Related papers: GEFL: Extended Filtration Learning for Graph Class…

Topology applied to real world data using persistent homology has started to find applications within machine learning, including deep learning. We present a differentiable topology layer that computes persistent homology based on level set…

Graph structure learning is a core problem in graph-based machine learning, essential for uncovering latent relationships and ensuring model interpretability. However, most existing approaches are ill-suited for large-scale and dynamically…

Neural Persistence is a prominent measure for quantifying neural network complexity, proposed in the emerging field of topological data analysis in deep learning. In this work, however, we find both theoretically and empirically that the…

Computational topology provides a tool, persistent homology, to extract quantitative descriptors from structured objects (images, graphs, point clouds, etc). These descriptors can then be involved in optimization problems, typically as a…

A persistence diagram provides a compact summary of persistent homology, which captures the topological features of a space at different scales. However, due to its nature as a set, incorporating it as a feature into a machine learning…

Edge detection is widely and fundamental feature used in various algorithms in computer vision to determine the edges in an image. The edge detection algorithm is used to determine the edges in an image which are further used by various…

Graph representation learning on vast datasets, like web data, has made significant strides. However, the associated computational and storage overheads raise concerns. In sight of this, Graph condensation (GCond) has been introduced to…

We introduce the Geometric Evolution Graph Convolutional Network (GEGCN), a novel framework that enhances graph representation learning through explicit modeling of geometric evolution on graph structures. Specifically, GEGCN leverages a…

Convolution Neural Networks on Graphs are important generalization and extension of classical CNNs. While previous works generally assumed that the graph structures of samples are regular with unified dimensions, in many applications, they…

We propose a study of multipartite entanglement through persistent homology, a tool used in topological data analysis. In persistent homology, a 1-parameter filtration of simplicial complexes called persistence complex is used to reveal…

Biological and physical systems often exhibit distinct structures at different spatial/temporal scales. Persistent homology is an algebraic tool that provides a mathematical framework for analyzing the multi-scale structures frequently…

Persistent homology is a cornerstone of topological data analysis, offering a multiscale summary of topology with robustness to nuisance transformations, such as rotations and small deformations. Persistent homology has seen broad use…

We define persistent homology groups over any set of spaces which have inclusions defined so that the corresponding directed graph between the spaces is acyclic, as well as along any subgraph of this directed graph. This method…

Graph Representation Learning (GRL) methods have impacted fields from chemistry to social science. However, their algorithmic implementations are specialized to specific use-cases e.g.message passing methods are run differently from node…

Federated learning (FL), aimed at leveraging vast distributed datasets, confronts a crucial challenge: the heterogeneity of data across different silos. While previous studies have explored discrete representations to enhance model…

Graph similarity learning (GSL), also referred to as graph matching in many scenarios, is a fundamental problem in computer vision, pattern recognition, and graph learning. However, previous GSL methods assume that graphs are homogeneous…

Representation learning in dynamic graphs is a challenging problem because the topology of graph and node features vary at different time. This requires the model to be able to effectively capture both graph topology information and…

Graph is powerful for representing various types of real-world data. The topology (edges' presence) and edges' features of a graph decides the message passing mechanism among vertices within the graph. While most existing approaches only…

Graph embeddings play a critical role in graph representation learning, allowing machine learning models to explore and interpret graph-structured data. However, existing methods often rely on opaque, high-dimensional embeddings, limiting…

While Graph Neural Networks (GNNs) have achieved remarkable results in a variety of applications, recent studies exposed important shortcomings in their ability to capture the structure of the underlying graph. It has been shown that the…