Related papers: Spectral Echolocation via the Wave Embedding

A method for numerical approximation of a new class of fractional parabolic stochastic evolution equations is introduced and analysed. This class of equations has recently been proposed as a space-time extension of the SPDE-method in…

The propagation of internal gravity waves in stratified media, such as those found in ocean basins and lakes, leads to the development of geometrical patterns called "attractors". These structures accumulate much of the wave energy and make…

We propose a graph spectral representation of time series data that 1) is parsimoniously encoded to user-demanded resolution; 2) is unsupervised and performant in data-constrained scenarios; 3) captures event and event-transition structure…

Spectral functions play a central role in the characterization of a wide range of physical systems, including strongly interacting quantum field theories and many-body systems. Their non-perturbative determination from Euclidean correlation…

We consider and analyze applying a spectral inverse iteration algorithm and its subspace iteration variant for computing eigenpairs of an elliptic operator with random coefficients. With these iterative algorithms the solution is sought…

We approximate the spectral data (eigenvalues and eigenfunctions) of compact Riemannian manifold by the spectral data of a sequence of (computable) discrete Laplace operators associated to some graphs immersed in the manifold. We give an…

Hyperspectral images often have hundreds of spectral bands of different wavelengths captured by aircraft or satellites that record land coverage. Identifying detailed classes of pixels becomes feasible due to the enhancement in spectral and…

spectral-based subspace learning is a common data preprocessing step in many machine learning pipelines. The main aim is to learn a meaningful low dimensional embedding of the data. However, most subspace learning methods do not take into…

Estimation of the covariance structure of spatial processes is of fundamental importance in spatial statistics. In the literature, several non-parametric and semi-parametric methods have been developed to estimate the covariance structure…

A compact Riemannian manifold may be immersed into Euclidean space by using high frequency Laplace eigenfunctions. We study the geometry of the manifold viewed as a metric space endowed with the distance function from the ambient Euclidean…

Spectral dimensionality reduction algorithms are widely used in numerous domains, including for recognition, segmentation, tracking and visualization. However, despite their popularity, these algorithms suffer from a major limitation known…

This paper considers the problem of embedding directed graphs in Euclidean space while retaining directional information. We model a directed graph as a finite set of observations from a diffusion on a manifold endowed with a vector field.…

We derive the invariant imbedding equations for plane electromagnetic waves propagating in stratified magnetic media, where both dielectric and magnetic permeabilities vary in one spatial direction in an arbitrary manner. These equations…

An embedding method for solving the time-dependent Schr\"odinger equation is developed using the Dirac-Frenkel variational principle. Embedding allows the time-evolution of the wavefunction to be calculated explicitly in a limited region of…

Diffusion models provide a principled framework for generative modeling via stochastic differential equations and time-reversed dynamics. Extending spectral diffusion approaches to spherical data, however, raises nontrivial geometric and…

This paper provides a new similarity detection algorithm. Given an input set of multi-dimensional data points, where each data point is assumed to be multi-dimensional, and an additional reference data point for similarity finding, the…

The output of spectral clustering is a collection of eigenvalues and eigenvectors that encode important connectivity information about a graph or a manifold. This connectivity information is often not cleanly represented in the eigenvectors…

We present Spectral Inference Networks, a framework for learning eigenfunctions of linear operators by stochastic optimization. Spectral Inference Networks generalize Slow Feature Analysis to generic symmetric operators, and are closely…

We study the coherence in time and space of electromagnetic fields propagated through complex media. Whether for localization, imaging or telecommunication, the development of dedicated numerical techniques is generally based on the…

The second eigenvalue of the Laplacian matrix and its associated eigenvector are fundamental features of an undirected graph, and as such they have found widespread use in scientific computing, machine learning, and data analysis. In many…