From One Point to a Manifold: Knowledge Graph Embedding for Precise Link Prediction

By Han Xiao, Minlie Huang, Xiaoyan Zhu. 2015

157 citations recorded by the source corpus.

Knowledge graph embedding aims at offering a numerical knowledge representation paradigm by transforming the entities and relations into continuous vector space. However, existing methods could not characterize the knowledge graph in a fine degree to make a precise prediction. There are two reasons: being an ill-posed algebraic system and applying an overstrict geometric form. As precise prediction is critical, we propose an manifold-based embedding principle (\textbf{ManifoldE}) which could be treated as a well-posed algebraic system that expands the position of golden triples from one point in current models to a manifold in ours. Extensive experiments show that the proposed models achieve substantial improvements against the state-of-the-art baselines especially for the precise prediction task, and yet maintain high efficiency.

Subfields: Artificial Intelligence, Graph Learning

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Citations in the corpus

Knowledge Enhanced Contextual Word Representations (2019, methodology): “These methods broadly fall into two categories: translational distance models (Bordes et al., 2013; Wang et al., 2014b; Lin et al., 2015; Xiao et al., 2016) which use a distance-based scoring function, and linear models (Nickel et al., 2011; Yang et al., 2014; Trouillon et al., 2016; Dettmers et…”
A Comprehensive Survey of Graph Embedding: Problems, Techniques, and Applications (2017, neutral): “ManifoldE [129] Sphere: k’ðhÞ þ ’ðrÞ ’ðtÞk(2) Hyperplane: ð’ðhÞ þ ’ðrheadÞÞ ð’ðtÞ þ ’ðrtailÞÞ”
TransG : A Generative Model for Knowledge Graph Embedding (2015, methodology): “Since the previous models are point-wise modeling methods, ManifoldE (Xiao et al., 2016) proposes a novel manifold-based approach for knowledge graph embedding.”
GAKE: Graph Aware Knowledge Embedding (2016, methodology): “…our proposed approach with two experiments: (1) triple classiﬁcation (Bordes et al., 2013; Wang et al., 2014; Lin et al., 2015b), which determines whether a given triple is correct or not, and (2) link prediction (Wang et al., 2014; Xiao et al., 2016b), which aims to predict missing entities.”
SSP: Semantic Space Projection for Knowledge Graph Embedding with Text Descriptions (2016, background): “ManifoldE (Xiao, Huang, and Zhu 2016a) opens a classic branch, where a manifold is applied for the translation.”
Knowledge Transfer for Out-of-Knowledge-Base Entities : A Graph Neural Network Approach (2017, methodology): “The following pairwise-margin objective function is commonly used with KBC methods including TransE [Bordes et al., 2013; Xiao et al., 2016b]: L = N∑ i=1 [τ + f(hi, ri, ti)− f(h′i, ri, t′i)]+ (7) where [x]+ is the hinge function [x]+ = max(0, x) and scalar τ ∈ R is a threshold (called margin), with…”
KBGAN: Adversarial Learning for Knowledge Graph Embeddings (2017, background): “MANIFOLDE (Xiao et al., 2016) embeds a triple as a manifold rather than a point.”
Learning Hierarchy-Aware Knowledge Graph Embeddings for Link Prediction (2019, background): “Huang, and Zhu 2016 RESCAL (Nickel, Tresp, and Kriegel 2011) guishing entities at different levels of the hierarchy.”
Knowledge Graph Embedding: A Survey of Approaches and Applications (2017, unknown): “ManifoldE [53] relaxes hþ r t to khþ r tk22 u2r for each ðh; r; tÞ 2 IDþ.”