Generating valid Euclidean distance matrices
Generating point clouds, e.g., molecular structures, in arbitrary rotations, translations, and enumerations remains a challenging task. Meanwhile, neural networks utilizing symmetry invariant layers have been shown to be able to optimize their training objective in a data-efficient way. In this spirit, we present an architecture which allows to produce valid Euclidean distance matrices, which by construction are already invariant under rotation and translation of the described object. Motivated by the goal to generate molecular structures in Cartesian space, we use this architecture to construct a Wasserstein GAN utilizing a permutation invariant critic network. This makes it possible to generate molecular structures in a one-shot fashion by producing Euclidean distance matrices which have a three-dimensional embedding.
Code (1)
Tasks
TranslationvalidMethods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Deterministic Equivalent of the Log-Euclidean Distance between Sample Covariance Matrices
Log-Euclidean distances are commonly used to quantify the similarity between positive definite matrices using geometric considerations. This paper analyzes the behavior of this distance when it is used to measure closene…
Weighted Euclidean Distance Matrices over Mixed Continuous and Categorical Inputs for Gaussian Process Models
Gaussian Process (GP) models are widely utilized as surrogate models in scientific and engineering fields. However, standard GP models are limited to continuous variables due to the difficulties in establishing correlati…
Bayesian OptimizationRiemannian Metric Learning for Symmetric Positive Definite Matrices
Over the past few years, symmetric positive definite (SPD) matrices have been receiving considerable attention from computer vision community. Though various distance measures have been proposed in the past for comparing…
ClusteringMetric LearningA new metric on the manifold of kernel matrices with application to matrix geometric means
Symmetric positive definite (spd) matrices are remarkably pervasive in a multitude of scientific disciplines, including machine learning and optimization. We consider the fundamental task of measuring distances between t…
Kinetic Euclidean Distance Matrices
Euclidean distance matrices (EDMs) are a major tool for localization from distances, with applications ranging from protein structure determination to global positioning and manifold learning. They are, however, static o…