Related papers: D-GRIL: End-to-End Topological Learning with 2-par…

Random Fourier features (RFFs) provide a promising way for kernel learning in a spectral case. Current RFFs-based kernel learning methods usually work in a two-stage way. In the first-stage process, learning the optimal feature map is often…

Recently, over-parameterized neural networks have been extensively analyzed in the literature. However, the previous studies cannot satisfactorily explain why fully trained neural networks are successful in practice. In this paper, we…

Topological data analysis (TDA) is gaining prominence across a wide spectrum of machine learning tasks that spans from manifold learning to graph classification. A pivotal technique within TDA is persistent homology (PH), which furnishes an…

Graph neural networks (GNNs) are a powerful architecture for tackling graph learning tasks, yet have been shown to be oblivious to eminent substructures such as cycles. We present TOGL, a novel layer that incorporates global topological…

Deep reinforcement learning (DRL) has been proven to be a powerful paradigm for learning complex control policy autonomously. Numerous recent applications of DRL in robotic grasping have successfully trained DRL robotic agents end-to-end,…

Graph representation learning (GRL) is to encode graph elements into informative vector representations, which can be used in downstream tasks for analyzing graph-structured data and has seen extensive applications in various domains.…

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…

Topological descriptors have been increasingly utilized for capturing multiscale structural information in relational data. In this work, we consider various filtrations on the (box) product of graphs and the effect on their outputs on the…

Digraph Representation Learning (DRL) aims to learn representations for directed homogeneous graphs (digraphs). Prior work in DRL is largely constrained (e.g., limited to directed acyclic graphs), or has poor generalizability across tasks…

Graph neural networks (GNNs) have emerged as a powerful tool for graph classification and representation learning. However, GNNs tend to suffer from over-smoothing problems and are vulnerable to graph perturbations. To address these…

We present a method for learning "spectrally descriptive" edge weights for graphs. We generalize a previously known distance measure on graphs (Graph Diffusion Distance), thereby allowing it to be tuned to minimize an arbitrary loss…

Recently, a novel two-phase framework named mol-infer for inference of chemical compounds with prescribed abstract structures and desired property values has been proposed. The framework mol-infer is primarily based on using mixed integer…

Subgraph-based graph representation learning (SGRL) has been recently proposed to deal with some fundamental challenges encountered by canonical graph neural networks (GNNs), and has demonstrated advantages in many important data science…

Biological data may be separated into primary data, such as gene expression, and secondary data, such as pathways and protein-protein interactions. Methods using secondary data to enhance the analysis of primary data are promising, because…

The theory of multidimensional persistence captures the topology of a multifiltration -- a multiparameter family of increasing spaces. Multifiltrations arise naturally in the topological analysis of scientific data. In this paper, we give a…

Graph Neural Networks usually rely on the assumption that the graph topology is available to the network as well as optimal for the downstream task. Latent graph inference allows models to dynamically learn the intrinsic graph structure of…

This paper presents a despeckling method for Sentinel-1 GRD images based on the recently proposed framework "SAR2SAR": a self-supervised training strategy. Training the deep neural network on collections of Sentinel 1 GRD images leads to a…

Persistence diagrams, the most common descriptors of Topological Data Analysis, encode topological properties of data and have already proved pivotal in many different applications of data science. However, since the (metric) space of…

Topological features based on persistent homology capture high-order structural information so as to augment graph neural network methods. However, computing extended persistent homology summaries remains slow for large and dense graphs and…

Graph Neural Networks (GNNs) have been a prevailing technique for tackling various analysis tasks on graph data. A key premise for the remarkable performance of GNNs relies on complete and trustworthy initial graph descriptions (i.e., node…