Related papers: A generalized spectral concentration problem and t…
The theoretical analysis of spectral clustering mainly focuses on consistency, while there is relatively little research on its generalization performance. In this paper, we study the excess risk bounds of the popular spectral clustering…
Spectral algorithms are an important building block in machine learning and graph algorithms. We are interested in studying when such algorithms can be applied directly to provide optimal solutions to inference tasks. Previous works by…
We present a technique novel in numerical methods. It compiles the domain of the numerical methods as a discretized volume. Congruent elements are glued together to compile the domain over which the solution of a boundary value problem of a…
Modern deep neural networks suffer from performance degradation when evaluated on testing data under different distributions from training data. Domain generalization aims at tackling this problem by learning transferable knowledge from…
The main content of this work is devoted to study various explicit family of special functions generalizing the famous 2D Sleipain functions, founded in 1960's by D. Slepian and his co-authors. As a consequence, many desirable spectral…
We present algorithms for solving spatially nonlocal diffusion models on the unit sphere with spectral accuracy in space. Our algorithms are based on the diagonalizability of nonlocal diffusion operators in the basis of spherical harmonics,…
In recent years, spectral clustering has become a standard method for data analysis used in a broad range of applications. In this paper we propose a new class of algorithms for multiway spectral clustering based on optimization of a…
Spectral clustering techniques are valuable tools in signal processing and machine learning for partitioning complex data sets. The effectiveness of spectral clustering stems from constructing a non-linear embedding based on creating a…
Simon's problem is one of the most important problems demonstrating the power of quantum algorithms, as it greatly inspired the proposal of Shor's algorithm. The generalized Simon's problem is a natural extension of Simon's problem, and…
Solution of the Cox-Thompson inverse scattering problem at fixed energy [1,2,3] is reformulated resulting in semi-analytic equations. The new set of equations for the normalization constants and the nonphysical (shifted) angular momenta are…
We present spatial-Slepian transform~(SST) for the representation of signals on the sphere to support localized signal analysis. We use well-optimally concentrated Slepian functions, obtained by solving the Slepian spatial-spectral…
Spectral clustering has become a popular technique due to its high performance in many contexts. It comprises three main steps: create a similarity graph between N objects to cluster, compute the first k eigenvectors of its Laplacian matrix…
We advocate Laplacian K-modes for joint clustering and density mode finding, and propose a concave-convex relaxation of the problem, which yields a parallel algorithm that scales up to large datasets and high dimensions. We optimize a tight…
Factorization of matrices of Laurent polynomials plays an important role in mathematics and engineering such as wavelet frame construction and filter bank design. Wavelet frames (a.k.a. framelets) are useful in applications such as signal…
We address the problem of approximating parametric Fourier imaging problems via interpolation/ extrapolation algorithms that impose smoothing constraints across contiguous values of the parameter. Previous works already proved that…
Inspired by the quantum computing algorithms for Linear Algebra problems [HHL,TaShma] we study how the simulation on a classical computer of this type of "Phase Estimation algorithms" performs when we apply it to solve the Eigen-Problem of…
In this paper, we study a matricial version of the Byrnes-Georgiou-Lindquist generalized moment problem with complexity constraint. We introduce a new metric on multivariable spectral densities induced by the family of their spectral…
Subspace clustering is the problem of clustering data that lie close to a union of linear subspaces. In the abstract form of the problem, where no noise or other corruptions are present, the data are assumed to lie in general position…
This paper presents a robust numerical solution to the electromagnetic scattering problem involving multiple multi-layered cavities in both transverse magnetic and electric polarizations. A transparent boundary condition is introduced at…
A domain decomposition method for the solution of general variable-coefficient elliptic partial differential equations on regular domains is introduced. The method is based on tessellating the domain into overlapping thin slabs or shells,…