Related papers: A generalized spectral concentration problem and t…
We advocate a compressed sensing strategy that consists of multiplying the signal of interest by a wide bandwidth modulation before projection onto randomly selected vectors of an orthonormal basis. Firstly, in a digital setting with random…
The stochastic inverse eigenvalue problem aims to reconstruct a stochastic matrix from its spectrum. While there exists a large literature on the existence of solutions for special settings, there are only few numerical solution methods…
In hyperspectral sparse unmixing, a successful approach employs spectral bundles to address the variability of the endmembers in the spatial domain. However, the regularization penalties usually employed aggregate substantial computational…
We consider spectral clustering algorithms for community detection under a general bipartite stochastic block model (SBM). A modern spectral clustering algorithm consists of three steps: (1) regularization of an appropriate adjacency or…
In this paper, we propose an efficient algorithm for data clustering based on the Moreau envelope, which approximates nonsmooth and nonconvex components of the generalized multi-source Weber problem. The number of clusters is not fixed in…
This paper focuses on the regularization of backward time-fractional diffusion problem on unbounded domain. This problem is well-known to be ill-posed, whence the need of a regularization method in order to recover stable approximate…
We consider the problem of clustering datasets in the presence of arbitrary outliers. Traditional clustering algorithms such as k-means and spectral clustering are known to perform poorly for datasets contaminated with even a small number…
Spectral clustering is a popular and effective algorithm designed to find $k$ clusters in a graph $G$. In the classical spectral clustering algorithm, the vertices of $G$ are embedded into $\mathbb{R}^k$ using $k$ eigenvectors of the graph…
Despite being the most popular methods of data analysis, Fourier-based techniques suffer from the problem of static resolution that is currently believed to be a fundamental limitation of the Fourier Transform. Although alternative…
Spectral clustering is a technique that clusters elements using the top few eigenvectors of their (possibly normalized) similarity matrix. The quality of spectral clustering is closely tied to the convergence properties of these principal…
In this paper we study variants of the widely used spectral clustering that partitions a graph into k clusters by (1) embedding the vertices of a graph into a low-dimensional space using the bottom eigenvectors of the Laplacian matrix, and…
Simulating a Gaussian process requires sampling from a high-dimensional Gaussian distribution, which scales cubically with the number of sample locations. Spectral methods address this challenge by exploiting the Fourier representation,…
We prove sharp upper bounds for sums of eigenvalues (and other spectral functionals) of Laplace-like operators, including bi-Laplacian and fractional Laplacian. We show that among linear images of a highly symmetric domain, our spectral…
This paper considers the well-studied algorithmic regime of designing a $(1+\epsilon)$-approximation algorithm for a $k$-clustering problem that runs in time $f(k,\epsilon)poly(n)$ (sometimes called an efficient parameterized approximation…
Slepian functions provide a solution to the optimization problem of joint time-frequency localization. Here, this concept is extended by using a generalized optimization criterion that favors energy concentration in one interval while…
Based on the Fourier extension, we propose an oversampling collocation method for solving the elliptic partial differential equations with variable coefficients over arbitrary irregular domains. This method only uses the function values on…
A method for solving linear initial boundary value problems was recently reimplemented as a true spectral transform method. As part of this reformulation, the precise sense in which the spectral transforms diagonalize the underlying spatial…
Spectral algorithms are graph partitioning algorithms that partition a node set of a graph into groups by using a spectral embedding map. Clustering techniques based on the algorithms are referred to as spectral clustering and are widely…
Efficient and accurate spectral solvers for nonlocal models in any spatial dimension are presented. The approach we pursue is based on the Fourier multipliers of nonlocal Laplace operators introduced in a previous work. It is demonstrated…
We propose a Fourier-based approach for optimization of several clustering algorithms. Mathematically, clusters data can be described by a density function represented by the Dirac mixture distribution. The density function can be smoothed…