SINE: Scalable Incomplete Network Embedding

Abstract

Attributed network embedding aims to learn lowdimensional vector representations for nodes in a network, where each node contains rich attributes/features describing node content. Because network topology structure and node attributes often exhibit high correlation, incorporating node attribute proximity into network embedding is beneficial for learning good vector representations. In reality, large-scale networks often have incomplete/missing node content or linkages, yet existing attributed network embedding algorithms all operate under the assumption that networks are complete. Thus, their performance is vulnerable to missing data and suffers from poor scalability.In this paper, we propose a Scalable Incomplete Network Embedding (SINE) algorithm for learning node representations from incomplete graphs. SINE formulates a probabilistic learning framework that separately models pairs of node-context and node-attribute relationships. Different from existing attributed network embedding algorithms, SINE provides greater flexibility to make the best of useful information and mitigate negative effects of missing information on representation learning. A stochastic gradient descent based online algorithm is derived to learn node representations, allowing SINE to scale up to large-scale networks with high learning efficiency. We evaluate the effectiveness and efficiency of SINE through extensive experiments on real-world networks. Experimental results confirm that SINE outperforms state-of-the-art baselines in various tasks, including node classification, node clustering, and link prediction, under settings with missing links and node attributes. SINE is also shown to be scalable and efficient on large-scale networks with millions of nodes/edges and high-dimensional node features. The source code of this paper is available at https://github.com/daokunzhang/SINE.

Karate Club

“…These average AUC values are reported in Table 5 with standard errors. The results in Table 5 generally demonstrate that the included neighbourhood based [4,6,15,20,24,25,27,33,37], structural role preserving [2,10], and attributed [3,30,45,48,50,53] node embedding techniques all generate reasonable quality representations for this classification task. There are additional conclusions; (i) multi-scale node embeddings such as GraRep [6], Walklets, [25], and MUSAE [30] create high quality node features , (ii) combining neighbourhood and attribute information results in the best representations [30,53], (iii) there is not a single model which is generally superior.…”

“…Attributed embedding retains the neighbourhood structure and generic feature similarity of nodes when the embedding is learned. This learning involves the joint factorization of the node-node and node-feature matrices with a direct [45,48] or implicit matrix decomposition technique [30,53].…”

“…Dense linear algebra operations are done with NumPy and their sparse counterparts use SciPy. Implicit matrix factorization techniques[2,24,25,30,53] utilize the GenSim[29] package and methods which rely on graph signal processing use PyGSP[9].…”

An Unsupervised Learning Method for Attributed Network Based on Non-Euclidean Geometry

“…The reason is that, as shown in Figure 1b, the Ricci curvature can better distinguish the strength of the connection relationship in the network structure and can distinguish the meso structure of the network, namely, community. For example, the curvature of edge (3,4) in Figure 1a is −0.667, which is a characteristic property of the Ricci curvature, that is, the curvatures of edges between communities are negative. Of course, RCGCN, like GCN, uses semi-supervised learning, while, here, we are going to conduct unsupervised learning.…”

“…As a new approach, network embedding [1,2], which maps network nodes to low-dimensional vector representations, can deal with this problem well. The obtained node representations can be further applied to node classification [3], graph classification [4,5], recommendation [6,7], community detection [8,9], etc. Take the Cora dataset used in the experimental part of this paper as an example.…”