Concept2Box.

## introduction knowledge graphs (kgs) like freebase @xcite and dbpedia @xcite have motivated various knowledge-driven applications @xcite . they contain structured and semantic information among nodes and relations where knowledge is instantiated as factual triples. one critical fact being ignored is that many kgs consist of two fundamentally different views as depicted in figure 1: (1) an ontology-view component with high-level concepts and meta-relations, e.g., ("singer", "is_a", figure 1 : a two-view kg consisting of (1) an ontologyview kg with high-level concepts and meta-relations, (2) an instance-view kg with fine-grained instances and relations, and, (3) a set of cross-view links between two views of kg. concept2box learns dual geometric embeddings where each concept is modeled as a box in the latent space and entities are learned as point vectors. modern kgs are usually far from complete as new knowledge is rapidly emerging @xcite . how to automatically harvest unknown knowledge from data has been an important research area for years. knowledge graph embedding (kge) methods achieve promising results for modeling kgs by learning low-dimensional vector representations of nodes and relations. however, most existing methods @xcite @xcite have a major limitation of only considering kgs of a single view. the valuable semantics brought by jointly modeling the two views are omitted. in contrast, modeling two-view kgs in a holistic way has a key advantage: entity embeddings provide rich information for understanding corresponding ontological concepts; and, in turn, a concept embedding provides a high-level summary of linked entities, guiding the learning process of entities with only few relational facts. modeling two-view kg is non-trivial where the challenges are three-fold: first, there exists a significant structural difference between the two views, where the ontology-view kg usually forms a hierarchical structure with concept nodes of different granularity, and the instance-view kg usually follows a flat or cyclical structure @xcite with each entity associated with a specific meaning. second, concepts often exhibit complex relations such as intersect, contain and disjoint. traditional vector-based embeddings @xcite fail to adequately express them and capture interpretable probabilistic semantics to explain the granularity of concepts. third, to bridge the knowledge from two views, effective semantic mappings from fine-grained entities to their corresponding concepts need to be carefully considered. for work that models two-view kgs, they either model concepts and entities all as points in the euclidean space @xcite and in the product manifold space @xcite , which can fail to capture the structural differences among the two views and result in suboptimal performance, or they embed concepts and entities separately as points in the hyperbolic and spherical space respectively @xcite , which cannot provide interpretation towards concepts' granularity. to this end, we propose concept2box, a novel two-view kg embedding model for jointly learning the representations of concepts and instances using dual geometric objects. specifically, we propose to leverage the geometric objects of boxes (i.e. axisaligned hyperrectangle) to embed concept nodes in the ontology-view kg. this is motivated by the desirable geometric properties of boxes to represent more complex relationships among concepts such as intersect, contain, and disjoint, and also capture the hierarchy structure. for example, in figure 1 we can see city is contained within location, denoting it's a sub-concept of location; artist and scientist intersects with each other, denoting they are correlated. in addition, box embeddings provide probabilistic measures of concepts' granularity based on the volumes, such as person is a larger box than scientist. entities in the instance-view kg are modeled with classic vector representations to capture their specific meanings. as we model concepts and entities using boxes and vectors respectively, we further design a new metric function to measure the distance from a vector to a box in order to bridge the semantics of the two views. based on this vector-to-box distance function, the proposed model is trained to jointly model the semantics of the instance-view kg, the ontology-view kg, and the cross-view links. empirically, concept2box outperforms popular baselines on both public and our newly-created industrial recipe datasets. our contributions are as follows: (1) we propose a novel model for learning two-view kg representations by jointly embedding concepts and instances with different geometric objects. (2) we design a new metric function to measure the distance between concept boxes and entity vectors to bridge the two views. (3) we construct a new industriallevel recipe-related kg dataset. (4) extensive experiments verify the effectiveness of concept2box. ## method in this section, we introduce concept2box, a novel kge model to learn two-view knowledge graph embeddings with dual geometric representations. as shown in figure 2 , concept2box consists of three main components: (1). the ontology-view box-based kg embedding module that captures the hierarchical structure and complex relations of concepts trained via the kg completion loss over g o ; (2). the instance-view vector-based kg embedding module trained via the kg completion loss over g i . it has the flexibility to incorporate any off-the-shelf vector-based kge methods @xcite ; (3). the cross-view module trained via the concept linking loss over s. this module relies on a new distance metric for bridging the semantics between a vector and a box. we now present each component in detail. ## experiments in this section, we introduce our empirical results against existing baselines to evaluate our model performance. we start with the datasets and baselines introduction and then conduct the performance evaluation. finally, we conduct a model generalization experiment and a case study to better illustrate our model design. ## conclusion in this paper, we propose concept2box, a novel two-view knowledge graph embedding method with dual geometric representations. we model high-level concepts as boxes to capture the hierarchical structure and complex relations among them and reflect concept granularity based on box volumes. for the instance-view kg, we model fine-grained entities as vectors and propose a novel metric function to define the distance between a box to a vector to bridge the semantics of the two views. concept2box is jointly trained to model the instance-view kg, the ontology-view kg, and the cross-view links. empirical experiment results on two real-world datasets including a newlycreated recipe dataset verify the effectiveness of concept2box.