Homogeneous network embedding for massive graphs via reweighted personalized PageRank

Abstract

Given an input graph G and a node v ∈ G, homogeneous network embedding (HNE) maps the graph structure in the vicinity of v to a compact, fixed-dimensional feature vector. This paper focuses on HNE for massive graphs, e.g., with billions of edges. On this scale, most existing approaches fail, as they incur either prohibitively high costs, or severely compromised result utility.Our proposed solution, called Node-Reweighted PageRank (NRP), is based on a classic idea of deriving embedding vectors from pairwise personalized PageRank (PPR) values. Our contributions are twofold: first, we design a simple and efficient baseline HNE method based on PPR that is capable of handling billion-edge graphs on commodity hardware; second and more importantly, we identify an inherent drawback of vanilla PPR, and address it in our main proposal NRP. Specifically, PPR was designed for a very different purpose, i.e., ranking nodes in G based on their relative importance from a source node's perspective. In contrast, HNE aims to build node embeddings considering the whole graph. Consequently, node embeddings derived directly from PPR are of suboptimal utility.The proposed NRP approach overcomes the above deficiency through an effective and efficient node reweighting algorithm, which augments PPR values with node degree information, and iteratively adjusts embedding vectors accordingly. Overall, NRP takes O(m log n) time and O(m) space to compute all node embeddings for a graph with m edges and n nodes. Our extensive experiments that compare NRP against 18 existing solutions over 6 real graphs demonstrate that NRP achieves higher result utility than all the solutions for link prediction, graph reconstruction and node classification, while being up to orders of magnitude faster. In particular, on a billion-edge Twitter graph, NRP terminates within 4 hours, using a single CPU core.

Boosting Graph Embedding on a Single GPU

“…The literature is carefully documented in [17] and can be categorized into three branches: factorization-, deep-learning-, and sampling-based embedding. The first class of tools factorizes the adjacency/similarity matrices [18], [19], [20], [21], [22], [23], [24]. Deep-learningbased approaches utilize deep autoencoders to reduce the dimensionality of the graph [25], [26].…”

PPRviz: Effective and Efficient Graph Visualization based on Personalized PageRank

“…This indicates that the PPR between adjacent nodes in a graph could vary considerably. The reason is that PPR is designed to rank nodes based on their relative importance from the perspective of a source node, but it is unsuitable for comparing the strength of connections between nodes when different source nodes are considered [93]. As a consequence, directly transforming PPR values into node distances would lead to a large variance in edge lengths in graph visualization.…”

Gaussian mixture embedding of multiple node roles in networks

“…More recently, using matrix factorization to generate proximity matrix is a new thread. Papers like [64][65][66] optimize the representation by incorporating the proximity matrix.…”