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Semi-supervised Learning Based on Joint Diffusion of Graph Functions and Laplacians [chapter]

Kwang In Kim
2016 Lecture Notes in Computer Science  
We observe the distances between estimated function outputs on data points to create an anisotropic graph Laplacian which, through an iterative process, can itself be regularized.  ...  Our algorithm is instantiated as a discrete regularizer on a graph's diffusivity operator.  ...  an anisotropic diffusion process with a new metric on M [2] .  ... 
doi:10.1007/978-3-319-46454-1_43 fatcat:qtzgd247ojdbziwhjvnkah3s4y

Metadata-conscious anonymous messaging

Giulia Fanti, Peter Kairouz, Sewoong Oh, Kannan Ramchandran, Pramod Viswanath
2016 IEEE Transactions on Signal and Information Processing over Networks  
The spread of messages on these platforms can be modeled by a diffusion process over a graph.  ...  We further demonstrate empirically that adaptive diffusion hides the source effectively on real social networks.  ...  ACKNOWLEDGMENTS The authors thank the anonymous reviewers for their helpful comments and Paul Cuff for helpful discussions and for pointing out the Bayesian interpretation of the Polya's urn process.  ... 
doi:10.1109/tsipn.2016.2605761 fatcat:rugyvh2ojfb3xa7jrnddmzehy4

Geometric PDEs on Weighted Graphs for Semi-supervised Classification

Matthieu Toutain, Abderrahim Elmoataz, Olivier Lezoray
2014 2014 13th International Conference on Machine Learning and Applications  
In this paper, we consider the adaptation of two Partial Differential Equations (PDEs) on weighted graphs, p-Laplacian and eikonal equations, for semi-supervised classification tasks.  ...  While the p-Laplacian on graphs was intensively used in data classification, few works relate to the eikonal equation for data classification.  ...  for label diffusion over a graph using regularization [8] .  ... 
doi:10.1109/icmla.2014.43 dblp:conf/icmla/ToutainEL14 fatcat:btihul5v4rfnnjz65xeax6vgnq

Adaptive graph filtering: Multiresolution classification on graphs

Siheng Chen, Aliaksei Sandryhaila, Jose M. F. Moura, Jelena Kovacevic
2013 2013 IEEE Global Conference on Signal and Information Processing  
Adaptive graph filters combine decisions from multiple graph filters using a weighting function that is optimized in a semi-supervised manner.  ...  We also demonstrate the multiresolution property of adaptive graph filters by connecting them to the diffusion wavelets.  ...  graph filter coincides with the diffusion function.  ... 
doi:10.1109/globalsip.2013.6736906 dblp:conf/globalsip/ChenSMK13 fatcat:k5h4tezxgja5lk2tffotxfr5fy

Nonlocal graph regularization for image colorization

Olivier Lezoray, Vinh Thong Ta, Abderrahim Elmoataz
2008 Pattern Recognition (ICPR), Proceedings of the International Conference on  
Image colorization is then considered as a graph regularization problem for a function mapping vertices to chrominances.  ...  Then, p-Laplace regularization on weighted graphs problem is presented and the associated filter family.  ...  Construction of graphs The minimization problem (2) , and the discrete diffusion processes (6) , can be used to regularize any function defined on a finite set V of discrete data.  ... 
doi:10.1109/icpr.2008.4761617 dblp:conf/icpr/LezorayTE08a fatcat:4zjfxc3qvjes7cx5xk4axu3cym

Domain adaptive semantic diffusion for large scale context-based video annotation

Yu-Gang Jiang, Jun Wang, Shih-Fu Chang, Chong-Wah Ngo
2009 2009 IEEE 12th International Conference on Computer Vision  
In addition, the proposed approach is very efficient, completing DASD over 374 concepts within just 2 milliseconds for each video shot on a regular PC.  ...  Starting with a large set of concept detectors, the proposed DASD refines the initial annotation results using graph diffusion technique, which preserves the consistency and smoothness of the annotation  ...  From Equation 2, the gradient of with respect to on the semantic graph is: (7) Thus we can derive the following iterative diffusion process (8) Through exponentiating the graph Laplacian with step size  ... 
doi:10.1109/iccv.2009.5459295 dblp:conf/iccv/JiangWCN09 fatcat:vrhzwcuggzeqtcgfpixqpvbhpe

A scale-space based hierarchical representation of discrete data

M. Hidane, O. Lezoray, A. Elmoataz
2011 2011 18th IEEE International Conference on Image Processing  
A new hierarchical representation of general discrete data sets living on graphs is proposed. The approach takes advantage of recent works on graph regularization.  ...  Moreover, the approach is particularly well adapted to the processing of digital images, where nonlocal processing allows to better handle repetitive patterns usually present in natural images.  ...  Bougleux, "Nonlocal discrete regularization on weighted graphs: A framework for image and manifold processing," IEEE Transactions on Image Processing, vol. 17, no. 7, 2008.  ... 
doi:10.1109/icip.2011.6116144 dblp:conf/icip/HidaneLE11 fatcat:aioan5mvkjhsrnygqxbml7kv24

APRP: An Anonymous Propagation Method in Bitcoin Network

Yuhang Yao, Xiao Zeng, Tianyue Cao, Luoyi Fu, Xinbing Wang
delay factor and constantly adjusts PR-value of nodes to adapt to network dynamics.  ...  Experiments on both simulated and real Bitcoin networks confirm the superiority of APRP in terms of 20-50% performance enhancement under various deanonymization attacks.  ...  APRP(Trickle) estimation on d-regular trees. θ = 1. (c) Diffusion vs. APRP(Diffusion) estimation on dregular trees. θ = 1. (d) Diffusion vs. APRP(Diffusion) estimation on 4-regular trees.  ... 
doi:10.1609/aaai.v33i01.330110073 fatcat:nc5mjkjhyrdrlbr4jvdmgzve5m

