Related papers: Geometric Scattering on Manifolds
We present an approach to learning features that represent the local geometry around a point in an unstructured point cloud. Such features play a central role in geometric registration, which supports diverse applications in robotics and 3D…
Non-Euclidean constraints are inherent in many kinds of data in computer vision and machine learning, typically as a result of specific invariance requirements that need to be respected during high-level inference. Often, these geometric…
The knowledge that data lies close to a particular submanifold of the ambient Euclidean space may be useful in a number of ways. For instance, one may want to automatically mark any point far away from the submanifold as an outlier or to…
Exploiting symmetries and invariance in data is a powerful, yet not fully exploited, way to achieve better generalisation with more efficiency. In this paper, we introduce two graph network architectures that are equivariant to several…
Palmprint recognition has drawn a lot of attention during the recent years. Many algorithms have been proposed for palmprint recognition in the past, majority of them being based on features extracted from the transform domain. Many of…
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…
Incorporating Euclidean symmetries (e.g. rotation equivariance) as inductive biases into graph neural networks has improved their generalization ability and data efficiency in unbounded physical dynamics modeling. However, in various…
Face recognition has been an active research area in the past few decades. In general, face recognition can be very challenging due to variations in viewpoint, illumination, facial expression, etc. Therefore it is essential to extract…
The success of deep learning has revolutionized many fields of research including areas of computer vision, text and speech processing. Enormous research efforts have led to numerous methods that are capable of efficiently analyzing data,…
Euclidean geometry is among the earliest forms of mathematical thinking. While the geometric primitives underlying its constructions, such as perfect lines and circles, do not often occur in the natural world, humans rarely struggle to…
We propose a manifold matching approach to generative models which includes a distribution generator (or data generator) and a metric generator. In our framework, we view the real data set as some manifold embedded in a high-dimensional…
We propose a novel technique for training deep networks with the objective of obtaining feature representations that exist in a Euclidean space and exhibit strong clustering behavior. Our desired features representations have three traits:…
Graph Neural Networks (GNNs) have significant advantages in handling non-Euclidean data and have been widely applied across various areas, thus receiving increasing attention in recent years. The framework of GNN models mainly includes the…
Convolutional Neural Networks(CNNs) has achieved remarkable performance breakthrough in Euclidean structure data. Recently, aggregation-transformation based Graph Neural networks(GNNs) gradually produce a powerful performance on…
We propose two graph neural network layers for graphs with features in a Riemannian manifold. First, based on a manifold-valued graph diffusion equation, we construct a diffusion layer that can be applied to an arbitrary number of nodes and…
The enduring legacy of Euclidean geometry underpins classical machine learning, which, for decades, has been primarily developed for data lying in Euclidean space. Yet, modern machine learning increasingly encounters richly structured data…
This paper tackles the pressing challenge of mutagenicity prediction by introducing three ground-breaking approaches. First, it showcases the superior performance of 2D scattering coefficients extracted from molecular images, compared to…
We define a class of Euclidean distances on weighted graphs, enabling to perform thermodynamic soft graph clustering. The class can be constructed form the "raw coordinates" encountered in spectral clustering, and can be extended by means…
Many recent efforts have been devoted to designing sophisticated deep learning structures, obtaining revolutionary results on benchmark datasets. The success of these deep learning methods mostly relies on an enormous volume of labeled…
Dataset distillation aims to synthesize a compact subset of the original data, enabling models trained on it to achieve performance comparable to those trained on the original large dataset. Existing distribution-matching methods are…