Related papers: Graph Reconstruction by Discrete Morse Theory

Graph Neural Networks have achieved tremendous success in modeling complex graph data in a variety of applications. However, there are limited studies investigating privacy protection in GNNs. In this work, we propose a learning framework…

We present an alternative application of discrete Morse theory for two-particle graph configuration spaces. In contrast to previous constructions, which are based on discrete Morse vector fields, our approach is through Morse functions,…

Graph Neural Networks (GNNs) are popular models for graph learning problems. GNNs show strong empirical performance in many practical tasks. However, the theoretical properties have not been completely elucidated. In this paper, we…

Real-world graph data environments intrinsically exist noise (e.g., link and structure errors) that inevitably disturb the effectiveness of graph representation and downstream learning tasks. For homogeneous graphs, the latest works use…

This paper studies linear reconstruction of partially observed functional data which are recorded on a discrete grid. We propose a novel estimation approach based on approximate factor models with increasing rank taking into account…

Practical image segmentation tasks concern images which must be reconstructed from noisy, distorted, and/or incomplete observations. A recent approach for solving such tasks is to perform this reconstruction jointly with the segmentation,…

Many modern applications involve accessing and processing graphical data, i.e. data that is naturally indexed by graphs. Examples come from internet graphs, social networks, genomics and proteomics, and other sources. The typically large…

Analyzing interconnection structures among underlying entities or objects in a dataset through the use of graph analytics has been shown to provide tremendous value in many application domains. However, graphs are not the primary…

Sparse graph recovery methods work well where the data follows their assumptions but often they are not designed for doing downstream probabilistic queries. This limits their adoption to only identifying connections among the input…

The network reconstruction task aims to estimate a complex system's structure from various data sources such as time series, snapshots, or interaction counts. Recent work has examined this problem in networks whose relationships involve…

When learning from graph data, the graph and the node features both give noisy information about the node labels. In this paper we propose an algorithm to jointly denoise the features and rewire the graph (JDR), which improves the…

Publishing open graph data while preserving individual privacy remains challenging when data publishers and data users are distinct entities. Although differential privacy (DP) provides rigorous guarantees, most existing approaches enforce…

Graphs are a fundamental representation of complex, nonlinear structured data across various domains, including social networks and quantum systems. Quantum Graph Recurrent Neural Networks (QGRNNs) have been proposed to model quantum…

For many tracking and surveillance applications, background subtraction provides an effective means of segmenting objects moving in front of a static background. Researchers have traditionally used combinations of morphological operations…

Signals sparse in a transformation domain can be recovered from a reduced set of randomly positioned samples by using compressive sensing algorithms. Simple re- construction algorithms are presented in the first part of the paper. The…

We propose a novel probabilistic dimensionality reduction framework that can naturally integrate the generative model and the locality information of data. Based on this framework, we present a new model, which is able to learn a smooth…

Denoising-based models, including diffusion and flow matching, have led to substantial advances in graph generation. Despite this progress, such models remain constrained by two fundamental limitations: a computational cost that scales…

Knowledge graphs serve as critical resources supporting intelligent systems, but they can be noisy due to imperfect automatic generation processes. Existing approaches to noise detection often rely on external facts, logical rule…

Data-driven discovery of partial differential equations (PDEs) offers a promising paradigm for uncovering governing physical laws from observational data. However, in practical scenarios, measurements are often contaminated by noise and…

Many material response functions depend strongly on microstructure, such as inhomogeneities in phase or orientation. Homogenization presents the task of predicting the mean response of a sample of the microstructure to external loading for…