Related papers: $ \mathrm{SE} (3) $ Synchronization by Eigenvector…
Spectral methods have emerged as a simple yet surprisingly effective approach for extracting information from massive, noisy and incomplete data. In a nutshell, spectral methods refer to a collection of algorithms built upon the eigenvalues…
We introduce a new hybrid control strategy, which is conceptually different from the commonly used synergistic hybrid approaches, to efficiently deal with the problem of the undesired equilibria that precludes smooth vectors fields on…
In this paper, we propose a unified approach for solving structure-preserving eigenvalue embedding problem (SEEP) for quadratic regular matrix polynomials with symmetry structures. First, we determine perturbations of a quadratic matrix…
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…
Group synchronization aims to recover the group elements from their noisy pairwise measurements. It has found many applications in community detection, clock synchronization, and joint alignment problem. This paper focuses on the orthogonal…
Spectral embedding is a popular technique for the representation of graph data. Several regularization techniques have been proposed to improve the quality of the embedding with respect to downstream tasks like clustering. In this paper, we…
Spectral clustering is one of the most widely used techniques for extracting the underlying global structure of a data set. Compressed sensing and matrix completion have emerged as prevailing methods for efficiently recovering sparse and…
Spectral clustering is a leading and popular technique in unsupervised data analysis. Two of its major limitations are scalability and generalization of the spectral embedding (i.e., out-of-sample-extension). In this paper we introduce a…
In this paper we address the rotation synchronization problem, where the objective is to recover absolute rotations starting from pairwise ones, where the unknowns and the measures are represented as nodes and edges of a graph,…
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…
We develop a practical approach to semidefinite programming (SDP) that includes the von Neumann entropy, or an appropriate variant, as a regularization term. In particular we solve the dual of the regularized program, demonstrating how a…
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…
In computational homogenization, a fast solution of the microscopic problem can be achieved by model order reduction in combination with hyper-reduction. Such a technique, which has recently been proposed in the context of magnetostatics,…
Spectral clustering is a popular clustering method. It first maps data into the spectral embedding space and then uses Kmeans to find clusters. However, the two decoupled steps prohibit joint optimization for the optimal solution. In…
This paper is concerned with the interplay between statistical asymmetry and spectral methods. Suppose we are interested in estimating a rank-1 and symmetric matrix $\mathbf{M}^{\star}\in \mathbb{R}^{n\times n}$, yet only a randomly…
The spectral bundle method proposed by Helmberg and Rendl is well established for solving large-scale semidefinite programs (SDP) thanks to its low per iteration computational complexity and strong practical performance. In this paper, we…
Graph embedding has been proven to be efficient and effective in facilitating graph analysis. In this paper, we present a novel spectral framework called NOn-Backtracking Embedding (NOBE), which offers a new perspective that organizes graph…
In the tensor completion problem, one seeks to estimate a low-rank tensor based on a random sample of revealed entries. In terms of the required sample size, earlier work revealed a large gap between estimation with unbounded computational…
The recently emerged spectral clustering surpasses conventional clustering methods by detecting clusters of any shape without the convexity assumption. Unfortunately, with a computational complexity of $O(n^3)$, it was infeasible for…
The global attitude synchronization problem is studied for networked rigid bodies under directed topologies. To avoid the asynchronous pitfall where only vector parts converge to some identical value but scalar parts do not, multiplicative…