Related papers: Building Deep Networks on Grassmann Manifolds
Deep neural networks have enabled researchers to create powerful generalized frameworks, such as transformers, that can be used to solve well-studied problems in various application domains, such as text and image. However, such generalized…
In this paper, we evaluate the accuracy of deep learning approaches on geospatial vector geometry classification tasks. The purpose of this evaluation is to investigate the ability of deep learning models to learn from geometry coordinates…
In this paper, we present a novel deep learning approach, deeply-fused nets. The central idea of our approach is deep fusion, i.e., combine the intermediate representations of base networks, where the fused output serves as the input of the…
Deep Neural Networks have shown tremendous success in the area of object recognition, image classification and natural language processing. However, designing optimal Neural Network architectures that can learn and output arbitrary graphs…
Manifold learning is a fundamental task at the core of data analysis and visualisation. It aims to capture the simple underlying structure of complex high-dimensional data by preserving pairwise dissimilarities in low-dimensional…
In this work, we propose to train a graph neural network via resampling from a graphon estimate obtained from the underlying network data. More specifically, the graphon or the link probability matrix of the underlying network is first…
Representation learning of networks has witnessed significant progress in recent times. Such representations have been effectively used for classic network-based machine learning tasks like node classification, link prediction, and network…
Euclidean representation learning methods have achieved promising results in image fusion tasks, which can be attributed to their clear advantages in handling with linear space. However, data collected from a realistic scene usually has a…
Network-structured data becomes ubiquitous in daily life and is growing at a rapid pace. It presents great challenges to feature engineering due to the high non-linearity and sparsity of the data. The local and global structure of the…
Systematic relations between multiple objects that occur in various fields can be represented as networks. Real-world networks typically exhibit complex topologies whose structural properties are key factors in characterizing and further…
Symmetric positive definite (SPD) matrices (e.g., covariances, graph Laplacians, etc.) are widely used to model the relationship of spatial or temporal domain. Nevertheless, SPD matrices are theoretically embedded on Riemannian manifolds.…
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…
Deep neural networks have shown great potential in image reconstruction problems in Euclidean space. However, many reconstruction problems involve imaging physics that are dependent on the underlying non-Euclidean geometry. In this paper,…
In this paper, we study deep diagonal circulant neural networks, that is deep neural networks in which weight matrices are the product of diagonal and circulant ones. Besides making a theoretical analysis of their expressivity, we…
Existing EEG foundation models mainly treat neural signals as generic time series in Euclidean space, ignoring the intrinsic geometric structure of neural dynamics that constrains brain activity to low-dimensional manifolds. This…
We present a framework for efficiently approximating differential-geometric primitives on arbitrary manifolds via construction of an atlas graph representation, which leverages the canonical characterization of a manifold as a finite…
The use of distributions and high-level features from deep architecture has become commonplace in modern computer vision. Both of these methodologies have separately achieved a great deal of success in many computer vision tasks. However,…
Deep neural networks for learning Symmetric Positive Definite (SPD) matrices are gaining increasing attention in machine learning. Despite the significant progress, most existing SPD networks use traditional Euclidean classifiers on an…
We propose a deep neural network for supervised learning on neuroanatomical shapes. The network directly operates on raw point clouds without the need for mesh processing or the identification of point correspondences, as spatial…
Graph Convolutional Networks (GCNs) have been drawing significant attention with the power of representation learning on graphs. Unlike Convolutional Neural Networks (CNNs), which are able to take advantage of stacking very deep layers,…