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Early Fire Detection Based on Aerial 360-Degree Sensors, Deep Convolution Neural Networks and Exploitation of Fire Dynamic Textures

Panagiotis Barmpoutis, Tania Stathaki, Kosmas Dimitropoulos, Nikos Grammalidis
2020 Remote Sensing  
Then, two DeepLab V3+ networks are applied to perform flame and smoke segmentation, respectively.  ...  More specifically, once optical 360-degree raw data are obtained using an RGB 360-degree camera mounted on an unmanned aerial vehicle, we convert the equirectangular projection format images to stereographic  ...  To address the k-NN problem, we apply the inverse exponential map between two points on the manifold, e.g., G 1 and G 2 , to map the first Grassmannian point to a tangent space of the second one, while  ... 
doi:10.3390/rs12193177 fatcat:tju6cx4dizgpfhrzb2wbsc7zyu

Active Learning by Spherical Subdivision

Falk-Florian Henrich, Klaus Obermayer
2008 Journal of machine learning research  
In order to reduce computational complexity the version space is restricted to spherical simplices and learning procedes by subdividing the edges of maximal length.  ...  The method is then extended to other separable classification problems using products of spheres as data spaces and isometries induced by charts of the sphere.  ...  We now apply the isometries discussed in Section 4 to product manifolds. For each factor in Equation 4 , we may choose one of stereographic or gnomonic projection. M n 1 +...  ... 
dblp:journals/jmlr/HenrichO08 fatcat:ez27jgxghzgdjg6iii4wzt5daq

Representing Data by a Mixture of Activated Simplices [article]

Chunyu Wang, John Flynn, Yizhou Wang, Alan L. Yuille
2014 arXiv   pre-print
We give a simple geometric understanding that allows us to learn a simplicial structure efficiently. Our method requires that the data are unit normalized (and thus lie on the unit sphere).  ...  The simplices are easy to interpret and extremes within the data can be discovered among the vertices. The method provides good reconstruction and regularization.  ...  For synthesis one might map the synthesized points back to R d with inverse stereographic projection. But it can also be useful to map the simplicial structure back to R d .  ... 
arXiv:1412.4102v1 fatcat:czz3d4yllbcazowmqsiiwxq44e

Local conformal autoencoder for standardized data coordinates

Erez Peterfreund, Ofir Lindenbaum, Felix Dietrich, Tom Bertalan, Matan Gavish, Ioannis G. Kevrekidis, Ronald R. Coifman
2020 Proceedings of the National Academy of Sciences of the United States of America  
We assume a repeated measurement sampling strategy, common in scientific measurements, and present a method for learning an embedding in Rd that is isometric to the latent variables of the manifold.  ...  Finally, we demonstrate LOCA's efficacy in single-site Wi-Fi localization data and for the reconstruction of three-dimensional curved surfaces from two-dimensional projections.  ...  ACKNOWLEDGMENTS This work was partially supported by the Defense Advanced Research Projects Agency Physics of Artificial Intelligence program (Agreement HR00111890032, Dr. T. Senator).  ... 
doi:10.1073/pnas.2014627117 pmid:33229581 fatcat:5hfcfmevqjdtpgckfgsltp2wgm

Rigid quantum Monte Carlo simulations of condensed molecular matter: Water clusters in the n=2→8 range

Stephen F. Langley, E. Curotto, D. L. Freeman, J. D. Doll
2007 Journal of Chemical Physics  
The reweighted random series approach for stereographic path integral Monte Carlo is refined and implemented for the quantum simulation of water clusters treated as an assembly of rigid asymmetric tops  ...  ; the stereographic projection path integral adapted for quantum simulations of asymmetric tops is a significantly more efficient strategy compared with Cartesian coordinate simulations for molecular condensed  ...  Campbell for many long constructive conversations surrounding water clusters. This work has been supported by the National Science Foundation ͑Grant No. CHE0554922͒.  ... 
doi:10.1063/1.2484229 pmid:17343457 fatcat:xflgahj4rvad7lnumlyhihp5k4

LOCA: LOcal Conformal Autoencoder for standardized data coordinates [article]

Erez Peterfreund, Ofir Lindenbaum, Felix Dietrich, Tom Bertalan, Matan Gavish, Ioannis G. Kevrekidis, Ronald R. Coifman
2021 arXiv   pre-print
Finally, we apply LOCA to single-site Wi-Fi localization data, and to 3-dimensional curved surface estimation based on a 2-dimensional projection.  ...  By leveraging a repeated measurement sampling strategy, we present a method for learning an embedding in ℝ^d that is isometric to the latent variables of the manifold.  ...  Army Research Laboratory and the U. S. Army Research Office under contract/grant number W911NF1710306.  ... 
arXiv:2004.07234v2 fatcat:bnsxbtl6g5ekzdcqnp7xuc7mue

Importance sampling for quantum Monte Carlo in manifolds: Addressing the time scale problem in simulations of molecular aggregates

T. Luan, E. Curotto, Massimo Mella
2008 Journal of Chemical Physics  
Several importance sampling strategies are developed and tested for stereographic projection diffusion Monte Carlo in manifolds.  ...  We test a family of one parameter trial wavefunctions for variational Monte Carlo in stereographically projected manifolds which can be used to produce importance sampling.  ...  Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the ACS ͑Grant No. 40946-B6͒ for partial support of this research.  ... 
doi:10.1063/1.2898539 pmid:18447416 fatcat:tab7hejyknhvrf2jiggza547q4

