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Graph Summarization [article]

Angela Bonifati, Stefania Dumbrava, Haridimos Kondylakis
2020 arXiv   pre-print
One method for condensing and simplifying such datasets is graph summarization.  ...  The focus of our chapter is to pinpoint the main graph summarization methods, but especially to focus on the most recent approaches and novel research trends on this topic, not yet covered by previous  ...  To this end, the authors introduce the query-oriented normalized cut and cluster balance metrics and combine these to compute the output clustering.  ... 
arXiv:2004.14794v3 fatcat:4g4l3exin5dxpoe6pdggbtcory

Distance Metric Learning for Graph Structured Data [article]

Tomoki Yoshida, Ichiro Takeuchi, Masayuki Karasuyama
2020 arXiv   pre-print
Our method, named interpretable graph metric learning (IGML), learns discriminative metrics in a subgraph-based feature space, which has a strong graph representation capability.  ...  Although many of those learning methods depend on the measurement of differences between input graphs, defining an appropriate distance metric for a graph remains a controversial issue.  ...  Conclusions We proposed an interpretable metric learning method for graph data, named interpretable graph metric learning (IGML).  ... 
arXiv:2002.00727v1 fatcat:5wvlulx42nb6vfsj5stisrtamm

Principal Graph and Structure Learning Based on Reversed Graph Embedding

Qi Mao, Li Wang, Ivor W. Tsang, Yijun Sun
2017 IEEE Transactions on Pattern Analysis and Machine Intelligence  
As showcases, models that can learn a spanning tree or a weighted undirected 1 graph are proposed, and a new learning algorithm is developed that learns a set of principal points and a graph structure  ...  To address these issues, we develop a novel principal graph and structure learning framework that captures the local information of the underlying graph structure based on reversed graph embedding.  ...  We use the alternate convex search algorithm to solve the proposed formulations by simultaneously learning a set of principal points and an undirected graph with guaranteed convergence.  ... 
doi:10.1109/tpami.2016.2635657 pmid:28114001 pmcid:PMC5899072 fatcat:ashwrjrr6nedpn422d2uxalbzy

GRASPEL: Graph Spectral Learning at Scale [article]

Yongyu Wang, Zhiqiang Zhao, Zhuo Feng
2020 arXiv   pre-print
Compared with prior state-of-the-art graph learning approaches, GRASPEL is more scalable and allows substantially improving computing efficiency and solution quality of a variety of data mining and machine  ...  Learning meaningful graphs from data plays important roles in many data mining and machine learning tasks, such as data representation and analysis, dimension reduction, data clustering, and visualization  ...  Compared with prior state-of-the-art graph learning approaches, GRASPEL is more scalable and leads to substantially improved computing efficiency and solution quality for a variety of data mining and machine  ... 
arXiv:1911.10373v3 fatcat:csaj7yuokrg7fbuhrgk53jvx5u

Signed Graph Metric Learning via Gershgorin Disc Perfect Alignment [article]

Cheng Yang, Gene Cheung, Wei Hu
2021 arXiv   pre-print
Given a convex and differentiable objective Q() for a real symmetric matrix in the positive definite (PD) cone – used to compute Mahalanobis distances – we propose a fast general metric learning framework  ...  Using this theorem, we replace the PD cone constraint in the metric learning problem with tightest possible linear constraints per iteration, so that the alternating optimization of the diagonal / off-diagonal  ...  Thus, S is a union of convex sets of graph metric matrices of the same signs, and S is locally convex.  ... 
arXiv:2006.08816v6 fatcat:hcrpzmttxrgkjl7lphjvvrswli

GraKeL: A Graph Kernel Library in Python [article]

Giannis Siglidis, Giannis Nikolentzos, Stratis Limnios, Christos Giatsidis, Konstantinos Skianis, Michalis Vazirgiannis
2020 arXiv   pre-print
It is simple to use and can be naturally combined with scikit-learn's modules to build a complete machine learning pipeline for tasks such as graph classification and clustering.  ...  Here, we present GraKeL, a library that unifies several graph kernels into a common framework. The library is written in Python and adheres to the scikit-learn interface.  ...  GraKeL can also interoperate with scikit-learn for performing machine learning tasks on graphs (Pedregosa et al., 2011) . • BLISS: a tool for computing automorphism groups and canonical labelings of graphs  ... 
arXiv:1806.02193v2 fatcat:6kriueyit5c2hjqzmrzmfnidxe

Some Advances in Role Discovery in Graphs [article]

Sean Gilpin, Chia-Tung Kuo, Tina Eliassi-Rad, Ian Davidson
2016 arXiv   pre-print
A natural representation of a multi-relational graph is an order 3 tensor (rather than a matrix) and that a Tucker decomposition allows us to find complex interactions between collections of entities (  ...  Our framework allows convex constraints to be placed on the role discovery problem which can provide useful supervision.  ...  FA8650-10-C-7061 and in part by DAPRA under SMISC Program Agreement No. W911NF-12-C-0028.  ... 
arXiv:1609.02646v1 fatcat:3tctaeacjrgwfnwngaukdyqd3a

Survey on graph embeddings and their applications to machine learning problems on graphs

