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Phase Transitions for Detecting Latent Geometry in Random Graphs [article]

Matthew Brennan, Guy Bresler, Dheeraj Nagaraj
2020 arXiv   pre-print
We address this question for two of the most well-studied models of random graphs with latent geometry – the random intersection and random geometric graph.  ...  A fundamental initial question regarding these models is: when are these random graphs affected by their latent geometry and when are they indistinguishable from simpler models without latent structure  ...  This work was supported in part by the grants ONR N00014-17-1-2147.  ... 
arXiv:1910.14167v3 fatcat:vkqbq4lncjhjhcused6nwam66e

Random Geometric Graph: Some recent developments and perspectives [article]

Quentin Duchemin
2022 arXiv   pre-print
The Random Geometric Graph (RGG) is a random graph model for network data with an underlying spatial representation.  ...  We also explain how this model differs from classical community based random graph models and we review recent works that try to take the best of both worlds.  ...  How the phase transition phenomenon in geometry detection evolves when other latent spaces are considered?  ... 
arXiv:2203.15351v2 fatcat:iscoenjkxrdd3pcjagpgup6zf4

Network Geometry [article]

Marian Boguna, Ivan Bonamassa, Manlio De Domenico, Shlomo Havlin, Dmitri Krioukov, M. Angeles Serrano
2020 arXiv   pre-print
Other forms of network geometry are the geometry of latent spaces underlying many networks, and the effective geometry induced by dynamical processes in networks.  ...  Yet the geometry induced by shortest path distances in a network is definitely not its only geometry.  ...  In the stable phase (s ≡ α/d B > 2) the RG flows towards the fractal fixed point, while in the unstable phase (s < 2) it flows towards a complete graph.  ... 
arXiv:2001.03241v2 fatcat:n3kqsgmpxffr5klzoihs525mrm

Change Detection in Graph Streams by Learning Graph Embeddings on Constant-Curvature Manifolds [article]

Daniele Grattarola, Daniele Zambon, Cesare Alippi, Lorenzo Livi
2019 arXiv   pre-print
The space of graphs is often characterised by a non-trivial geometry, which complicates learning and inference in practical applications.  ...  In this paper, we focus on the problem of detecting changes in stationarity in a stream of attributed graphs.  ...  Acknowledgements This research is funded by the Swiss National Science Foundation project 200021_172671: "ALPSFORT: A Learning graPh-baSed framework FOr cybeR-physical sysTems".  ... 
arXiv:1805.06299v3 fatcat:v3xpdicj3zg6higeso2gwmij4u

A probabilistic view of latent space graphs and phase transitions [article]

Suqi Liu, Miklos Z. Racz
2021 arXiv   pre-print
We prove phase transitions of detecting geometry in these graphs, in terms of the dimension of the underlying geometric space and the variance parameter of the conditional probability.  ...  We study random graphs with latent geometric structure, where the probability of each edge depends on the underlying random positions corresponding to the two endpoints.  ...  Acknowledgements We thank Ramon van Handel for insightful comments on several results and Jiacheng Zhang for suggesting the proofs of Lemma 2.6 and Lemma 4.3.  ... 
arXiv:2110.15886v1 fatcat:zogihtorkna65pq4vscwuyzx6y

Threshold for Detecting High Dimensional Geometry in Anisotropic Random Geometric Graphs [article]

Matthew Brennan, Guy Bresler, Brice Huang
2022 arXiv   pre-print
In the anisotropic random geometric graph model, vertices correspond to points drawn from a high-dimensional Gaussian distribution and two vertices are connected if their distance is smaller than a specified  ...  We study when it is possible to hypothesis test between such a graph and an Erdős-Rényi graph with the same edge probability.  ...  This work was done in part while the authors were participating in the Probability, Geometry, and Computation in High Dimensions program at the Simons Institute for the Theory of Computing in Fall 2020  ... 
arXiv:2206.14896v1 fatcat:ozoelchyi5anpew5j6wqhqif4y

Automated identification of transiting exoplanet candidates in NASA Transiting Exoplanets Survey Satellite (TESS) data with machine learning methods [article]

Leon Ofman, Amir Averbuch, Adi Shliselberg, Idan Benaun, David Segev, Aron Rissman
2021 arXiv   pre-print
., is applied to NASA's Transiting Exoplanets Survey Satellite (TESS) dataset to identify exoplanetary candidates.  ...  Existing and new features of the data, based on various observational parameters, are constructed and used in the AI/ML analysis by employing semi-supervised and unsupervised machine learning techniques  ...  We thank the referee for the invaluable input that helped improve this paper, and with assistance in vetting the TCE targets.  ... 
arXiv:2102.10326v2 fatcat:ayhwdzr4ejhmlmupvv2qwvyusa

Change Point Geometry for Change Detection in Surveillance Video [chapter]