Statistical Modeling of Curves Using Shapes and Related Features

Sebastian Kurtek, Anuj Srivastava, Eric Klassen, Zhaohua Ding
2012 Journal of the American Statistical Association  
Truncated Gaussian Under the Stereographic Projection Another possibility to map a pdf from R k to S k is by using the stereographic projection.  ...  The basic idea is to define a truncated Gaussian distribution in a tangent space of the manifold and then map it back to the manifold.  ... 
doi:10.1080/01621459.2012.699770 fatcat:gihgmymcnrauln3yskbwfo7igi

Thermodynamic properties of ammonia clusters (NH3)n n=2–11: Comparing classical and quantum simulation results for hydrogen bonded species

C. Lubombo, E. Curotto, Paula E. Janeiro Barral, Massimo Mella
2009 Journal of Chemical Physics  
Classical and quantum simulations of ammonia clusters in the dimer through the hendecamer range are performed using the stereographic projection path integral.  ...  We develop a first order finite difference algorithm to integrate the geodesic equations in the inertia ellipsoid generated by n rigid nonlinear bodies mapped with stereographic projections.  ...  Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the ACS ͑Grant No. 41846-B6͒ for partial support of this research.  ... 
doi:10.1063/1.3159398 pmid:19624202 fatcat:t7anfcoqzrcdjirfef7xdbxwyq

Mixed-curvature Variational Autoencoders [article]

Ondrej Skopek, Octavian-Eugen Ganea, Gary Bécigneul
2020 arXiv   pre-print
Euclidean geometry has historically been the typical "workhorse" for machine learning applications due to its power and simplicity.  ...  This generalizes the Euclidean VAE to curved latent spaces and recovers it when curvatures of all latent space components go to 0.  ...  Stereographic projection Remark A.9 (Homeomorphism between S n K and R n ).  ... 
arXiv:1911.08411v2 fatcat:iav2ct7mqrahxacx5g4biec4jy

Hyperbolic Deep Neural Networks: A Survey [article]

Wei Peng, Tuomas Varanka, Abdelrahman Mostafa, Henglin Shi, Guoying Zhao
2021 arXiv   pre-print
It also presents current applicationsaround various machine learning tasks on several publicly available datasets, together with insightful observations and identifying openquestions and promising future  ...  Recently, there has been a rising surge of momentum for deep representation learning in hyperbolic spaces due to theirhigh capacity of modeling data like knowledge graphs or synonym hierarchies, possessing  ...  This work is supported by the Academy of Finland for ICT 2023 project (grant 328115) and project MiGA (grant 316765) and Infotech Oulu.  ... 
arXiv:2101.04562v3 fatcat:yqj4zohrqjbplpsdy5f5uglnbu

Hyperbolic Deep Neural Networks: A Survey

Wei Peng, Tuomas Varanka, Abdelrahman Mostafa, Henglin Shi, Guoying Zhao
2021 IEEE Transactions on Pattern Analysis and Machine Intelligence  
leading deep approaches to the hyperbolic space.  ...  To stimulate future research, this paper presents a coherent and a comprehensive review of the literature around the neural components in the construction of HDNN, as well as the generalization of the  ...  This work is supported by the Academy of Finland for ICT 2023 project (grant 328115), Academy Professor project Emo-tionAI (grants 336116, 345122), project MiGA (grant 316765) and Infotech Oulu.  ... 
doi:10.1109/tpami.2021.3136921 pmid:34932472 fatcat:ccpfqsjlevgyxpetwd73kvbf4y

Low-dimensional statistical manifold embedding of directed graphs [article]

Thorben Funke, Tian Guo, Alen Lancic, Nino Antulov-Fantulin
2020 arXiv   pre-print
We propose a novel node embedding of directed graphs to statistical manifolds, which is based on a global minimization of pairwise relative entropy and graph geodesics in a non-linear way.  ...  Furthermore, we analyze the connection between the geometrical properties of such embedding and their efficient learning procedure.  ...  From here, we read that the inverse of the stereographic projection is as stated above.  ... 
arXiv:1905.10227v3 fatcat:zaxy7tsejvgsjnvplae47kydyq

Non-Euclidean Self-Organizing Maps [article]

Dorota Celińska-Kopczyńska Eryk Kopczyński
2022 arXiv   pre-print
Our proposition can be successfully applied to dimension reduction, clustering or finding similarities in big data (both hierarchical and non-hierarchical).  ...  Self-Organizing Maps (SOMs, Kohonen networks) belong to neural network models of the unsupervised class. In this paper, we present the generalized setup for non-Euclidean SOMs.  ...  Stereographic projection. Stereographic projection projects the point a of the unit sphere to the point b on the plane z = 1 such that a, b, and (0, 0, −1) are colinear.  ... 
arXiv:2109.11769v2 fatcat:upybklcs6bhrfmmt64gfnjphry

The Structure of Isoperimetric Bubbles on ℝ^n and 𝕊^n [article]

Emanuel Milman, Joe Neeman
2022 arXiv   pre-print
In fact, we show that for all q ≤ n+1, a minimizing cluster necessarily has spherical interfaces, and after stereographic projection to 𝕊^n, its cells are obtained as the Voronoi cells of q affine-functions  ...  The proof makes crucial use of considering ℝ^n and 𝕊^n in tandem and of Möbius geometry and conformal Killing fields; it does not rely on establishing a PDI for the isoperimetric profile as in the Gaussian  ...  ; in particular, it is a pleasure to thank Rachel Ward and Francesco Maggi.  ... 
arXiv:2205.09102v2 fatcat:o6wdos6tvfgotiht3d634vv63m
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