相关论文: Persistent reachability homology in machine learni…

Instance Search (INS) is a fundamental problem for many applications, while it is more challenging comparing to traditional image search since the relevancy is defined at the instance level. Existing works have demonstrated the success of…

Persistent Homology (PH) offers stable, multi-scale descriptors of intrinsic shape structure by capturing connected components, loops, and voids that persist across scales, providing invariants that complement purely geometric…

Persistent homology (PH) is an approach to topological data analysis (TDA) that computes multi-scale topologically invariant properties of high-dimensional data that are robust to noise. While PH has revealed useful patterns across various…

Proposing scoring functions to effectively understand, analyze and learn various properties of high dimensional hidden representations of large-scale transformer models like BERT can be a challenging task. In this work, we explore a new…

The Hough transform is a popular and classical technique in computer vision for the detection of lines (or more general objects). It maps a pixel into a dual space -- the Hough space: each pixel is mapped to the set of lines through this…

Massive social media data can reflect people's authentic thoughts, emotions, communication, etc., and therefore can be analyzed for early detection of mental health problems such as depression. Existing works about early depression…

High-accuracy prediction of the physical properties of amorphous materials is challenging in condensed-matter physics. A promising method to achieve this is machine-learning potentials, which is an alternative to computationally demanding…

Hypergraphs are useful mathematical models for describing complex relationships among members of a structured graph, while hyperdigraphs serve as a generalization that can encode asymmetric relationships in the data. However, obtaining…

The local inductive bias of message-passing graph neural networks (GNNs) hampers their ability to exploit key structural information (e.g., connectivity and cycles). Positional encoding (PE) and Persistent Homology (PH) have emerged as two…

Techniques from computational topology, in particular persistent homology, are becoming increasingly relevant for data analysis. Their stable metrics permit the use of many distance-based data analysis methods, such as multidimensional…

Hypergraphs provide a natural way to represent higher-order interactions among multiple entities. While undirected hypergraphs have been extensively studied, the case of directed hypergraphs, which can model oriented group interactions,…

Determining whether two graphs are isomorphic is a fundamental problem with practical applications in areas such as molecular chemistry or social network analysis, yet it remains a challenging task, with exact solutions often being…

We outline a detection method for adversarial inputs to deep neural networks. By viewing neural network computations as graphs upon which information flows from input space to out- put distribution, we compare the differences in graphs…

Hypergraph is the most general model for complex networks involving group interactions. Taking the ideas of path homology from Alexander Grigor'yan, Yong Lin, Yuri Muranov and Shing-Tung Yau [18-22], Stephane Bressan, Jingyan Li and the…

Topological Data Analysis (TDA) offers a suite of computational tools that provide quantified shape features in high dimensional data that can be used by modern statistical and predictive machine learning (ML) models. In particular,…

We propose an efficient framework that integrates distance-aware multi-hop message passing with dynamic topology refinement. Unlike standard GNNs that rely on shallow, fixed-hop aggregation, DRTR leverages both static preprocessing and…

Graphs with heterophily, where adjacent nodes carry different labels, are prevalent in real-world applications, from social networks to molecular interactions. However, existing spectral Graph Neural Network (GNN) approaches tailored for…

We propose an approach to learning with graph-structured data in the problem domain of graph classification. In particular, we present a novel type of readout operation to aggregate node features into a graph-level representation. To this…

Persistent homology has been applied to brain network analysis for finding the shape of brain networks across multiple thresholds. In the persistent homology, the shape of networks is often quantified by the sequence of $k$-dimensional…

The Persistent Homology Transform (PHT) was introduced in the field of Topological Data Analysis about 10 years ago, and has since been proven to be a very powerful descriptor of Euclidean shapes. The PHT consists of scanning a shape from…