[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-118123-en":3,"doc-seo-118123-105":30,"detail-sidebar-cat-0-en-105":91},{"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":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},118123,5909877438554,"Maeve","https://ap-avatar.wpscdn.com/avatar/5600025385ad2bf12a7?_k=1778553567797529272",8,"Research & Report","Graph Filters for Signal Processing and Machine Learning on Graphs - Overview Article","Filters are fundamental for extracting task-relevant information from data, and the work extends this idea from Euclidean signals to data defined on graphs. By leveraging graph structure, graph filters enable both signal processing and machine learning methods on irregular domains such as networks. The overview organizes filtering categories, design strategies, and their trade-offs, and shows how to build filter banks and connect graph filters to graph neural networks for stronger representation of signals, patterns, and relationships across application areas.","Graph Filters for Signal Processing and Machine Learning on Graphs  \nElvin Isufi, Fernando Gama, David I Shuman, and Santiago Segarra  \nOverview Article  \narXiv :2211 .08854v2 [ ee ss . SP] 19 Feb 2024  \nAbstract—Filters are fundamental in extracting information from data. For time series and image data that reside on Euclidean domains, filters are the crux of many signal processing and machine learning techniques, including convolutional neural networks. Increasingly, modern data also reside on networks and other irregular domains whose structure is better captured by a graph. To process and learn from such data, graph filters account for the structure of the underlying data domain. In this article, we provide a comprehensive overview of graph filters, including the different filtering categories, design strategies for each type, and trade-offs between different types of graph filters. We discuss how to extend graph filters into filter banks and graph neural networks to enhance the representational power; that is, to model a broader variety of signal classes, data patterns, and relationships. We also showcase the fundamental role of graph filters in signal processing and machine learning applications. Our aim is that this article provides a unifying framework for both beginner and experienced researchers, as well as a common understanding that promotes collaborations at the intersections of signal processing, machine learning, and application domains.  \nIndex Terms—Graph signal processing, graph machine learning, graph convolution, filter identification, graph filter banks and wavelets, graph neural networks, distributed processing, collaborative filtering, graph-based image processing, mesh processing, point clouds, topology identification, spectral clustering, matrix completion, graph Gaussian processes.  \nI. INTRODUCTION  \nFilters are information processing architectures that preserve only the relevant content of the input for the task at hand. In signal processing (SP), filtering preserves specific spectral content of input signals and is a common building block in domains including audio, speech, radar, communication, and multimedia [1] . In machine learning (ML), filtering is used to extract relevant patterns from the data or as an inductive bias for building neural networks [2] . For instance, principal component analysis (PCA) can be seen as a low-pass filter in the correlation matrix, where only the parts of the data contributing to the directions of the largest variance are preserved [3] . Likewise, the success of convolutional neural networks (CNNs) can be attributed to the convolutional filters used in each layer, allowing for easier training and scalability, as well as exploiting structural invariances in the data [2], [4] .  \nConventional filtering applies to signals defined on Euclidean domains, but cannot be directly applied to irregular data structures arising in biological, financial, social, economic, power, water, sensor, and multi-agent networks, among others [5], [6] . Graph filters are information processing architectures tailored to  \nE. Isufi is with the Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, Delft, The Netherlands. [Email: e-isufi.1@tudelft.nl](Email: e-isufi.1@tudelft.nl).  \nF. Gama was with the Department of Electrical and Computer Engineering,  \nRice University, Houston, TX 77005 USA. Email: [fgama@ieee.org](fgama@ieee.org)  \nD. I Shuman is with Franklin W. Olin College of Engineering, Needham, MA 02492 USA. Email: [dshuman@olin.edu](dshuman@olin.edu)  \nS. Segarra is with the Department of Electrical and Computer Engineering, Rice University, Houston, TX 77005 USA. Email: [segarra@rice.edu](segarra@rice.edu)  \ngraph-structured data, generalizing the conventional Euclidean counterparts.  \nGraph filters have many similarities with conventional ones; they are linear, shift invariant, parametric functions of the input, they enjoy a spectral","cbCaib48isp0jVB8","https://ap.wps.com/l/cbCaib48isp0jVB8","pdf",5378235,1,32,"English","en",105,"# Overview Article\n## Introduction\n## Graph Filters: Motivation and Key Properties\n## Historical Development\n## Role in Signal Processing and Machine Learning","[{\"question\":\"What problem do graph filters solve compared with conventional filters?\",\"answer\":\"Conventional filters target signals on Euclidean domains and do not directly apply to irregular network-based data. Graph filters are tailored to graph-structured domains, capturing the underlying data structure for filtering and learning.\"},{\"question\":\"How does the article relate graph filters to spectral graph theory?\",\"answer\":\"Graph filters share similarities with conventional filters, including spectral interpretations through spectral graph theory. Their design can be framed as function fitting on the graph spectrum.\"},{\"question\":\"What is the connection between graph filters and graph neural networks (GNNs)?\",\"answer\":\"The article describes graph filters as a fundamental component for learning representations from graph-based data in modern GNNs, enabling models to capture structure-aware patterns.\"}]","Graph Filters for Signal Processing and Machine Learning on Graphs - Overview Article | PDF",1785681719,81,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"graph-filters-for-signal-processing-and-machine-learning-on-graphs-overview-article","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/graph-filters-for-signal-processing-and-machine-learning-on-graphs-overview-article/118123/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-02",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What problem do graph filters solve compared with conventional filters?","Question",{"text":75,"@type":76},"Conventional filters target signals on Euclidean domains and do not directly apply to irregular network-based data. Graph filters are tailored to graph-structured domains, capturing the underlying data structure for filtering and learning.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the article relate graph filters to spectral graph theory?",{"text":80,"@type":76},"Graph filters share similarities with conventional filters, including spectral interpretations through spectral graph theory. Their design can be framed as function fitting on the graph spectrum.",{"name":82,"@type":73,"acceptedAnswer":83},"What is the connection between graph filters and graph neural networks (GNNs)?",{"text":84,"@type":76},"The article describes graph filters as a fundamental component for learning representations from graph-based data in modern GNNs, enabling models to capture structure-aware patterns.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]