Brandon A. Mayer, Joseph L. Mundy
2015 Lecture Notes in Computer Science  
The geometry of the change point hull provides a discriminating feature for distinguishing coherent movement from random or stochastic appearance changes and is simultaneously a rich descriptor for reasoning  ...  State of the art results are shown in change detection, a fundamental computer vision problem for identifying regions of video that exhibit meaningful variations as defined by the application context.  ...  latent state pairs: (S 1 , D 1 ), (S 2 , D 2 ), . . ., (S l , D l )) where S i is a state label and D i is a random variable that represents the time spent in state S i [10] .  ... 
doi:10.1007/978-3-319-19665-7_31 fatcat:hmsf7d4jlfafjg4w5kuh7ppnvq

Adversarial Autoencoders with Constant-Curvature Latent Manifolds [article]

Daniele Grattarola, Lorenzo Livi, Cesare Alippi
2019 arXiv   pre-print
Constant-curvature Riemannian manifolds (CCMs) have been shown to be ideal embedding spaces in many application domains, as their non-Euclidean geometry can naturally account for some relevant properties  ...  graph-based molecule generation using the QM9 chemical database.  ...  We gratefully acknowledge the support of NVIDIA Corporation with the donation of the Titan Xp GPU used for this research.  ... 
arXiv:1812.04314v2 fatcat:gi53rlqla5gnvavb2cwqslawqe

Emergence of the Circle in a Statistical Model of Random Cubic Graphs [article]

Christy Kelly, Carlo Trugenberger, Fabio Biancalana
2021 arXiv   pre-print
We also present strong evidence for the existence of a second-order phase transition through an analysis of finite size effects.  ...  This – essentially solvable – toy model of emergent one-dimensional geometry is meant as a controllable paradigm for the nonperturbative definition of random flat surfaces.  ...  of flat geometries in a model of random graphs.  ... 
arXiv:2008.11779v3 fatcat:4sopddxir5f45kr7aar33cix3a

Scalability of Learning Tasks on 3D CAE Models Using Point Cloud Autoencoders

Thiago Rios, Patricia Wollstadt, Bas van Stein, Thomas Back, Zhao Xu, Bernhard Sendhoff, Stefan Menzel
2019 2019 IEEE Symposium Series on Computational Intelligence (SSCI)  
Geometric Deep Learning (GDL) methods have recently gained interest as powerful, high-dimensional models for approaching various geometry processing tasks.  ...  methods in realworld tasks.  ...  We furthermore applied data augmentation by generating three random rotations around the z-axis for each geometry [21] , with rotations within the interval [-π/2, π/2].  ... 
doi:10.1109/ssci44817.2019.9002982 dblp:conf/ssci/RiosWSBXSM19 fatcat:pa7xufpfsbcalijlyzq5y5c76y

TribeFlow: Mining & Predicting User Trajectories [article]

Flavio Figueiredo, Bruno Ribeiro, Jussara Almeida, Christos Faloutsos
2016 arXiv   pre-print
These applications have in common the prediction of user trajectories that are in a constant state of flux over a hidden network (e.g. website links, geographic location).  ...  What users are doing now may be unrelated to what they will be doing in an hour from now.  ...  Acknowledgments Research was funded by Brazil's National Institute of Science and Technology for Web Research (MCT/CNPq/INCT Web 573871/2008-6).  ... 
arXiv:1511.01032v2 fatcat:duz43vdamnailirs5saabzfwku

Statistical physics of inference: thresholds and algorithms

Lenka Zdeborová, Florent Krzakala
2016 Advances in Physics  
A growing body of work has shown that often we can understand and locate these fundamental barriers by thinking of them as phase transitions in the sense of statistical physics.  ...  In terms of applications we review two classes of problems: (i) inference of clusters on graphs and networks, with community detection as a special case and (ii) estimating a signal from its noisy linear  ...  and Phase Transitions", at the Simons Institute for the Theory of Computing, which we thank for the kind hospitality.  ... 
doi:10.1080/00018732.2016.1211393 fatcat:sobocrcytvd3hhefrce6ykkvse

Detecting hyperbolic geometry in networks: why triangles are not enough [article]

Nelly Litvak, Riccardo Michielan, Clara Stegehuis
2022 arXiv   pre-print
We show analytically, as well as on synthetic and real-world data, that this is a powerful statistic to detect hyperbolic geometry in networks.  ...  In this paper we show that triangle counts or clustering coefficients are insufficient because they fail to detect geometry induced by hyperbolic spaces.  ...  The similarity of vertices can be modeled through geometry in a random graph.  ... 
arXiv:2206.01553v1 fatcat:2x3xwfe5x5cplmlx3sqm4rko4e

Characterizing the Analogy Between Hyperbolic Embedding and Community Structure of Complex Networks

Ali Faqeeh, Saeed Osat, Filippo Radicchi
2018 Physical Review Letters  
We show that the community structure of a network can be used as a coarse version of its embedding in a hidden space with hyperbolic geometry.  ...  We take advantage of the analogy for reinterpreting results originally obtained through network hyperbolic embedding in terms of community structure only.  ...  In Fig. 2(a) , we show the phase diagrams for instances of the multiplex model when relabeling uses information about the community structure of the graph.  ... 
doi:10.1103/physrevlett.121.098301 pmid:30230906 fatcat:3wjnufzamrdgvfwwtgrxegvv4y
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