Related papers: GeoMM: On Geodesic Perspective for Multi-modal Lea…

We describe a novel metric-based learning approach that introduces a multimodal framework and uses deep audio and geophone encoders in siamese configuration to design an adaptable and lightweight supervised model. This framework eliminates…

The notion of task similarity is at the core of various machine learning paradigms, such as domain adaptation and meta-learning. Current methods to quantify it are often heuristic, make strong assumptions on the label sets across the tasks,…

Machine learning problems have an intrinsic geometric structure as central objects including a neural network's weight space and the loss function associated with a particular task can be viewed as encoding the intrinsic geometry of a given…

In the manifold learning problem one seeks to discover a smooth low dimensional surface, i.e., a manifold embedded in a higher dimensional linear vector space, based on a set of measured sample points on the surface. In this paper we…

Similarity distance measure between two trajectories is an essential tool to understand patterns in motion, for example, in Human-Robot Interaction or Imitation Learning. The problem has been faced in many fields, from Signal Processing,…

A new class of distances for graph vertices is proposed. This class contains parametric families of distances which reduce to the shortest-path, weighted shortest-path, and the resistance distances at the limiting values of the family…

Distance metric learning is a successful way to enhance the performance of the nearest neighbor classifier. In most cases, however, the distribution of data does not obey a regular form and may change in different parts of the feature…

Distance metric learning is a branch of machine learning that aims to learn distances from the data, which enhances the performance of similarity-based algorithms. This tutorial provides a theoretical background and foundations on this…

The choice of good distances and similarity measures between objects is important for many machine learning methods. Therefore, many metric learning algorithms have been developed in recent years, mainly for Euclidean data in order to…

The emergence of geometric deep learning as a novel framework to deal with graph-based representations has faded away traditional approaches in favor of completely new methodologies. In this paper, we propose a new framework able to combine…

Graphs are interesting structures: extremely useful to depict real-life problems, extremely easy to understand given a sketch, extremely complicated to represent formally, extremely complicated to compare. Phylogeny is the study of the…

Numerical computation of shortest paths or geodesics on curved domains, as well as the associated geodesic distance, arises in a broad range of applications across digital geometry processing, scientific computing, computer graphics, and…

Generative models are invaluable in many fields of science because of their ability to capture high-dimensional and complicated distributions, such as photo-realistic images, protein structures, and connectomes. How do we evaluate the…

We propose a novel method of introducing structure into existing machine learning techniques by developing structure-based similarity and distance measures. To learn structural information, low-dimensional structure of the data is captured…

For robots to work alongside humans and perform in unstructured environments, they must learn new motion skills and adapt them to unseen situations on the fly. This demands learning models that capture relevant motion patterns, while…

Graph comparison plays a major role in many network applications. We often need a similarity metric for comparing networks according to their structural properties. Various network features - such as degree distribution and clustering…

In this paper, we propose the use of geodesic distances in conjunction with multivariate distance matrix regression, called geometric-MDMR, as a powerful first step analysis method for manifold-valued data. Manifold-valued data is appearing…

The geometry of three-dimensional (3D) graphs, consisting of nodes and edges, plays a crucial role in many important applications. An excellent example is molecular graphs, whose geometry influences important properties of a molecule…

Elastic geodesic grids deploy from flat to spatial configurations via complex nonlinear motion that is difficult to represent robustly for simulation. We present a geometric guidance framework that discretizes deployment as synchronized,…

Many applications in pattern recognition represent patterns as a geometric graph. The geometric graph distance (GGD) has recently been studied as a meaningful measure of similarity between two geometric graphs. Since computing the GGD is…