[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-128777-en":3,"doc-seo-128777-105":31,"detail-sidebar-cat-0-en-105":92},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":28,"seo_description":14,"update_tm":29,"read_time":30},128777,1099523882367,"Hazel","https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc",8,"Research & Report","Task-Oriented Embedding for Node Heaviness Prediction in Graphs","Graph analysis has become central across domains such as biology, linguistics, and social sciences, where complex networks require accurate structural understanding. This thesis studies how node embedding techniques influence motif estimation quality and introduces Node Heaviness, measuring how strongly a node participates in motifs. A task-specific node embedding approach is proposed to predict node heaviness. Experiments compare matrix factorization, random-walk, and deep learning embeddings, showing dataset-dependent effectiveness, with deep models often weaker on dense graphs, while the custom method remains promising and highlights selection of embeddings for graph characteristics.","Universit degli Studi di Padova  \nDepartment of Information Engineering  \nMaster Degree in Computer engineering  \nTask-Oriented Embedding for Node Heaviness Prediction in Graphs  \nSupervisor: Master Candidate:  \nProf. Fabio Vandin Matteo Salvalaio  \n2088249  \nAcademic Year 2023/2024  \nDate 21/10/2024  \nAbstract  \nIn recent years, graph analysis has gained signi􀀌cant traction due to the widespread presence of networks across various domains, including biology, linguistics, and social sciences. This thesis explores the intricate relationship between node embedding techniques and the accuracy of motif estimation in complex networks, highlighting the critical role that embedding methods play in understanding network structures. We introduce the concept of Node Heaviness, which quanti􀀌es a node’s involvement in motifs, and propose a novel node embedding technique speci􀀌cally designed for predicting node heaviness.  \nThrough comprehensive experiments, we evaluate several embedding methods, including matrix factorization approaches, random walks, and deep learning techniques, with the goal of enhancing the accuracy of node heaviness predictions by capturing structural characteristics of nodes. Our analysis reveals varying e􀀋ectiveness based on dataset characteristics and the speci􀀌c nature of the graphs. While deep learning methods generally exhibit superior performance, they often struggle with dense graphs, where the complexity of the network structure can hinder their e􀀋ectiveness. In contrast, our custom node embedding technique tailored for this task demonstrates adequate performance, showcasing signi􀀌cant potential for improvement.  \nBy analyzing the strengths and weaknesses of di􀀋erent embedding strategies, this thesis contributes valuable insights to the 􀀌eld of network analysis. The 􀀌ndings underscore the importance of selecting appropriate embedding techniques for speci􀀌c graph characteristics.  \nContents  \n1 Introduction ..................................... 1  \n1.1 Graph Embeddings ............................... 2  \n1.2 Purpose of the thesis .............................. 5  \n2 Literature Review ................................. 6  \n2.1 Taxonomy of Graph Embeddings Methods .................. 6  \n2.1.1 Property Preservation ......................... 7  \n2.1.2 Encoder-Decoder Framework ...................... 8  \n2.2 Shallow Network Embeddings ......................... 9  \n2.2.1 Factorization-Based Methods ..................... 10  \n2.2.2 Random Walks-Based Methods .................... 12  \n2.2.3 Optimization-Based Methods ..................... 15  \n2.3 Deep Learning Embeddings .......................... 17  \n2.3.1 Permutation Invariance ......................... 18  \n2.3.2 Neural Message Passing Framework .................. 18  \n2.3.3 Limitations of Graph Neural Networks ................ 20  \n2.3.4 Advanced Graph Neural Network Models ............... 21  \n3 Short Walks Node Embedder (SNOW) .................... 23  \n3.1 Implementation Details ............................. 23  \n3.1.1 Embedding matrix initialization .................... 23  \n3.1.2 Negative Sampling ........................... 24  \n3.1.3 Random Walks ............................. 24  \n3.1.4 Loss Function .............................. 26  \n3.1.5 Complexity ............................... 28  \n4 Experimental Methodology ........................... 30  \n4.1 State of the art Embedding Methods and Their Applicability ........ 30  \n4.2 Direct Triangle Counting Methods ....................... 32  \n4.2.1 Simple Degree Predictor (SDP) .................... 32  \n4.2.2 NetworkX Triangle Counting Function ................ 33  \n4.3 Methodological Details ............................. 34  \n4.3.1 Model Architecture ........................... 34  \n4.3.2 Loss Function and Optimization .................... 35  \n4.3.3 Weight Decay .............................. 35  \n4.3.4 Weight Initialization .......................... 36  \n4.3.5 Hyperparameter Selection ......................","cbCaijrFqrcPrxav","https://ap.wps.com/l/cbCaijrFqrcPrxav","pdf",2088482,2,1,77,"English","en",105,"# Introduction\n## Graph Embeddings\n## Purpose of the thesis\n# Literature Review\n## Taxonomy of Graph Embeddings Methods\n## Shallow Network Embeddings\n## Deep Learning Embeddings\n# Short Walks Node Embedder (SNOW)\n## Implementation Details\n# Experimental Methodology\n## State of the art Embedding Methods and Their Applicability\n## Direct Triangle Counting Methods\n## Methodological Details\n## Datasets\n# Results\n## Accuracy of Predictions\n## Accuracy of Predictions on Partial Graph Visibility\n## Heavy Node Classification\n## Impact of Embedding Dimensions on Model Performance\n## Predicting Node Heaviness with more complex Motifs\n# Conclusions\n## Key Findings\n## Future Work","[{\"question\":\"What is Node Heaviness and why does it matter for motif estimation?\",\"answer\":\"Node Heaviness quantifies a node’s involvement in motifs, linking node embedding quality to how accurately motif-related structure can be estimated in complex networks.\"},{\"question\":\"What embedding methods are evaluated in the thesis?\",\"answer\":\"The thesis evaluates matrix factorization approaches, random walks, and deep learning techniques to determine how well different embeddings support node heaviness prediction.\"},{\"question\":\"How do deep learning embeddings typically perform on dense graphs?\",\"answer\":\"Deep learning methods generally achieve strong results, but they often struggle with dense graphs, where network complexity can reduce effectiveness.\"}]","Task-Oriented Embedding for Node Heaviness Prediction in Graphs | 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