Many successful methods have been proposed for learning low dimensional representations on large-scale networks, while almost all existing methods are designed in inseparable processes, learning embeddings for entire networks even when only a small proportion of nodes are of interest. This leads to great inconvenience, especially on super-large or dynamic networks, where these methods become almost impossible to implement. In this paper, we formalize the problem of separated matrix factorization, based on which we elaborate a novel objective function that preserves both local and global information. We further propose SepNE, a simple and flexible network embedding algorithm which independently learns representations for different subsets of nodes in separated processes. By implementing separability, our algorithm reduces the redundant efforts to embed irrelevant nodes, yielding scalability to super-large networks, automatic implementation in distributed learning and further adaptations. We demonstrate the effectiveness of this approach on several real-world networks with different scales and subjects. With comparable accuracy, our approach significantly outperforms state-of-the-art baselines in running times on large networks.
The most similar work to ours is @cite_6 , in which a similar partition was adopted to achieve separability, while other parts of the work had major differences with ours. Besides, it focused mainly on technical issues in distributed learning and preserved only link information, while SepNE is more generalized idea with a more elaborated optimization goal.
@cite_6
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Natural graphs, such as social networks, email graphs, or instant messaging patterns, have become pervasive through the internet. These graphs are massive, often containing hundreds of millions of nodes and billions of edges. While some theoretical models have been proposed to study such graphs, their analysis is still difficult due to the scale and nature of the data. We propose a framework for large-scale graph decomposition and inference. To resolve the scale, our framework is distributed so that the data are partitioned over a shared-nothing set of machines. We propose a novel factorization technique that relies on partitioning a graph so as to minimize the number of neighboring vertices rather than edges across partitions. Our decomposition is based on a streaming algorithm. It is network-aware as it adapts to the network topology of the underlying computational hardware. We use local copies of the variables and an efficient asynchronous communication protocol to synchronize the replicated values in order to perform most of the computation without having to incur the cost of network communication. On a graph of 200 million vertices and 10 billion edges, derived from an email communication network, our algorithm retains convergence properties while allowing for almost linear scalability in the number of computers.