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Scalable Global Alignment Graph Kernel Using Random Features: From Node Embedding to Graph Embedding [article]

Lingfei Wu, Ian En-Hsu Yen, Zhen Zhang, Kun Xu, Liang Zhao, Xi Peng, Yinglong Xia, Charu Aggarwal
2019 arXiv   pre-print
In this paper, we propose a new family of global alignment graph kernels, which take into account the global properties of graphs by using geometric node embeddings and an associated node transportation  ...  Some recent global graph kernels, which utilizes the alignment of geometric node embeddings of graphs, yield state-of-the-art performance.  ...  Recently, a new class of graph kernels, which focus on the use of geometric node embeddings of graph to capture global properties, are proposed.  ... 
arXiv:1911.11119v1 fatcat:jritbw24pjdjzahvp76gyppe2e

Transport based Graph Kernels [article]

Kai Ma, Peng Wan, Daoqiang Zhang
2020 arXiv   pre-print
Each graph is embedded into hierarchical structures of the pyramid. Then, the OT distance is utilized to measure the similarity between graphs in hierarchical structures.  ...  Graph kernel is a powerful tool measuring the similarity between graphs. Most of the existing graph kernels focused on node labels or attributes and ignored graph hierarchical structure information.  ...  Their method used OT to capture the graph global structure and measured the graph similarity.  ... 
arXiv:2011.00745v1 fatcat:rtyggqvyevfqrg7gpl2unb27gi

Variational Graph Embedding for Globally and Locally Consistent Feature Extraction [chapter]

Shuang-Hong Yang, Hongyuan Zha, S. Kevin Zhou, Bao-Gang Hu
2009 Lecture Notes in Computer Science  
Existing feature extraction methods explore either global statistical or local geometric information underlying the data.  ...  Using mutual information and Bayes error rate as example criteria, we show that high-quality features can be learned from a variational graph embedding procedure, which is solved through an iterative EM-style  ...  -Secondly, the graphs learned by our method, which encodes both global (statistical) and local (geometric) structures of the data, can be used in a wide variety of graph-based learning tasks, e.g., semi-supervised  ... 
doi:10.1007/978-3-642-04174-7_35 fatcat:pq7k4ewhsbejxomkfu5akxm3bi

Learning embeddings for cross-time geographic areas represented as graphs

Margarita Khokhlova, Nathalie Abadie, Valérie Gouet-Brunet, Liming Chen
2021 ACM Symposium on Applied Computing  
Several use-case scenarios are proposed for the end-to-end learning of a graph embedding using Graph Neural Networks (GNN), along with an effective baseline without learning.  ...  Over time, the natural and man made landscape may evolve and thus also their graph representations.  ...  Many of the classical graph kernels are also based on the graph distances [5, 39] . Graph Embeddings.  ... 
doi:10.1145/3412841.3441936 dblp:conf/sac/KhokhlovaAG021 fatcat:t7i5pqfw6fc33k5na4tg7zdq5q

Graph Learning Network: A Structure Learning Algorithm [article]

Darwin Saire Pilco, Adín Ramírez Rivera
2019 arXiv   pre-print
Our model uses graph convolutions to propose expected node features, and predict the best structure based on them. We repeat these steps recursively to enhance the prediction and the embeddings.  ...  We propose the Graph Learning Network (GLN), a simple yet effective process to learn node embeddings and structure prediction functions.  ...  We acknowledge the support of NVIDIA Corporation for the donation of a Titan X Pascal GPU used in this research.  ... 
arXiv:1905.12665v3 fatcat:k65zn7jerzg6tlscvlcyzmcno4

Efficient retrieval of 3D building models using embeddings of attributed subgraphs

Raoul Wessel, Sebastian Ochmann, Richard Vock, Ina Blümel, Reinhard Klein
2011 Proceedings of the 20th ACM international conference on Information and knowledge management - CIKM '11  
In contrast to common approaches our algorithm relies on the interior spatial arrangement of rooms instead of exterior geometric shape.  ...  Aggregating all similarity values finally provides us with a single vector for each RCG which enables fast retrieval and classification.  ...  In particular, we used geometric random walk kernels as well as exponential random walk kernels [2] .  ... 
doi:10.1145/2063576.2063899 dblp:conf/cikm/WesselOVBK11 fatcat:jgbi6qdbsnekdbx4g63eafmck4

The Analysis from Nonlinear Distance Metric to Kernel-based Drug Prescription Prediction System [article]

Der-Chen Chang, Ophir Frieder, Chi-Feng Hung, Hao-Ren Yao
2021 arXiv   pre-print
These different geometric properties lead to different submanifolds in the original embedded space, and hence, to different optimizing nonlinear kernel embedding frameworks.  ...  Moreover, when presenting to highly variant chronic disease, it is preferable to use cosine distance.  ...  Acknowledgments The author is grateful to the reviewers for useful suggestions which improved the contents of this paper.  ... 
arXiv:2102.02446v2 fatcat:ifksqjlmmbfllalhj4qwhknup4

Diffusion Maps for Signal Processing: A Deeper Look at Manifold-Learning Techniques Based on Kernels and Graphs

