DeepAI AI Chat
Log In Sign Up

FGOT: Graph Distances based on Filters and Optimal Transport

by   Hermina Petric Maretic, et al.

Graph comparison deals with identifying similarities and dissimilarities between graphs. A major obstacle is the unknown alignment of graphs, as well as the lack of accurate and inexpensive comparison metrics. In this work we introduce the filter graph distance. It is an optimal transport based distance which drives graph comparison through the probability distribution of filtered graph signals. This creates a highly flexible distance, capable of prioritising different spectral information in observed graphs, offering a wide range of choices for a comparison metric. We tackle the problem of graph alignment by computing graph permutations that minimise our new filter distances, which implicitly solves the graph comparison problem. We then propose a new approximate cost function that circumvents many computational difficulties inherent to graph comparison and permits the exploitation of fast algorithms such as mirror gradient descent, without grossly sacrificing the performance. We finally propose a novel algorithm derived from a stochastic version of mirror gradient descent, which accommodates the non-convexity of the alignment problem, offering a good trade-off between performance accuracy and speed. The experiments on graph alignment and classification show that the flexibility gained through filter graph distances can have a significant impact on performance, while the difference in speed offered by the approximation cost makes the framework applicable in practical settings.


page 1

page 2

page 3

page 4


GOT: An Optimal Transport framework for Graph comparison

We present a novel framework based on optimal transport for the challeng...

Wasserstein-based Graph Alignment

We propose a novel method for comparing non-aligned graphs of different ...

Robust Attributed Graph Alignment via Joint Structure Learning and Optimal Transport

Graph alignment, which aims at identifying corresponding entities across...

Graph Optimal Transport with Transition Couplings of Random Walks

We present a novel approach to optimal transport between graphs from the...

Distances for Markov Chains, and Their Differentiation

(Directed) graphs with node attributes are a common type of data in vari...

Embedding Signals on Knowledge Graphs with Unbalanced Diffusion Earth Mover's Distance

In modern relational machine learning it is common to encounter large gr...

Identifying networks with common organizational principles

Many complex systems can be represented as networks, and the problem of ...