GrowHON: A Scalable Algorithm for Growing Higher-order Networks of Sequences

Krieg, Steven J.; Kogge, Peter M.; Chawla, Nitesh V.

doi:10.1007/978-3-030-65351-4_39

Cited by 4 publications

(10 citation statements)

References 21 publications

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“…We prove Theorem 1 in Appendix A. The intuition is that u only exists in G k if the transition probabilities of a random walker are sufficiently different (measured via KL-divergence) from u in G 1 [33,22]. These differences will be consequently be represented in the expectation of the features gathered by AGGREGATE(N k (u )).…”

Section: Why Deep Graph Ensembles?mentioning

confidence: 99%

“…We define Ω k u = {u ∈ V k , a m = u} as the higher-order family of u (including u itself), and call each u ∈ Ω k u a relative of u. Like E 1 , the edge set E k is the set of node pairs (u, v) ∈ V k × V k that are adjacent in at least one sequence in S, but generalized to account for the fact that each node is a sequence rather than a single entity (prior work characterizes each edge as adjacent substrings in S [22]). Edges are directed such that (u, v) = (v, u) and weighted via w k : E k − → R ≥0 , where 0 indicates a missing edge.…”

Section: Background and Preliminariesmentioning

confidence: 99%

“…Because each node in V k can represent one or more entities, each edge in E k represents interactions between two or more entities while remaining a 2-tuple. This means that many graph operations can be easily applied to G k , which preserves more information than G 1 with respect to S but is less prone to overfitting than fixed-order models [45,33,22].…”

Section: Background and Preliminariesmentioning

confidence: 99%

“…There are a number of design challenges (CHs) we must address in order to realize the joint potential of GNNs and HONs. In a HON, entities are represented by a non-fixed number of higher-order nodes (CH1), each of which has a different neighborhood (CH2) and may be of varying importance (CH3) [45,33,31,22]. One intuitive idea is to compute a representation for u by sampling neighbors from any of u's relatives.…”

Section: Why Deep Graph Ensembles?mentioning

confidence: 99%

“…where u ∈ D and OUTDEG k (u ) is the weighted out-degree of u in G k . Because weighted out-degree in G k is the frequency with which u appears in S (in-edges are rewired to preserve connectivity and thus in-degree is less stable [22]), it is a natural measure of the importance of u in the graph.…”

Section: Why Deep Graph Ensembles?mentioning

confidence: 99%

See 4 more Smart Citations

Deep Ensembles for Graphs with Higher-order Dependencies

Krieg¹,

Burgis²,

Soga³

et al. 2022

Preprint

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Graph neural networks (GNNs) continue to achieve state-of-the-art performance on many graph learning tasks, but rely on the assumption that a given graph is a sufficient approximation of the true neighborhood structure. In the presence of higher-order sequential dependencies, we show that the tendency of traditional graph representations to underfit each node's neighborhood causes existing GNNs to generalize poorly. To address this, we propose a novel Deep Graph Ensemble (DGE), which captures neighborhood variance by training an ensemble of GNNs on different neighborhood subspaces of the same node within a higher-order network structure. We show that DGE consistently outperforms existing GNNs on semisupervised and supervised tasks on four real-world data sets with known higher-order dependencies, even under a similar parameter budget. We demonstrate that learning diverse and accurate base classifiers is central to DGE's success, and discuss the implications of these findings for future work on GNNs.

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Section: Why Deep Graph Ensembles?mentioning

confidence: 99%

Section: Background and Preliminariesmentioning

confidence: 99%

Section: Background and Preliminariesmentioning

confidence: 99%

Section: Why Deep Graph Ensembles?mentioning

confidence: 99%

Section: Why Deep Graph Ensembles?mentioning

confidence: 99%

See 3 more Smart Citations

Deep Ensembles for Graphs with Higher-order Dependencies

Krieg¹,

Burgis²,

Soga³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Toward random walk-based clustering of variable-order networks

Queiros

Coquidé

Queyroi

2022

Net Sci

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Higher-order networks aim at improving the classical network representation of trajectories data as memory-less order $1$ Markov models. To do so, locations are associated with different representations or “memory nodes” representing indirect dependencies between visited places as direct relations. One promising area of investigation in this context is variable-order network models as it was suggested by Xu et al. that random walk-based mining tools can be directly applied on such networks. In this paper, we focus on clustering algorithms and show that doing so leads to biases due to the number of nodes representing each location. To address them, we introduce a representation aggregation algorithm that produces smaller yet still accurate network models of the input sequences. We empirically compare the clustering found with multiple network representations of real-world mobility datasets. As our model is limited to a maximum order of $2$ , we discuss further generalizations of our method to higher orders.

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