Image Processing with Nonlocal Spectral Bases

Gabriel Peyré
2008 Multiscale Modeling & simulation  
This framework also allows one to define thresholding operators in adapted orthogonal bases. These bases are eigenvectors of the discrete Laplacian on a manifold adapted to the geometry of the image.  ...  All these schemes lead to regularizations that exploit the manifold structure of the lifted image.  ...  The geometric diffusion framework of Coifman et al. [16] can be used to process functions defined on a graph computed from M. Szlam et al.  ... 
doi:10.1137/07068881x fatcat:k7ti6526nvc7lpx4kisepctyoa

Graph Neural Networks With Lifting-based Adaptive Graph Wavelets [article]

Mingxing Xu, Wenrui Dai, Chenglin Li, Junni Zou, Hongkai Xiong, Pascal Frossard
2022 arXiv   pre-print
However, existing SGNNs are limited in implementing graph filters with rigid transforms (e.g., graph Fourier or predefined graph wavelet transforms) and cannot adapt to signals residing on graphs and tasks  ...  In this paper, we propose a novel class of graph neural networks that realizes graph filters with adaptive graph wavelets.  ...  GWNN [22] implements graph wavelet convolutions with diffusion wavelets [38] , where the wavelet coefficients are processed with parameter-intensive diagonal filters whose size depends on the number  ... 
arXiv:2108.01660v3 fatcat:liunq2ozw5dxlps7s3wcc52vry

Optimization of the Diffusion Time in Graph Diffused-Wasserstein Distances: Application to Domain Adaptation

Amelie Barbe, Paulo Goncalves, Marc Sebban, Pierre Borgnat, Remi Gribonval, Titouan Vayer
2021 2021 IEEE 33rd International Conference on Tools with Artificial Intelligence (ICTAI)  
distances on unsupervised graph domain adaptation tasks.  ...  The use of the heat kernel on graphs has recently given rise to a family of so-called Diffusion-Wasserstein distances which resort to the Optimal Transport theory for comparing attributed graphs.  ...  Domain Adaptation on synthetic data a) Synthetic data generation: The process for generating a synthetic graph of size N is the following.  ... 
doi:10.1109/ictai52525.2021.00125 fatcat:tfxm37hpjzcpjez7lzaj4mb7t4

Hiding the Rumor Source [article]

Giulia Fanti, Peter Kairouz, Sewoong Oh, Kannan Ramchandran, Pramod Viswanath
2016 arXiv   pre-print
Experiments on a sampled Facebook network demonstrate that adaptive diffusion effectively hides the location of the source even when the graph is finite, irregular and has cycles.  ...  We introduce a novel messaging protocol, which we call adaptive diffusion, and show that under the snapshot adversarial model, adaptive diffusion spreads content fast and achieves perfect obfuscation of  ...  Adaptive diffusion achieves the fundamental limit of Figure 18 ) on d-regular trees.  ... 
arXiv:1509.02849v2 fatcat:f4q6qv4nrnhifdy7yg7irii4bm

Neighborhood Adaptive Graph Convolutional Network for Node Classification

Peiliang Gong, Lihua Ai
2019 IEEE Access  
Besides, one learnable feature refinement process is used in the model to obtain high-level node representations with sufficient expressive power.  ...  Particularly, we construct a convolutional kernel abstracted from the diffusion process, named as the neighborhood adaptive kernel to more precisely learn and integrate related neighborhood node information  ...  To avoid over-fitting, we also use L2 regularization term on the loss function with coefficient 5 × 10 −4 and dropout mechanism with a dropout rate of 0.5.  ... 
doi:10.1109/access.2019.2955487 fatcat:lf5fyvge7za5bofhxwq4zvimcu

HAGEN: Homophily-Aware Graph Convolutional Recurrent Network for Crime Forecasting [article]

Chenyu Wang, Zongyu Lin, Xiaochen Yang, Jiao Sun, Mingxuan Yue, Cyrus Shahabi
2021 arXiv   pre-print
Specifically, our framework could jointly capture the crime correlation between regions and the temporal crime dynamics by combining an adaptive region graph learning module with the Diffusion Convolution  ...  Based on the homophily assumption of GNN, we propose a homophily-aware constraint to regularize the optimization of the region graph so that neighboring region nodes on the learned graph share similar  ...  Specifically, the directionaware diffusion convolution function f * (X; G, Θ, D W ) aggregates the input X on graph G(V, E, A r ) with parameters Θ and D W in the following way: where M is the total diffusion  ... 
arXiv:2109.12846v1 fatcat:2dhl3lhehnf5pki53wbtkbltk4

Discrete Regularization for Perceptual Image Segmentation via Semi-Supervised Learning and Optimal Control

Hongwei Zheng, Olaf Hellwich
2007 Multimedia and Expo, 2007 IEEE International Conference on  
Furthermore, the spectral segmentation is penalized and adjusted using labeling prior and optimal window-based affinity functions in a regularization framework on discrete graph spaces.  ...  In this approach, first, a spectral clustering method is embedded and extended into regularization on discrete graph spaces.  ...  DISCRETE REGULARIZATION ON GRAPHS A general weighted undirected graph G = (V, E) consists of two sets A and B with edges E, i.e., edges with one endpoint in A and the other in B, where V = {v i } n i=1  ... 
doi:10.1109/icme.2007.4285067 dblp:conf/icmcs/ZhengH07 fatcat:u46wpwjorraendk6gpparbb5ru
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