In this paper, we are interested to design neural networks for graphs with variable length in order to solve learning problems such as vertex classification, graph classification, graph regression, and graph generative tasks. We review existing graph RNN and ConvNet architectures, and propose natural extension of LSTM and ConvNet to graphs with arbitrary size.
Graph embedding is an effective method to represent graph data in a low dimensional space for graph analytics. Most existing embedding algorithms typically focus on preserving the topological structure or minimizing the reconstruction errors of graph data, but they have mostly ignored the data distribution of the latent codes from the graphs, which often results in inferior embedding in real-world graph data.
In this work we consider a privacy threat to a social network in which an attacker has access to a subset of random walk-based node similarities, such as effective resistances (i.e., commute times) or personalized PageRank scores. We also show that it is possible to learn a graph which accurately matches the underlying network on all other effective resistances.
We present a novel hierarchical graph clustering algorithm inspired by modularity-based clustering techniques. The algorithm is agglomerative and based on a simple distance between clusters induced by the probability of sampling node pairs.
We consider the clustering problem of attributed graphs. Our challenge is how we can design an effective and efficient clustering method that precisely captures the hidden relationship between the topology and the attributes in real-world graphs.
We outline a new approach for solving optimization problems which enforce triangle inequalities on output variables. We refer to this as metric-constrained optimization, and give several examples where problems of this form arise in machine learning applications and theoretical approximation algorithms for graph clustering.
One of the longstanding problems in spectral graph clustering (SGC) is the so-called model order selection problem: automated selection of the correct number of clusters. Consequently, AMOS outputs clusters of minimal model order with statistical clustering reliability guarantees.
One of the longstanding open problems in spectral graph clustering (SGC) is the so-called model order selection problem: automated selection of the correct number of clusters. This is equivalent to the problem of finding the number of connected components or communities in an undirected graph.