[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-126525-en":3,"doc-seo-126525-105":30,"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":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},126525,962085662650,"Jiven","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"Research & Report","Structural Optimization of Factor Graphs for Symbol Detection via Continuous Clustering and Machine Learning","A novel end-to-end method optimizes the structure of factor graphs for graph-based inference, targeting low-complexity symbol detection. The approach addresses the suboptimal and graph-sensitive sum-product algorithm on cyclic factor graphs by learning an improved factorization from data. Structural optimization is reformulated as a clustering problem of low-degree factor nodes that embeds the known channel model. For specific channels, the combination with neural belief propagation reaches near–maximum a posteriori symbol detection performance.","STRUCTURAL OPTIMIZATION OF FACTOR GRAPHS FOR SYMBOL DETECTION VIA CONTINUOUS CLUSTERING AND MACHINE LEARNING  \nLukas Rapp, Luca Schmid, Andrej Rode, and Laurent Schmalen Communications Engineering Lab, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany  \narXiv :2211 . 11406v1 [ cs .IT] 21 Nov 2022  \nABSTRACT  \nWe propose a novel method to optimize the structure of factor graphs for graph-based inference. As an example inference task, we consider symbol detection on linear inter-symbol interference channels. The factor graph framework has the potential to yield lowcomplexity symbol detectors. However, the sum-product algorithm on cyclic factor graphs is suboptimal and its performance is highly sensitive to the underlying graph. Therefore, we optimize the structure of the underlying factor graphs in an end-to-end manner using machine learning. For that purpose, we transform the structural optimization into a clustering problem of low-degree factor nodes that incorporates the known channel model into the optimization. Furthermore, we study the combination of this approach with neural belief propagation, yielding near-maximum a posteriori symbol detection performance for specific channels.  \nIndex Terms— Factor Graphs, Machine Learning, Symbol Detection  \n1. INTRODUCTION  \nFactor graphs are powerful frameworks to efficiently compute inference tasks. This makes them an important tool in communication engineering, where the essence of many tasks is based on statistical inference, e.g., decoding of channel codes or the Viterbi algorithm [1] . A factor graph represents the factorization of a global function of multiple variables in a graphical way. This enables the calculation of the marginals of the function for inference by a message passing algorithm called sum-product algorithm (SPA) [2] .  \nThe performance of the inference over a factor graph depends highly on the underlying graph itself. Therefore, an interesting problem is the learning of factor graphs to improve the inference performance for a given task. Shlezinger et al. [3] learn factor graph models to estimate distorted symbols by learning the factor nodes (FNs) with neural networks (NNs) . Another application where optimized factors graphs are useful is localization in robotics [4] . In [5], the local functions of a factor graph are calculated by NNs using data of a ground penetrating radar to estimate the location of the radar. Yi et al. [6] propose a general framework to optimize factor graphs for state estimation in the context of robotics. In contrast to the two previous works, the factor graph is optimized in an end-to-end fashion with respect to the inference performance by backpropagation [7, Sec. 6.5] . All of these approaches only focus on the optimization of the FNs and use a fixed factor graph structure.  \nFor factor graphs with cycles, however, the SPA performance heavily relies on the factor graph structure [8]. In many applications,  \nThis work has received funding in part from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 101001899) and in part from the German Federal Ministry of Education and Research (BMBF) within the project Open6GHub (grant agreement 16KISK010) .  \nfactor graphs with cycles are inevitable to keep the inference complexity low. Since the factor graph structure of a given global function is not unique, it can be optimized to improve the SPA performance. So far, to the best of our knowledge, research on learning the factor graph structure is rare. In [9], Abbeel et al. learn the structure and parameters of a factor graph simultaneously from observed data. On the other hand, machine learning of other probabilistic graphical models [10] like Bayesian networks and Markov random fields has been already intensively studied. An overview can be found in [10, Sec. 3] and [11] . Since Bayesian networks and Markov random fields can be transformed into factor grap","cbCairC9OGicpNZa","https://ap.wps.com/l/cbCairC9OGicpNZa","pdf",330271,1,5,"English","en",105,"# Abstract\n# 1. Introduction\n# 2. Background\n## 2.1 Factor Graphs and Marginalization","[{\"question\":\"What problem does the method address in factor-graph based symbol detection?\",\"answer\":\"It addresses the fact that sum-product inference on cyclic factor graphs can be suboptimal and highly sensitive to the exact underlying graph structure.\"},{\"question\":\"How is structural optimization formulated in the proposed approach?\",\"answer\":\"It is transformed into a clustering problem over low-degree factor nodes, while incorporating the known channel model into the optimization objective.\"},{\"question\":\"What performance can be achieved when combining the approach with neural belief propagation?\",\"answer\":\"For specific channels, the combination yields near–maximum a posteriori symbol detection performance.\"}]","Structural Optimization of Factor Graphs for Symbol Detection via Continuous Clustering and Machine Learning | PDF",1785933153,13,{"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":87,"head_meta":89,"extra_data":91,"updated_unix":28},"structural-optimization-of-factor-graphs-for-symbol-detection-via-continuous-clustering-and-machine-learning","",{"@graph":36,"@context":86},[37,54,69],{"@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/structural-optimization-of-factor-graphs-for-symbol-detection-via-continuous-clustering-and-machine-learning/126525/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-23","2026-08-05",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82],{"name":73,"@type":74,"acceptedAnswer":75},"What problem does the method address in factor-graph based symbol detection?","Question",{"text":76,"@type":77},"It addresses the fact that sum-product inference on cyclic factor graphs can be suboptimal and highly sensitive to the exact underlying graph structure.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"How is structural optimization formulated in the proposed approach?",{"text":81,"@type":77},"It is transformed into a clustering problem over low-degree factor nodes, while incorporating the known channel model into the optimization objective.",{"name":83,"@type":74,"acceptedAnswer":84},"What performance can be achieved when combining the approach with neural belief propagation?",{"text":85,"@type":77},"For specific channels, the combination yields near–maximum a posteriori symbol detection performance.","https://schema.org",{"og:url":52,"og:type":88,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":90,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":93},[94,98,102,106,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":95,"show_sort_weight":96,"slug":97},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":99,"show_sort_weight":100,"slug":101},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":103,"show_sort_weight":104,"slug":105},"Exam",70,"exam",{"id":21,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},"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":21,"slug":138},19,"General","general"]