Related papers: Shape Partitioning via L$_p$ Compressed Modes
We study the minimization problem of a non-convex sparsity promoting penalty function, the transformed $l_1$ (TL1), and its application in compressed sensing (CS). The TL1 penalty interpolates $l_0$ and $l_1$ norms through a nonnegative…
We use spectral embeddings to give upper bounds on the spectral function of the Laplace--Beltrami operator on homogeneous spaces in terms of the volume growth of balls. In the case of compact manifolds, our bounds extend the 1980 lower…
We develop numerical methods for elliptic systems governed by partial segregation constraints, in which three nonnegative components are required to have a vanishing pointwise product throughout the domain. This constraint enforces that at…
We consider nonconvex constrained optimization problems and propose a new approach to the convergence analysis based on penalty functions. We make use of classical penalty functions in an unconventional way, in that penalty functions only…
A proof of the optimality of the eigenfunctions of the Laplace-Beltrami operator (LBO) in representing smooth functions on surfaces is provided and adapted to the field of applied shape and data analysis. It is based on the Courant-Fischer…
Many contemporary signal processing, machine learning and wireless communication applications can be formulated as nonconvex nonsmooth optimization problems. Often there is a lack of efficient algorithms for these problems, especially when…
This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…
We consider a natural generalization of the Partial Vertex Cover problem. Here an instance consists of a graph G = (V,E), a positive cost function c: V-> Z^{+}, a partition $P_1,..., P_r$ of the edge set $E$, and a parameter $k_i$ for each…
We consider a general class of constrained optimization problems with an additional $\ell_0$- sparsity term in the objective function. Based on a recent reformulation of this difficult $\ell_0$-term, we consider a nonsmooth penalty approach…
Compressed manifold modes are locally supported analogues of eigenfunctions of the Laplace-Beltrami operator of a manifold. In this paper we describe an algorithm for the calculation of modes for discrete manifolds that, in experiments,…
We introduce a new multi-dimensional nonlinear embedding -- Piecewise Flat Embedding (PFE) -- for image segmentation. Based on the theory of sparse signal recovery, piecewise flat embedding with diverse channels attempts to recover a…
Minimizing a sum of simple submodular functions of limited support is a special case of general submodular function minimization that has seen numerous applications in machine learning. We develop fast techniques for instances where…
For $2\leq p<4$, we study the $L^p$ norms of restrictions of eigenfunctions of the Laplace-Beltrami operator on smooth compact $2$-dimensional Riemannian manifolds. Burq, G\'erard, and Tzvetkov \cite{BurqGerardTzvetkov2007restrictions}, and…
Representing a signal as a linear combination of a set of basis functions is central in a wide range of applications, such as approximation, de-noising, compression, shape correspondence and comparison. In this context, our paper addresses…
Piecewise affine functions are widely used to approximate nonlinear and discontinuous functions. However, most, if not all existing models only deal with fitting continuous functions. In this paper, we investigate the problem of fitting a…
The recent development of spectral method has been praised for its high-order convergence in simulating complex physical problems. The combination of embedded boundary method and spectral method becomes a mainstream way to tackle…
This paper is concerned with a class of optimization problems with the nonnegative orthogonal constraint, in which the objective function is $L$-smooth on an open set containing the Stiefel manifold ${\rm St}(n,r)$. We derive a locally…
The multi-objective optimization is to optimize several objective functions over a common feasible set. Since the objectives usually do not share a common optimizer, people often consider (weakly) Pareto points. This paper studies…
We introduce new variant of $H$-measures defined on spectra of general algebra of test symbols and derive the localization properties of such $H$-measures. Applications for the compensated compactness theory are given. In particular, we…
This work concerns the minimization of the pseudospectral abscissa of a matrix-valued function dependent on parameters analytically. The problem is motivated by robust stability and transient behavior considerations for a linear control…