Ilya Makarov, Dmitrii Kiselev, Nikita Nikitinsky, Lovro Subelj
2021 PeerJ Computer Science  
First, we start with the methodological approach and extract three types of graph embedding models based on matrix factorization, random-walks and deep learning approaches.  ...  Finally, we overview the existing applications of graph embeddings to computer science domains, formulate open problems and provide experiment results, explaining how different networks properties result  ...  It learns the vector by predicting masked words. Such tasks can be formulated as link prediction between context and masked words.  ... 
doi:10.7717/peerj-cs.357 pmid:33817007 pmcid:PMC7959646 fatcat:ntronyrbgfbedez5dks6h4hoq4

Online Graph Dictionary Learning [article]

Cédric Vincent-Cuaz, Titouan Vayer, Rémi Flamary, Marco Corneli, Nicolas Courty
2021 arXiv   pre-print
Yet, this analysis is not amenable in the context of graph learning, as graphs usually belong to different metric spaces.  ...  In our work, graphs are encoded through their nodes' pairwise relations and modeled as convex combination of graph atoms, i.e. dictionary elements, estimated thanks to an online stochastic algorithm, which  ...  The authors are grateful to the OPAL infrastructure from Université Côte d'Azur for providing resources and support.  ... 
arXiv:2102.06555v2 fatcat:eqg6e7s3lrfe5g5uuihpryjhwq

Analysis of sports statistics via graph-signal smoothness prior

Haitian Zheng, Gene Cheung, Lu Fang
2015 2015 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference (APSIPA)  
Finally, assuming a graph-signal smoothness prior, we compute the desired graph-signal on the constructed graph via an alternating convex programming procedure.  ...  k and l.  ...  Discussion Our graph-signal formulation in (12) means that the graphsignal in question can be interpreted as samples on a smooth continuous manifold [5, 6] , and an edge weight between two nodes is  ... 
doi:10.1109/apsipa.2015.7415436 dblp:conf/apsipa/ZhengCF15 fatcat:v3rshe4iencgbi4grc4kfd4zye

Graph Regularized Sparse Coding for Image Representation

Miao Zheng, Jiajun Bu, Chun Chen, Can Wang, Lijun Zhang, Guang Qiu, Deng Cai
2011 IEEE Transactions on Image Processing  
It is an unsupervised learning algorithm, which finds a basis set capturing high-level semantics in the data and learns sparse coordinates in terms of the basis set.  ...  In this paper, we propose a graph based algorithm, called graph regularized sparse coding, to learn the sparse representations that explicitly take into account the local manifold structure of the data  ...  Sparse representations encode many of the images using only a few active coefficients, which make the encoding easy to interpret and reduce the computational cost.  ... 
doi:10.1109/tip.2010.2090535 pmid:21047712 fatcat:6rfbyic7kzf55nra5sdoydbrda

Approximate Network Motif Mining Via Graph Learning [article]

Carlos Oliver, Dexiong Chen, Vincent Mallet, Pericles Philippopoulos, Karsten Borgwardt
2022 arXiv   pre-print
Finally, we demonstrate through MotiFiesta that this learning setting can be applied simultaneously to general-purpose data mining and interpretable feature extraction for graph classification tasks.  ...  In this work we seek to facilitate the development of machine learning approaches aimed at motif mining. We propose a formulation of the motif mining problem as a node labelling task.  ...  Contributions In this work, we (1) formalize the notion of approximate motif mining as a machine learning task and provide appropriate evaluation metrics as well as benchmarking datasets, (2) propose  ... 
arXiv:2206.01008v1 fatcat:bpgaoebxl5folap2t3exc4brqa

Implicit Graph Neural Networks [article]

Fangda Gu, Heng Chang, Wenwu Zhu, Somayeh Sojoudi, Laurent El Ghaoui
2021 arXiv   pre-print
Graph Neural Networks (GNNs) are widely used deep learning models that learn meaningful representations from graph-structured data.  ...  To overcome this difficulty, we propose a graph learning framework, called Implicit Graph Neural Networks (IGNN), where predictions are based on the solution of a fixed-point equilibrium equation involving  ...  Acknowledgments and Disclosure of Funding  ... 
arXiv:2009.06211v3 fatcat:dbdbxzrzgbhdtogkcp4ffuvrf4

Semi-Supervised Graph Classification: A Hierarchical Graph Perspective [article]

Jia Li, Yu Rong, Hong Cheng, Helen Meng, Wenbing Huang, Junzhou Huang
2019 arXiv   pre-print
meaningful interpretations of the learned representations.  ...  Node classification and graph classification are two graph learning problems that predict the class label of a node and the class label of a graph respectively.  ...  ACKNOWLEDGMENTS The authors would like to thank Tencent Security Platform Department for discussions and suggestions.  ... 
arXiv:1904.05003v1 fatcat:g2izleyzcvdhza73ceofpnxfxe

Graph-based data mining for biological applications

Leander Schietgat
2011 AI Communications  
In the second part, we consider the task of graph mining, in which the input data of the learning algorithm are represented as graphs.  ...  We use this algorithm to construct a metric for molecules and to generate features for them.  ...  Types of learning and mining The goal of machine learning and data mining is to learn models from data.  ... 
doi:10.3233/aic-2010-0482 fatcat:kguu6ugombfx7bvfia64d6mqii
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