<div dir="ltr">Seminari di Matematica Applicata, Dipartimento di Matematica "F. Casorati" e Istituto del CNR IMATI "E. Magenes" di Pavia.<br><br>Martedì 1 Aprile 2025, alle ore 15 precise, presso l'aula Beltrami del Dipartimento di Matematica,<br><br><h4 style="padding:0px;margin:0px 0px 10px;clear:none;color:rgb(23,28,36);font-weight:300;font-stretch:normal;font-size:24px;line-height:1.2;font-family:Montserrat,-apple-system,BlinkMacSystemFont,"Segoe UI",Roboto,sans-serif;font-size-adjust:none;font-kerning:auto;font-variant-alternates:normal;font-variant-ligatures:normal;font-variant-numeric:normal;font-variant-east-asian:normal;font-feature-settings:normal;box-sizing:border-box">Stefano Coniglio (Università di Bergamo)</h4><div><br></div><h4 style="padding:0px;margin:0px 0px 10px;clear:none;color:rgb(23,28,36);font-weight:300;font-stretch:normal;line-height:1.2;font-family:Montserrat,-apple-system,BlinkMacSystemFont,"Segoe UI",Roboto,sans-serif;box-sizing:border-box"><span style="color:rgb(34,34,34);font-family:Arial,Helvetica,sans-serif">terrà un seminario dal titolo:</span></h4><div><br></div><h3 style="padding:0px;margin:5px 0px 8px;clear:none;color:rgb(23,28,36);font-weight:300;font-stretch:normal;font-size:28px;line-height:1.2;font-family:Montserrat,-apple-system,BlinkMacSystemFont,"Segoe UI",Roboto,sans-serif;font-size-adjust:none;font-kerning:auto;font-variant-alternates:normal;font-variant-ligatures:normal;font-variant-numeric:normal;font-variant-east-asian:normal;font-feature-settings:normal;box-sizing:border-box">Advances in Spectral Graph and Hypergraph Learning: Towards More Expressive Laplacian Matrices.</h3><div><br></div><div><span style="color:rgb(61,61,61);font-family:Roboto,sans-serif;font-size:15px">Abstract: </span><span style="color:rgb(61,61,61);font-family:Roboto,sans-serif;font-size:15px">Graphs and hypergraphs have gained increasing attention in deep learning due to their effectiveness in modeling complex relationships across various domains, including chemistry, biology, and social network analysis. Hypergraphs, in particular, are crucial to capture real-world phenomena that involve polyadic (many-to-many) relationships, extending beyond the diadic (pairwise) connections typically represented by (standard) graphs.</span></div><span style="color:rgb(61,61,61);font-family:Roboto,sans-serif;font-size:15px">In this presentation, we will provide an overview of the Graph Neural Network (GNN) and Graph Convolutional (Neural) Network (GCN) literature, with a focus on the construction of spectral graph-convolutional operators that are grounded in graph signal theory. Next, we will introduce some recent advancements we made in this area, achieved through a series of novel graph Laplacian matrices of increasing generality. Specifically, we will present:</span><br style="padding:0px;margin:0px;box-sizing:border-box;color:rgb(61,61,61);font-family:Roboto,sans-serif;font-size:15px"><span style="color:rgb(61,61,61);font-family:Roboto,sans-serif;font-size:15px">– The Sign-Magnetic Laplacian and SigMaNet, a generalized GCN capable of processing both directed and undirected graphs with unrestricted edge weights.</span><br style="padding:0px;margin:0px;box-sizing:border-box;color:rgb(61,61,61);font-family:Roboto,sans-serif;font-size:15px"><span style="color:rgb(61,61,61);font-family:Roboto,sans-serif;font-size:15px">– A quaternion-valued extension of the Sign-Magnetic Laplacian, designed for graphs with digons (antiparallel edges) and asymmetric weights, along with its corresponding GCN, QuaterGCN.</span><br style="padding:0px;margin:0px;box-sizing:border-box;color:rgb(61,61,61);font-family:Roboto,sans-serif;font-size:15px"><span style="color:rgb(61,61,61);font-family:Roboto,sans-serif;font-size:15px">– The Generalized Directed Laplacian and GeDi-HNN, a Hypergraph Neural Network (HNN) tailored for learning tasks where hyperedge directionality is essential.</span><br style="padding:0px;margin:0px;box-sizing:border-box;color:rgb(61,61,61);font-family:Roboto,sans-serif;font-size:15px"><span style="color:rgb(61,61,61);font-family:Roboto,sans-serif;font-size:15px">– The Directed Line Graph Laplacian and DLGNet, an HNN designed for chemical-reaction classification, where input directed hypergraphs are transformed into directed line graphs with complex-valued edge weights.</span><div><div><span style="color:rgb(61,61,61);font-family:Roboto,sans-serif;font-size:15px;font-variant-ligatures:normal;text-decoration-style:initial;text-decoration-color:initial"><br>-----------------------------------------</span></div><div><span style="color:rgb(61,61,61);font-family:Roboto,sans-serif;font-size:15px;font-variant-ligatures:normal;text-decoration-style:initial;text-decoration-color:initial"><a href="https://matematica.unipv.it/ricerca/cicli-di-seminari/seminari-di-matematica-applicata/" target="_blank">https://matematica.unipv.it/ricerca/cicli-di-seminari/seminari-di-matematica-applicata/</a><div class="gmail-yj6qo"></div><div class="gmail-adL"></div><div class="gmail-adL"></div><div class="gmail-adL"></div><div class="gmail-adL"></div><div class="gmail-adL"></div><div class="gmail-adL"></div></span></div><div class="gmail-adL"><br></div></div><br class="gmail-Apple-interchange-newline"></div>