Characteristic Functions on Graphs: Birds of a Feather, from Statistical Descriptors to Parametric Models

By Benedek Rozemberczki, Rik Sarkar. International Conference on Information and Knowledge Management, 2020

429 citations recorded by the source corpus.

In this paper, we propose a flexible notion of characteristic functions defined on graph vertices to describe the distribution of vertex features at multiple scales. We introduce FEATHER, a computationally efficient algorithm to calculate a specific variant of these characteristic functions where the probability weights of the characteristic function are defined as the transition probabilities of random walks. We argue that features extracted by this procedure are useful for node level machine learning tasks. We discuss the pooling of these node representations, resulting in compact descriptors of graphs that can serve as features for graph classification algorithms. We analytically prove that FEATHER describes isomorphic graphs with the same representation and exhibits robustness to data corruption. Using the node feature characteristic functions we define parametric models where evaluation points of the functions are learned parameters of supervised classifiers. Experiments on real world large datasets show that our proposed algorithm creates high quality representations, performs transfer learning efficiently, exhibits robustness to hyperparameter changes and scales linearly with the input size.

Subfields: Artificial Intelligence, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/efb82dbf2c7d4166a86bacb13133d64e0e7d66eb

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Rik Sarkar
2. Carl Allen
3. Sitao Luan
4. Doina Precup
5. Mingde Zhao
6. Chenqing Hua
7. Shuyuan Zhang
8. Xiaoming Chang

In Statistical and Nonlinear Physics

1. Rik Sarkar
2. Carl Allen
3. Doina Precup
4. Benedek Rozemberczki
5. Muhan Zhang
6. Xiyuan Wang
7. Zhewei Wei

Citations in the corpus

• Revisiting Heterophily For Graph Neural Networks (2022, positive): “15We choose Deezer-Europe because MLP outperforms GCN on it [26].”
• Multi-scale Attributed Node Embedding (2019, methodology): “We use standard (well-established) node classification webgraph benchmark datasets (Cora, Citeseer [34], Pubmed [35]) together with publicly available social network benchmarks—LastFM Asia, Deezer Europe [8]).”
• Membership Inference Attacks on Machine Learning: A Survey (2021, neutral): “Data Classification Pubmed [175] 19,717 500 3 [42, 153] Citeseer [175] 3,327 3,703 6 [42, 64, 153] Cora [175] 2,708 1,433 7 [42, 64, 153] Lastfm [169] 7,624 7,842 18 [64]”