• Corpus ID: 252683435

Exact Representation of Sparse Networks with Symmetric Nonnegative Embeddings

  title={Exact Representation of Sparse Networks with Symmetric Nonnegative Embeddings},
  author={Sudhanshu Chanpuriya and Ryan A. Rossi and Anup B. Rao and Tung Mai and Nedim Lipka and Zhao Song and Cameron Musco},
Many models for undirected graphs are based on factorizing the graph’s adjacency matrix; these models find a vector representation of each node such that the predicted probability of a link between two nodes increases with the similarity (dot product) of their associated vectors. Recent work has shown that these models are unable to capture key structures in real-world graphs, particularly heterophilous structures, wherein links occur between dissimilar nodes. In contrast, a factorization with… 

Figures and Tables from this paper



Node Embeddings and Exact Low-Rank Representations of Complex Networks

This work proves that a minor relaxation of their model can generate sparse graphs with high triangle density and gives a simple algorithm based on logistic principal component analysis (LPCA) that succeeds in finding such exact embeddings.

The impossibility of low-rank representations for triangle-rich complex networks

It is mathematically proved that low-dimensional embeddings cannot generate graphs with both low average degree and large clustering coefficients, and any embedding that can successfully create these two properties must have a rank that is nearly linear in the number of vertices.

Capacity and Bias of Learned Geometric Embeddings for Directed Graphs

A novel variant of box embeddings is introduced that uses a learned smoothing parameter to achieve better representational capacity than vector models in low dimensions, while also avoiding performance saturation common to other geometric models in high dimensions.

An Attract-Repel Decomposition of Undirected Networks

The attract-repel (AR) decomposition is demonstrated in real social networks and it can be used to measure the amount of latent homophily and heterophily, and applied to co-occurrence networks to discover roles in teams and find substitutable ingredients in recipes.

Inductive Representation Learning on Large Graphs

GraphSAGE is presented, a general, inductive framework that leverages node feature information (e.g., text attributes) to efficiently generate node embeddings for previously unseen data and outperforms strong baselines on three inductive node-classification benchmarks.

Symmetric Nonnegative Matrix Factorization for Graph Clustering

Symmetric NMF is proposed as a general framework for graph clustering, which inherits the advantages of NMF by enforcing nonnegativity on the clustering assignment matrix, and serves as a potential basis for many extensions.

Beyond Homophily in Graph Neural Networks: Current Limitations and Effective Designs

This work identifies a set of key designs -- ego- and neighbor-embedding separation, higher-order neighborhoods, and combination of intermediate representations -- that boost learning from the graph structure under heterophily and combines them into a graph neural network, H2GCN, which is used as the base method to empirically evaluate the effectiveness of the identified designs.

Network Embedding as Matrix Factorization: Unifying DeepWalk, LINE, PTE, and node2vec

The NetMF method offers significant improvements over DeepWalk and LINE for conventional network mining tasks and provides the theoretical connections between skip-gram based network embedding algorithms and the theory of graph Laplacian.

Two Sides of the Same Coin: Heterophily and Oversmoothing in Graph Convolutional Neural Networks

This work takes a new unified perspective to understand the performance degradation of GCNs at the node level and shows the effectiveness of two strategies: degree correction, which learns to adjust degree coefflcients, and signed messages, which may be useful (under conditions) by learning to optionally negate the messages.

NetGAN without GAN: From Random Walks to Low-Rank Approximations

This paper investigates the implicit bias of NetGAN and finds that the root of its generalization properties does not lie in the GAN architecture, but in an inconspicuous low-rank approximation of the logits random walk transition matrix.