Ronen Talmon, Israel Cohen, Sharon Gannot, Ronald R. Coifman
2013 IEEE Signal Processing Magazine  
The authors thank the anonymous reviewers for their constructive comments and useful suggestions.  ...  This enables to construct a graph based on a kernel using the local metric.  ...  It is worthwhile to note that the construction of the graph based on a kernel with a notion of locality is different than global methods.  ... 
doi:10.1109/msp.2013.2250353 fatcat:n32gc65zhffpvnesbwznbv2u4m

The analysis from nonlinear distance metric to kernel-based prescription prediction system

2021 Journal of Nonlinear and Variational Analysis  
The analysis of the distance functions used therein, namely the Euclidean and cosine distance measures and their respective derived graph kernels, is provided.  ...  Recently, a distance-derived graph kernel approach was commercially licensed for drug prescription efficacy prediction.  ...  Acknowledgments The authors are grateful to the reviewers for useful suggestions which improved the contents of this paper.  ... 
doi:10.23952/jnva.5.2021.2.01 fatcat:klmhbcq4zneebofglbscxn2hmu

A Regularized Wasserstein Framework for Graph Kernels [article]

Asiri Wijesinghe, Qing Wang, Stephen Gould
2021 arXiv   pre-print
We propose a learning framework for graph kernels, which is theoretically grounded on regularizing optimal transport.  ...  The other is to take into account node degree distributions in order to better preserve the global structure of graphs.  ...  Acknowledgement: We gratefully acknowledge that the Titan Xp used for this research was donated by NVIDIA.  ... 
arXiv:2110.02554v2 fatcat:kwmv2zqiijf35o2djfbzoi7c7i

Defining functional distance using manifold embeddings of gene ontology annotations

G. Lerman, B. E. Shakhnovich
2007 Proceedings of the National Academy of Sciences of the United States of America  
Here, we present several manifold embedding techniques to compute distances between Gene Ontology (GO) functional annotations and consequently estimate functional distances between protein domains.  ...  applied to a wide array of biologically relevant investigations, such as accuracy of annotation transference, the relationship between sequence, structure, and function, or coherence of expression modules. kernel  ...  We thank Mark Green and Institute for Pure and Applied Mathematics (University of California, Los Angeles) for inviting us to participate in a proteomics workshop, where we first met and started our discussion  ... 
doi:10.1073/pnas.0702965104 pmid:17595300 pmcid:PMC2040899 fatcat:zky3jcbh3rhahiuyrddymfhsau

Geometric Characterisation of Graphs [chapter]

Bai Xiao, Edwin R. Hancock
2005 Lecture Notes in Computer Science  
The embedding is performed using the heat-kernel of the graph, computed by exponentiating the Laplacian eigen-system.  ...  In this paper, we explore whether the geometric properties of the point distribution obtained by embedding the nodes of a graph on a manifold can be used for the purposes of graph clustering.  ...  ]φ i (u)φ i (v) (8) Geometric Properties of the Manifold In this paper our aim is to explore whether the geometric properties of the embedding can be used for the purposes of characterising and clustering  ... 
doi:10.1007/11553595_58 fatcat:mpltznnxfbb5fm5s4g3js7osqe

Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps

R. R. Coifman, S. Lafon, A. B. Lee, M. Maggioni, B. Nadler, F. Warner, S. W. Zucker
2005 Proceedings of the National Academy of Sciences of the United States of America  
We provide a framework for structural multiscale geometric organization of graphs and subsets of R n .  ...  We use diffusion semigroups to generate multiscale geometries in order to organize and represent complex structures.  ...  The authors would like to thank Naoki Saito for his useful comments and suggestions during the preparation of the manuscript.  ... 
doi:10.1073/pnas.0500334102 pmid:15899970 pmcid:PMC1140422 fatcat:ctdhxdych5cstcghuam5xzwaeu

Ricci flow embedding for rectifying non-Euclidean dissimilarity data

Weiping Xu, Edwin R. Hancock, Richard C. Wilson
2014 Pattern Recognition  
Such non-Euclidean dissimilarities are often corrected or a consistent Euclidean geometry imposed on them via embedding.  ...  Article: Xu, Weiping, Hancock, Edwin R and Wilson, Richard Charles (2014) Ricci flow embedding for rectifying non-Euclidean dissimilarity data  ...  To evaluate the global structure of the data before and after Ricci flow embedding, we use the linear SVM and the RBF SVM 3 .  ... 
doi:10.1016/j.patcog.2014.04.021 fatcat:fq5hrz4t3rc35hxlyabdwedg4y

A Kernel Based Neighborhood Discriminant Submanifold Learning for Pattern Classification

Xu Zhao
2014 Journal of Applied Mathematics  
KNDA nonlinearly maps the original data into a kernel space in which two graphs are constructed to depict the within-class submanifold and the between-class submanifold.  ...  We propose a novel method, called Kernel Neighborhood Discriminant Analysis (KNDA), which can be regarded as a supervised kernel extension of Locality Preserving Projection (LPP).  ...  Here, by using a different locally geometrical intuition, we proposed a novel submanifold learning method, called Kernel Neighborhood Discriminant Analysis (KNDA), which is based on the kernel tricks  ... 
doi:10.1155/2014/950349 fatcat:qn4j2zwpnncxnikcwol2tl224m
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