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Principal Neighbourhood Aggregation for Graph Nets [article]

Gabriele Corso, Luca Cavalleri, Dominique Beaini, Pietro Liò, Petar Veličković
2020 arXiv   pre-print
Accordingly, we propose Principal Neighbourhood Aggregation (PNA), a novel architecture combining multiple aggregators with degree-scalers (which generalize the sum aggregator).  ...  Graph Neural Networks (GNNs) have been shown to be effective models for different predictive tasks on graph-structured data.  ...  Acknowledgements The authors thank Saro Passaro for the valuable insights and discussion for the mathematical proofs. 9 Funding Disclosure Dominique Beaini is currently a Machine Learning Researcher  ... 
arXiv:2004.05718v5 fatcat:lbrxuhwqw5b5zm7ye6xzgacorq

2D-3D Geometric Fusion network using Multi-Neighbourhood Graph Convolution for RGB-D indoor scene classification

Albert Mosella-Montoro, Javier Ruiz-Hidalgo
2021 Information Fusion  
The first layer, Multi-Neighbourhood Graph Convolution, aims to learn a more robust geometric descriptor of the scene combining two different neighbourhoods: one in the Euclidean space and the other in  ...  Multi-Neighbourhood Graph Convolution (MUNEGC) The proposed Multi-Neighbourhood Graph Convolution (MUNEGC) is an extension of the Attention Graph Convolution (AGC) [17] .  ...  Furthermore, in Table 7 , the influence of the aggregation method of both neighbourhoods in MUNEGC can be seen. The average aggregation shows a better performance than the maximum aggregation.  ... 
doi:10.1016/j.inffus.2021.05.002 fatcat:a2lib6r5v5ewjawrytl46h6dn4

Hierarchical Graph Representations in Digital Pathology [article]

Pushpak Pati and Guillaume Jaume and Antonio Foncubierta and Florinda Feroce and Anna Maria Anniciello and Giosuè Scognamiglio and Nadia Brancati and Maryse Fiche and Estelle Dubruc and Daniel Riccio and Maurizio Di Bonito and Giuseppe De Pietro and Gerardo Botti and Jean-Philippe Thiran and Maria Frucci and Orcun Goksel and Maria Gabrani
2021 arXiv   pre-print
Specifically, for input histology images we utilize well-defined cells and tissue regions to build HierArchical Cell-to-Tissue (HACT) graph representations, and devise HACT-Net, a graph neural network,  ...  Thus, adequate tissue representations for encoding histological entities is imperative for computer aided cancer patient care.  ...  In this work, we leverage the recent advances in GNNs and model HACT-Net using Principal Neighbourhood Aggregation (PNA) layers [62] .  ... 
arXiv:2102.11057v2 fatcat:uuk5hlscwfddnku5rgr4evxxlm

Natural Graph Networks [article]

Pim de Haan, Taco Cohen, Max Welling
2020 arXiv   pre-print
A key requirement for graph neural networks is that they must process a graph in a way that does not depend on how the graph is described.  ...  Here we show that instead of equivariance, the more general concept of naturality is sufficient for a graph network to be well-defined, opening up a larger class of graph networks.  ...  P contains as objects principal bundle fibers P x for each x P M. A morphism φ : P x Ñ P y is any equivariant map.  ... 
arXiv:2007.08349v2 fatcat:bble7vlwiza77k7i2jv3tvvcce

Shape-Oriented Convolution Neural Network for Point Cloud Analysis [article]

Chaoyi Zhang, Yang Song, Lina Yao, Weidong Cai
2020 arXiv   pre-print
Point cloud is a principal data structure adopted for 3D geometric information encoding.  ...  This shape-oriented operator is stacked into our hierarchical learning architecture, namely Shape-Oriented Convolutional Neural Network (SOCNN), developed for point cloud analysis.  ...  Finally, we propose the shape-oriented convolution neural network (SOCNN) for point cloud analysis and evaluate its significance in the point cloud tasks of shape classification and shape part segmentation  ... 
arXiv:2004.09411v1 fatcat:z2vcd4yrpzayjllzisxfcoj2ky

Shape-Oriented Convolution Neural Network for Point Cloud Analysis

Chaoyi Zhang, Yang Song, Lina Yao, Weidong Cai
2020 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
Point cloud is a principal data structure adopted for 3D geometric information encoding.  ...  This shape-oriented operator is stacked into our hierarchical learning architecture, namely Shape-Oriented Convolutional Neural Network (SOCNN), developed for point cloud analysis.  ...  dynamically constructed among these points, and is the feature aggregation function covering the entire local neighbourhood.  ... 
doi:10.1609/aaai.v34i07.6972 fatcat:5gsr6way3vgyjosggpthp2iwie

The two faces of knowledge diffusion: the Chilean case

Piergiuseppe Morone
2005 Journal of International Development  
We have constructed socialaffinity neighbourhoods using principal component and cluster analysis.  ...  Through the methodology of principal components we identified the most significant variables for our analysis.  ... 
doi:10.1002/jid.1198 fatcat:mvdzuupwkjgajnvjby4gycdtiu

Ethnic Segregation and Xenophobic Party Preference: Exploring the Influence of the Presence of Visible Minorities on Local Electoral Support for the Sweden Democrats

