Gaussian processes (GPs) provide a nonparametric representation of functions. However, classical GP inference suffers from high computational cost for big data. In this paper, we propose a new Bayesian approach, EigenGP, that learns both basis dictionary elements—eigenfunctions of a GP prior—and prior precisions in a sparse finite model. It is well known that, among all orthogonal basis functio...

0885–3010/$25.00 © 2014 IEEE Abstract—Across a range of spectral estimation problems and beam focusing problems, it is necessary to constrain the properties of a function and its Fourier transform. In many cases, compact functions in both domains are desired, within the theoretical bounds of the uncertainty principle. Recently, a hyperbolic sine function of modified argument and power was found...

The problem of using the Karhunen – Lò eve transform with partial data is addressed. Given a set of empirical eigenfunctions , we show how to recover the modal coefficients for each gappy snapshot by a least-squares procedure. This method gives an unbiased estimate of the data that lie in the gaps and permits gaps to be filled in a reasonable manner. In addition , a scheme is advanced for findi...

We present the Quantum Section Method as a quantization technique to compute the eigenvalues and the eigenfunctions of quantum systems. As an instructive example we apply this procedure to quantize the annular billiard. The method uses the symmetry of the system to determine an auxiliary section separating the system into partial regions and computes the Green's functions for Schroedinger's equ...

We examine consequences of image-forming inhomogeneity in the form of a point-spread function that changes with position on the image plane. The familiar self-replicating sinusoids, which a homogeneous system simply multiplies by its spatial modulation-transfer function, generalize to eigenfunctions, which the system multiplies by eigenvalues. We give a way to calculate the eigenfunctions and e...

In this paper we prove the existence of a solution to a nonlinear Schrödinger–Poisson eigenvalue problem in dimension less than 3. Our proof is based on a global approach to the determination of eigenvalues and eigenfunctions which allows us to characterize the complete sequence of eigenvalues and eigenfunctions at once, via a variational approach, and thus differs from the usual and less gener...

We present a novel surface smoothing framework using the Laplace-Beltrami eigenfunctions. The Green’s function of an isotropic diffusion equation on a manifold is analytically represented using the eigenfunctions of the Laplace-Beltraimi operator. The Green’s function is then used in explicitly constructing heat kernel smoothing as a series expansion of the eigenfunctions. Unlike many previous ...

LetM be a complete Riemannian manifold with finite volume which we initially assume to be compact. Then since M is compact, L(M) is spanned by the eigenfunctions of the Laplacian ∆ on M . Many interesting questions can be asked about these eigenfunctions and their properties, and of these we focus on one, quantum ergodicity, which to the best of my knowledge was first considered by A. I. Šnirel...