Related papers: A Hierarchical Sheaf Spectral Embedding Framework …

This paper outlines a program in what one might call spectral sheaf theory --- an extension of spectral graph theory to cellular sheaves. By lifting the combinatorial graph Laplacian to the Hodge Laplacian on a cellular sheaf of vector…

The absence of intrinsic adjacency relations and orientation systems in hypergraphs creates fundamental challenges for constructing sheaf Laplacians of arbitrary degrees. We resolve these limitations through symmetric simplicial sets…

We propose a multi-dimensional persistent sheaf Laplacian (MPSL) framework on simplicial complexes for image analysis. The proposed method is motivated by the strong sensitivity of commonly used dimensionality reduction techniques, such as…

Stack autoencoder (SAE), as a representative deep network, has unique and excellent performance in feature learning, and has received extensive attention from researchers. However, existing deep SAEs focus on original samples without…

In this work, we introduce a novel approach based on algebraic topology to enhance graph convolution and attention modules by incorporating local topological properties of the data. To do so, we consider the framework of sheaf neural…

We introduce the Graph Sylvester Embedding (GSE), an unsupervised graph representation of local similarity, connectivity, and global structure. GSE uses the solution of the Sylvester equation to capture both network structure and…

Convolutional neural networks (CNNs) have demonstrated strong performance in visual recognition tasks, but their inherent reliance on regular grid structures limits their capacity to model complex topological relationships and non-local…

Due to the sequential sample arrival, changing experiment conditions, and evolution of knowledge, the demand to continually visualize evolving structures of sequential and diverse single-cell RNA-sequencing (scRNA-seq) data becomes…

Semantic segmentation of electron microscopy (EM) images of biological samples remains a challenge in the life sciences. EM data captures details of biological structures, sometimes with such complexity that even human observers can find it…

Humans are able to recognize structured relations in observation, allowing us to decompose complex scenes into simpler parts and abstract the visual world in multiple levels. However, such hierarchical reasoning ability of human perception…

Single-cell sequencing is revolutionizing biology by enabling detailed investigations of cell-state transitions. Many biological processes unfold along continuous trajectories, yet it remains challenging to extract smooth, low-dimensional…

Representation learning methods for heterogeneous networks produce a low-dimensional vector embedding for each node that is typically fixed for all tasks involving the node. Many of the existing methods focus on obtaining a static vector…

Scene graph generation aims to produce structured representations for images, which requires to understand the relations between objects. Due to the continuous nature of deep neural networks, the prediction of scene graphs is divided into…

Sheaf Neural Networks (SNNs) were introduced as an extension of Graph Convolutional Networks to address oversmoothing on heterophilous graphs by attaching a sheaf to the input graph and replacing the adjacency-based operator with a sheaf…

Higher-order relations are widespread in nature, with numerous phenomena involving complex interactions that extend beyond simple pairwise connections. As a result, advancements in higher-order processing can accelerate the growth of…

We present a new and effective approach for Hyperspectral Image (HSI) classification and clutter detection, overcoming a few long-standing challenges presented by HSI data characteristics. Residing in a high-dimensional spectral attribute…

Standard Adjacency Spectral Embedding (ASE) relies on a global low-rank assumption often incompatible with the sparse, transitive structure of real-world networks, causing local geometric features to be 'smeared'. To address this, we…

Constructing approximations that can accurately mimic the behavior of complex models at reduced computational costs is an important aspect of uncertainty quantification. Despite their flexibility and efficiency, classical surrogate models…

Single-cell RNA sequencing (scRNA-seq) has emerged as a transformative technology, offering unparalleled insights into the intricate landscape of cellular diversity and gene expression dynamics. The analysis of scRNA-seq data poses…

Visual data and text data are composed of information at multiple granularities. A video can describe a complex scene that is composed of multiple clips or shots, where each depicts a semantically coherent event or action. Similarly, a…