We present HARP, a novel method for learning low dimensional embeddings of a graph's nodes which preserves higher-order structural features. Our proposed method achieves this by compressing the input graph prior to embedding it, effectively avoiding troublesome embedding configurations (i.e. local minima) which can pose problems to non-convex optimization. HARP works by finding a smaller graph which approximates the global structure of its input. This simplified graph is used to learn a set of initial representations, which serve as good initializations for learning representations in the original, detailed graph. We inductively extend this idea, by decomposing a graph in a series of levels, and then embed the hierarchy of graphs from the coarsest one to the original graph. HARP is a general meta-strategy to improve all of the state-of-the-art neural algorithms for embedding graphs, including DeepWalk, LINE, and Node2vec. Indeed, we demonstrate that applying HARP's hierarchical paradigm yields improved implementations for all three of these methods, as evaluated on both classification tasks on real-world graphs such as DBLP, BlogCatalog, CiteSeer, and Arxiv, where we achieve a performance gain over the original implementations by up to 14 Macro F1.
. Most early methods treated representation learning as performing dimension reduction on the Laplacian and adjacency matrices @cite_13 @cite_22 @cite_9 . These methods work well on small graphs, but the time complexity of these algorithms is too high for the large-scale graphs commonly encountered today.
@cite_9 @cite_13 @cite_22
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Representation learning has shown its effectiveness in many tasks such as image classification and text mining. Network representation learning aims at learning distributed vector representation for each vertex in a network, which is also increasingly recognized as an important aspect for network analysis. Most network representation learning methods investigate network structures for learning. In reality, network vertices contain rich information (such as text), which cannot be well applied with algorithmic frameworks of typical representation learning methods. By proving that DeepWalk, a state-of-the-art network representation method, is actually equivalent to matrix factorization (MF), we propose text-associated DeepWalk (TADW). TADW incorporates text features of vertices into network representation learning under the framework of matrix factorization. We evaluate our method and various baseline methods by applying them to the task of multi-class classification of vertices. The experimental results show that, our method outperforms other baselines on all three datasets, especially when networks are noisy and training ratio is small. The source code of this paper can be obtained from https: github.com albertyang33 TADW. Representation learning (RL) of knowledge graphs aims to project both entities and relations into a continuous low-dimensional space. Most methods concentrate on learning representations with knowledge triples indicating relations between entities. In fact, in most knowledge graphs there are usually concise descriptions for entities, which cannot be well utilized by existing methods. In this paper, we propose a novel RL method for knowledge graphs taking advantages of entity descriptions. More specifically, we explore two encoders, including continuous bag-of-words and deep convolutional neural models to encode semantics of entity descriptions. We further learn knowledge representations with both triples and descriptions. We evaluate our method on two tasks, including knowledge graph completion and entity classification. Experimental results on real-world datasets show that, our method outperforms other baselines on the two tasks, especially under the zero-shot setting, which indicates that our method is capable of building representations for novel entities according to their descriptions. The source code of this paper can be obtained from https: github.com xrb92 DKRL. Representation learning of knowledge graphs aims to encode both entities and relations into a continuous low-dimensional vector space. Most existing methods only concentrate on learning representations with structured information located in triples, regardless of the rich information located in hierarchical types of entities, which could be collected in most knowledge graphs. In this paper, we propose a novel method named Type-embodied Knowledge Representation Learning (TKRL) to take advantages of hierarchical entity types. We suggest that entities should have multiple representations in different types. More specifically, we consider hierarchical types as projection matrices for entities, with two type encoders designed to model hierarchical structures. Meanwhile, type information is also utilized as relation-specific type constraints. We evaluate our models on two tasks including knowledge graph completion and triple classification, and further explore the performances on long-tail dataset. Experimental results show that our models significantly outperform all baselines on both tasks, especially with long-tail distribution. It indicates that our models are capable of capturing hierarchical type information which is significant when constructing representations of knowledge graphs. The source code of this paper can be obtained from https: github.com thunlp TKRL. Representation learning has become an invaluable approach for learning from symbolic data such as text and graphs. However, state-of-the-art embedding methods typically do not account for latent hierarchical structures which are characteristic for many complex symbolic datasets. In this work, we introduce a new approach for learning hierarchical representations of symbolic data by embedding them into hyperbolic space -- or more precisely into an n-dimensional Poincare ball. Due to the underlying hyperbolic geometry, this allows us to learn parsimonious representations of symbolic data by simultaneously capturing hierarchy and similarity. We present an efficient algorithm to learn the embeddings based on Riemannian optimization and show experimentally that Poincare embeddings can outperform Euclidean embeddings significantly on data with latent hierarchies, both in terms of representation capacity and in terms of generalization ability.