Per Strömblad, Bo Malmberg
2016 Journal of Urban Affairs  
Utilising aggregate level data for all electoral districts in Sweden, our contribution is built on a GIS-based novel methodological approach, through which neighbourhoods with a fixed population size is  ...  empirically defined for each individual in each electoral district.  ...  Hence, in contrast to the largely parallel shifts of curves in the graphs when the aggregate level of education is varied (compare for instance the location of the solid lines of Figure 3A and 3B), different  ... 
doi:10.1111/juaf.12227 fatcat:nw4ivrv7enbsxpdyjohpoaxf7q

A Spatial-Channel Collaborative Attention Network for Enhancement of Multiresolution Classification

Wenping Ma, Jiliang Zhao, Hao Zhu, Jianchao Shen, Licheng Jiao, Yue Wu, Biao Hou
2020 Remote Sensing  
In this paper, from the perspective of deep learning, we design a dual-branch interactive spatial-channel collaborative attention enhancement network (SCCA-net) for multiresolution classification.  ...  And it also adaptively adjust the sampling angle according to the texture distribution of the homogeneous region to capture neighbourhood information that is more conducive for classification.  ...  Subsequently, GSoP [34] introduces a second-order pooling for more effective feature aggregation.  ... 
doi:10.3390/rs13010106 fatcat:fbbp3f243ffi3ccfooe542cvmy

Exploration-exploitation trade-off features a saltatory search behaviour [article]

Dimitri Volchenkov, Jonathan Helbach, Marko Tscherepanow, Sina Kühnel
2013 arXiv   pre-print
It is obvious that such an intensive space scan is performed by subjects only within their immediate neighbourhoods and principally cannot be extended neither to the entire VE, nor even to any of its significant  ...  of the net displacements from 0.1 m to 6 m, and from 0.3 m to 10 m, for the VE model B.  ... 
arXiv:1305.5650v1 fatcat:p5qzvqfphnf6vf3jyqaadulqfe

Exploration-exploitation trade-off features a saltatory search behaviour

D. Volchenkov, J. Helbach, M. Tscherepanow, S. Kuhnel
2013 Journal of the Royal Society Interface  
net displacements from 0.1 to 6 m, and from 0.3 to 10 m for VE model B.  ...  It is obvious that such an intensive space scan is performed by subjects only within their immediate neighbourhoods and principally cannot be extended either to the entire VE, or even to any of its significant  ... 
doi:10.1098/rsif.2013.0352 pmid:23782535 pmcid:PMC4043171 fatcat:ijkyu3kvivckxkjwg4skz6hqsa

Exploration-exploitation Trade-off in a Treasure Hunting Game

Dimitri Volchenkov, Jonathan Helbach, Marko Tscherepanow, Sina Küheel
2013 Electronical Notes in Theoretical Computer Science  
It is obvious that such an intensive space scan is performed by subjects only within their immediate neighbourhoods and principally cannot be extended neither to the entire VE, nor even to any of its significant  ...  of the net displacements from 0.1 m to 6 m, and from 0.3 m to 10 m, for the VE model B.  ... 
doi:10.1016/j.entcs.2013.11.009 fatcat:owvobytizzby7ct6flmhtswqo4

Implementing a Multilevel Index of Dissimilarity in R with a case study of the changing scales of residential ethnic segregation in England and Wales

Richard Harris, Dewi Owen
2017 Environment and Planning B Urban Analytics and City Science  
Acknowledgements My grateful thanks for the comments of the referees for improving the clarity of the work.  ...  Funding The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The research was funded under the Economic and Social Research  ...  Critically, the scales are examined net of one another.  ... 
doi:10.1177/2399808317748328 fatcat:nzvwory4cbazholkvldzcg66du

Toward a Theory of Chaos [article]

A. Sengupta
2004 arXiv   pre-print
approach to the study of chaos in discrete dynamical systems based on the notions of inverse ill-posed problems, set-valued mappings, generalized and multivalued inverses, graphical convergence of a net  ...  numerically exact results obtained by this approximation of the Case singular eigenfunction solution is due to the graphical convergence of the Poisson and conjugate Poisson kernels to the Dirac delta and the principal  ...  Leon O Chua for suggesting a pedagogically self-contained, jargonless no-page limit version accessible to a wider audience for the present form of the paper.  ... 
arXiv:nlin/0408044v1 fatcat:igx7fsbyores7diqfmqaig6g2a

Subspace Graph Physics: Real-Time Rigid Body-Driven Granular Flow Simulation [article]

Amin Haeri, Krzysztof Skonieczny
2021 arXiv   pre-print
Principal component analysis (PCA) is used to reduce the dimensionality of data. We show that the first few principal components of our high-dimensional data keep almost the entire variance in data.  ...  A promising direction for accurate, yet efficient, modeling is using continuum methods. Also, a new direction for real-time physics modeling is the use of deep learning.  ...  Isomorphic nodes are defined as the nodes that have the same computational graphs (i.e. same features and neighbourhood structure).  ... 
arXiv:2111.10206v1 fatcat:vntwi2zoevfsrfmvohvydhqqte
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