There is recently a surge in approaches that learn low-dimensional embeddings of nodes in networks. As there are many large-scale real-world networks, it's inefficient for existing approaches to store amounts of parameters in memory and update them edge after edge. With the knowledge that nodes having similar neighborhood will be close to each other in embedding space, we propose COSINE (COmpresSIve NE) algorithm which reduces the memory footprint and accelerates the training process by parameters sharing among similar nodes. COSINE applies graph partitioning algorithms to networks and builds parameter sharing dependency of nodes based on the result of partitioning. With parameters sharing among similar nodes, COSINE injects prior knowledge about higher structural information into training process which makes network embedding more efficient and effective. COSINE can be applied to any embedding lookup method and learn high-quality embeddings with limited memory and shorter training time. We conduct experiments of multi-label classification and link prediction, where baselines and our model have the same memory usage. Experimental results show that COSINE gives baselines up to 23 increase on classification and up to 25 increase on link prediction. Moreover, time of all representation learning methods using COSINE decreases from 30 to 70 .
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 there has been a surge of interest in designing graph embedding methods. Few, if any, can scale to a large-sized graph with millions of nodes due to both computational complexity and memory requirements. In this paper, we relax this limitation by introducing the MultI-Level Embedding (MILE) framework -- a generic methodology allowing contemporary graph embedding methods to scale to large graphs. MILE repeatedly coarsens the graph into smaller ones using a hybrid matching technique to maintain the backbone structure of the graph. It then applies existing embedding methods on the coarsest graph and refines the embeddings to the original graph through a novel graph convolution neural network that it learns. The proposed MILE framework is agnostic to the underlying graph embedding techniques and can be applied to many existing graph embedding methods without modifying them. We employ our framework on several popular graph embedding techniques and conduct embedding for real-world graphs. Experimental results on five large-scale datasets demonstrate that MILE significantly boosts the speed (order of magnitude) of graph embedding while also often generating embeddings of better quality for the task of node classification. MILE can comfortably scale to a graph with 9 million nodes and 40 million edges, on which existing methods run out of memory or take too long to compute on a modern workstation.