Related papers: Siegel Neural Networks
Graph representation learning received increasing attentions in recent years. Most of existing methods ignore the complexity of the graph structures and restrict graphs in a single constant-curvature representation space, which is only…
Representations in the form of Symmetric Positive Definite (SPD) matrices have been popularized in a variety of visual learning applications due to their demonstrated ability to capture rich second-order statistics of visual data. There…
Deep metric learning, which learns discriminative features to process image clustering and retrieval tasks, has attracted extensive attention in recent years. A number of deep metric learning methods, which ensure that similar examples are…
Semi-supervised learning (SSL) over graph-structured data emerges in many network science applications. To efficiently manage learning over graphs, variants of graph neural networks (GNNs) have been developed recently. By succinctly…
We present a novel adaptive random subspace learning algorithm (RSSL) for prediction purpose. This new framework is flexible where it can be adapted with any learning technique. In this paper, we tested the algorithm for regression and…
Symmetric positive definite (SPD) matrices are useful for capturing second-order statistics of visual data. To compare two SPD matrices, several measures are available, such as the affine-invariant Riemannian metric, Jeffreys divergence,…
Low-dimensional embeddings are a cornerstone in the modelling and analysis of complex networks. However, most existing approaches for mining network embedding spaces rely on computationally intensive machine learning systems to facilitate…
Although many machine learning algorithms involve learning subspaces with particular characteristics, optimizing a parameter matrix that is constrained to represent a subspace can be challenging. One solution is to use Riemannian…
Hyperbolic geometry has emerged as an effective latent space for representing complex networks, owing to its ability to capture hierarchical organization and heterogeneous connectivity patterns using low-dimensional embeddings. As a result,…
Machine learning models can be used to predict physical quantities like homogenized elasticity stiffness tensors, which must always be symmetric positive definite (SPD) based on conservation arguments. Two datasets of homogenized elasticity…
Deep learning approaches to generic (non-semantic) segmentation have so far been indirect and relied on edge detection. This is in contrast to semantic segmentation, where DNNs are applied directly. We propose an alternative approach called…
Identifying symmetries in data sets is generally difficult, but knowledge about them is crucial for efficient data handling. Here we present a method how neural networks can be used to identify symmetries. We make extensive use of the…
Deep learning (DL) has achieved great success in many applications, but it has been less well analyzed from the theoretical perspective. The unexplainable success of black-box DL models has raised questions among scientists and promoted the…
A neural network with the widely-used ReLU activation has been shown to partition the sample space into many convex polytopes for prediction. However, the parameterized way a neural network and other machine learning models use to partition…
The task of building footprint segmentation has been well-studied in the context of remote sensing (RS) as it provides valuable information in many aspects, however, difficulties brought by the nature of RS images such as variations in the…
In recent years, graph neural networks (GNNs) have emerged as a promising tool for solving machine learning problems on graphs. Most GNNs are members of the family of message passing neural networks (MPNNs). There is a close connection…
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…
Recurrent neural networks have gained widespread use in modeling sequential data. Learning long-term dependencies using these models remains difficult though, due to exploding or vanishing gradients. In this paper, we draw connections…
Stochastic recurrent neural networks with latent random variables of complex dependency structures have shown to be more successful in modeling sequential data than deterministic deep models. However, the majority of existing methods have…
Graph neural networks face two fundamental challenges rooted in the linear structure of Euclidean vector spaces: (1) Current architectures represent geometry through vectors (directions, gradients), yet many tasks require matrix-valued…