Vertex nomination: The canonical sampling and the extended spectral nomination schemes

Yoder, Jordan; Chen, Li; Pao, Henry; Bridgeford, Eric; Levin, Keith; Fishkind, Donniell E.; Priebe, Carey E.; Lyzinski, Vince

doi:10.1016/j.csda.2020.106916

Cited by 14 publications

(10 citation statements)

References 38 publications

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“…Geodesic learning is an essential statistical primitive for many subsequent inference tasks. For example, manifold learning, high-dimensional clustering, anomaly detection, and vertex nomination [52] all rely on geodesic learning. More generally, any Learning to rank (LTR) problem can be formulated as a geodesic learning problem.…”

Section: Discussionmentioning

confidence: 99%

Geodesic Forests

Madhyastha

Strnadová-Neeley

et al. 2020

Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery &Amp; Data Mining

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Together with the curse of dimensionality, nonlinear dependencies in large data sets persist as major challenges in data mining tasks. A reliable way to accurately preserve nonlinear structure is to compute geodesic distances between data points. Manifold learning methods, such as Isomap, aim to preserve geodesic distances in a Riemannian manifold. However, as manifold learning algorithms operate on the ambient dimensionality of the data, the essential step of geodesic distance computation is sensitive to high-dimensional noise. Therefore, a direct application of these algorithms to highdimensional, noisy data often yields unsatisfactory results and does not accurately capture nonlinear structure.We propose an unsupervised random forest approach called geodesic forests (GF) to geodesic distance estimation in linear and nonlinear manifolds with noise. GF operates on low-dimensional sparse linear combinations of features, rather than the full observed dimensionality. To choose the optimal split in a computationally efficient fashion, we developed Fast-BIC, a fast Bayesian Information Criterion statistic for Gaussian mixture models. We additionally propose geodesic precision and geodesic recall as novel evaluation metrics that quantify how well the geodesic distances of a latent manifold are preserved. Empirical results on simulated and real data demonstrate that GF is robust to high-dimensional noise, whereas other methods, such as Isomap, UMAP, and FLANN, quickly deteriorate in such settings. Notably, GF is able to estimate geodesic distances better than other approaches on a real connectome dataset.

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Section: Discussionmentioning

confidence: 99%

Geodesic Forests

Madhyastha

Strnadová-Neeley

et al. 2020

Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery &Amp; Data Mining

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“…Recently proposed methods for vertex nomination [3,[17][18][19][20][21][22] have been quite successful in a variety of settings when the definition of similar is defined explicitly by a domain expert. Approaches are mainly combinatorial or spectral.…”

Section: Vertex Nominationmentioning

confidence: 99%

Leveraging semantically similar queries for ranking via combining representations

Helm¹,

Abdin²,

Pedigo³

et al. 2021

Preprint

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In modern ranking problems, different and disparate representations of the items to be ranked are often available. It is sensible, then, to try to combine these representations to improve ranking. Indeed, learning to rank via combining representations is both principled and practical for learning a ranking function for a particular query. In extremely data-scarce settings, however, the amount of labeled data available for a particular query can lead to a highly variable and ineffective ranking function. One way to mitigate the effect of the small amount of data is to leverage information from semantically similar queries. Indeed, as we demonstrate in simulation settings and real data examples, when semantically similar queries are available it is possible to gainfully use them when ranking with respect to a particular query. We describe and explore this phenomenon in the context of the bias-variance trade off and apply it to the data-scarce settings of a Bing navigational graph and the Drosophila larva connectome.

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“…Given graphs G 1 and G 2 and vertices of interest V * ⊂ V (G 1 ), the aim of the vertex nomination (VN) problem is to rank the vertices of G 2 into a nomination list with the corresponding vertices of interest concentrating at the top of the nomination list. In recent years, a host of VN procedures have been introduced (see, for example, [14,30,26,17,37,48]) that have proven to be effective information retrieval tools in both synthetic and real data applications. Moreover, recent work establishing a fundamental statistical framework for VN has led to a novel understanding of the limitations of VN efficacy in evolving network environments [27].…”

Section: Introductionmentioning

confidence: 99%

Vertex nomination, consistent estimation, and adversarial modification

Agterberg¹,

Park²,

Larson³

et al. 2020

Electron. J. Statist.

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Given a pair of graphs G 1 and G 2 and a vertex set of interest in G 1 , the vertex nomination (VN) problem seeks to find the corresponding vertices of interest in G 2 (if they exist) and produce a rank list of the vertices in G 2 , with the corresponding vertices of interest in G 2 concentrating, ideally, at the top of the rank list. In this paper, we define and derive the analogue of Bayes optimality for VN with multiple vertices of interest, and we define the notion of maximal consistency classes in vertex nomination. This theory forms the foundation for a novel VN adversarial contamination model, and we demonstrate with real and simulated data that there are VN schemes that perform effectively in the uncontaminated setting, and adversarial network contamination adversely impacts the performance of our VN scheme. We further define a network regularization method for mitigating the impact of the adversarial contamination, and we demonstrate the effectiveness of regularization in both real and synthetic data.

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Vertex nomination: The canonical sampling and the extended spectral nomination schemes

Cited by 14 publications

References 38 publications

Geodesic Forests

Geodesic Forests

Leveraging semantically similar queries for ranking via combining representations

Vertex nomination, consistent estimation, and adversarial modification

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