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.
Recently, neural network-based methods have been proposed for constructing node representation in large-scale graphs. Deepwalk @cite_0 presents a two-phase algorithm for graph representation learning. In the first phase, Deepwalk samples sequences of neighboring nodes of each node by random walking on the graph. Then, the node representation is learned by training a Skip-gram model @cite_7 on the random walks. A number of methods have been proposed which extend this idea. First, several methods use different strategies for sampling neighboring nodes. LINE @cite_21 learns graph embeddings which preserve both the first-order and second-order proximities in a graph. Walklets @cite_3 captures multiscale node representation on graphs by sampling edges from higher powers of the graph adjacency matrix. Node2vec @cite_10 combines DFS-like and BFS-like exploration within the random walk framework. Second, matrix factorization methods and deep neural networks have also been proposed @cite_18 @cite_5 @cite_11 @cite_4 as alternatives to the Skip-gram model for learning the latent representations.
@cite_18 @cite_4 @cite_7 @cite_21 @cite_3 @cite_0 @cite_5 @cite_10 @cite_11
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Since the invention of word2vec, the skip-gram model has significantly advanced the research of network embedding, such as the recent emergence of the DeepWalk, LINE, PTE, and node2vec approaches. In this work, we show that all of the aforementioned models with negative sampling can be unified into the matrix factorization framework with closed forms. Our analysis and proofs reveal that: (1) DeepWalk empirically produces a low-rank transformation of a network's normalized Laplacian matrix; (2) LINE, in theory, is a special case of DeepWalk when the size of vertices' context is set to one; (3) As an extension of LINE, PTE can be viewed as the joint factorization of multiple networks» Laplacians; (4) node2vec is factorizing a matrix related to the stationary distribution and transition probability tensor of a 2nd-order random walk. We further provide the theoretical connections between skip-gram based network embedding algorithms and the theory of graph Laplacian. Finally, we present the NetMF method as well as its approximation algorithm for computing network embedding. Our method offers significant improvements over DeepWalk and LINE for conventional network mining tasks. This work lays the theoretical foundation for skip-gram based network embedding methods, leading to a better understanding of latent network representation learning. We present DeepWalk, a novel approach for learning latent representations of vertices in a network. These latent representations encode social relations in a continuous vector space, which is easily exploited by statistical models. DeepWalk generalizes recent advancements in language modeling and unsupervised feature learning (or deep learning) from sequences of words to graphs. DeepWalk uses local information obtained from truncated random walks to learn latent representations by treating walks as the equivalent of sentences. We demonstrate DeepWalk's latent representations on several multi-label network classification tasks for social networks such as BlogCatalog, Flickr, and YouTube. Our results show that DeepWalk outperforms challenging baselines which are allowed a global view of the network, especially in the presence of missing information. DeepWalk's representations can provide F1 scores up to 10 higher than competing methods when labeled data is sparse. In some experiments, DeepWalk's representations are able to outperform all baseline methods while using 60 less training data. DeepWalk is also scalable. It is an online learning algorithm which builds useful incremental results, and is trivially parallelizable. These qualities make it suitable for a broad class of real world applications such as network classification, and anomaly detection. In this paper, we propose a novel representation learning framework, namely HIN2Vec, for heterogeneous information networks (HINs). The core of the proposed framework is a neural network model, also called HIN2Vec, designed to capture the rich semantics embedded in HINs by exploiting different types of relationships among nodes. Given a set of relationships specified in forms of meta-paths in an HIN, HIN2Vec carries out multiple prediction training tasks jointly based on a target set of relationships to learn latent vectors of nodes and meta-paths in the HIN. In addition to model design, several issues unique to HIN2Vec, including regularization of meta-path vectors, node type selection in negative sampling, and cycles in random walks, are examined. To validate our ideas, we learn latent vectors of nodes using four large-scale real HIN datasets, including Blogcatalog, Yelp, DBLP and U.S. Patents, and use them as features for multi-label node classification and link prediction applications on those networks. Empirical results show that HIN2Vec soundly outperforms the state-of-the-art representation learning models for network data, including DeepWalk, LINE, node2vec, PTE, HINE and ESim, by 6.6 to 23.8 of @math - @math in multi-label node classification and 5 to 70.8 of @math in link prediction. DeepWalk is a typical representation learning method that learns low-dimensional representations for vertices in social networks. Similar to other network representation learning (NRL) models, it encodes the network structure into vertex representations and is learnt in unsupervised form. However, the learnt representations usually lack the ability of discrimination when applied to machine learning tasks, such as vertex classification. In this paper, we overcome this challenge by proposing a novel semi-supervised model, max-margin Deep-Walk (MMDW). MMDW is a unified NRL framework that jointly optimizes the max-margin classifier and the aimed social representation learning model. Influenced by the max-margin classifier, the learnt representations not only contain the network structure, but also have the characteristic of discrimination. The visualizations of learnt representations indicate that our model is more discriminative than unsupervised ones, and the experimental results on vertex classification demonstrate that our method achieves a significant improvement than other state-of-the-art methods. The source code can be obtained from https: github.com thunlp MMDW.