Related papers: GRIL: A $2$-parameter Persistence Based Vectorizat…

Proposing an effective and flexible matrix to represent a graph is a fundamental challenge that has been explored from multiple perspectives, e.g., filtering in Graph Fourier Transforms. In this work, we develop a novel and general…

In this work, we develop a pipeline that associates Persistence Diagrams to digital data via the most appropriate filtration for the type of data considered. Using a grid search approach, this pipeline determines optimal representation…

Graph Neural Networks (GNNs) have shown remarkable success across various scientific fields, yet their adoption in critical decision-making is often hindered by a lack of interpretability. Recently, intrinsically interpretable GNNs have…

Graph representation learning aims at transforming graph data into meaningful low-dimensional vectors to facilitate the employment of machine learning and data mining algorithms designed for general data. Most current graph representation…

Representational limits of message-passing graph neural networks (MP-GNNs), e.g., in terms of the Weisfeiler-Leman (WL) test for isomorphism, are well understood. Augmenting these graph models with topological features via persistent…

Including intricate topological information (e.g., cycles) provably enhances the expressivity of message-passing graph neural networks (GNNs) beyond the Weisfeiler-Leman (WL) hierarchy. Consequently, Persistent Homology (PH) methods are…

Graph Neural Networks (GNNs) have emerged as prominent models for representation learning on graph structured data. GNNs follow an approach of message passing analogous to 1-dimensional Weisfeiler Lehman (1-WL) test for graph isomorphism…

Persistent homology (PH) has been widely applied to graph data to extract topological features. However, little attention has been paid to how different distance functions on a graph affect the resulting persistence barcodes and their…

Graph representation learning has attracted much attention in supporting high quality candidate search at scale. Despite its effectiveness in learning embedding vectors for objects in the user-item interaction network, the computational…

Node2vec is a graph embedding method that learns a vector representation for each node of a weighted graph while seeking to preserve relative proximity and global structure. Numerical experiments suggest Node2vec struggles to recreate the…

This work introduces a number of algebraic topology approaches, such as multicomponent persistent homology, multi-level persistent homology and electrostatic persistence for the representation, characterization, and description of small…

Geometric Deep Learning (GDL) unifies a broad class of machine learning techniques from the perspectives of symmetries, offering a framework for introducing problem-specific inductive biases like Graph Neural Networks (GNNs). However, the…

Combinatorial and topological structures, such as graphs, simplicial complexes, and cell complexes, form the foundation of geometric and topological deep learning (GDL and TDL) architectures. These models aggregate signals over such…

While message passing graph neural networks result in informative node embeddings, they may suffer from describing the topological properties of graphs. To this end, node filtration has been widely used as an attempt to obtain the…

Heterogeneous graphs with heterophily have emerged as a powerful abstraction for modeling complex real-world systems, where nodes of different types and labels interact in diverse and often non-homophilous ways. Despite recent advances,…

Learning distributed representations of source code has been a challenging task for machine learning models. Earlier works treated programs as text so that natural language methods can be readily applied. Unfortunately, such approaches do…

Recently a variety of methods have been developed to encode graphs into low-dimensional vectors that can be easily exploited by machine learning algorithms. The majority of these methods start by embedding the graph nodes into a…

Graph representation learning is a fast-growing field where one of the main objectives is to generate meaningful representations of graphs in lower-dimensional spaces. The learned embeddings have been successfully applied to perform various…

Graph representation learning has emerged as a powerful tool for preserving graph topology when mapping nodes to vector representations, enabling various downstream tasks such as node classification and community detection. However, most…

The integration of Large Language Models (LLMs) with Graph Representation Learning (GRL) marks a significant evolution in analyzing complex data structures. This collaboration harnesses the sophisticated linguistic capabilities of LLMs to…