Related papers: Group Orbit Optimization: A Unified Approach to Da…
The normaliser problem takes as input subgroups $G$ and $H$ of the symmetric group $S_n$, and asks one to compute $N_G(H)$. The fastest known algorithm for this problem is simply exponential, whilst more efficient algorithms are known for…
We present methods for computing the generalized polar decomposition of a matrix based on the dynamically weighted Halley (DWH) iteration. This method is well established for computing the standard polar decomposition. A stable…
Product quantization (PQ) coupled with a space rotation, is widely used in modern approximate nearest neighbor (ANN) search systems to significantly compress the disk storage for embeddings and speed up the inner product computation.…
Recently, several studies have explored the use of neural network to solve different routing problems, which is an auspicious direction. These studies usually design an encoder-decoder based framework that uses encoder embeddings of nodes…
We present a novel approach for model reduction of nonlinear dynamical systems based on proper orthogonal decomposition (POD). Our method, derived from Density Matrix Renormalization Group (DMRG), provides a significant reduction in…
In this paper, we propose a framework under which the decentralized optimization algorithms suggested in \cite{JKJJ,MA, NO,NO2} can be treated in a unified manner. More precisely, we show that the distributed subgradient descent algorithms…
Vector set orthogonal normalization and matrix QR decomposition are fundamental problems in matrix analysis with important applications in many fields. We know that Gram-Schmidt process is a widely used method to solve these two problems.…
We introduce a continuous global optimization method to the field of surface reconstruction from discrete noisy cloud of points with weak information on orientation. The proposed method uses an energy functional combining flux-based…
We develop a package using the computer algebra system GAP for computing the decomposition of a representation $\rho$ of a finite group $G$ over $\mathbb{C}$ into irreducibles, as well as the corresponding decomposition of the centraliser…
This work presents a novel approach for the optimization of dynamic systems on finite-dimensional Lie groups. We rephrase dynamic systems as so-called neural ordinary differential equations (neural ODEs), and formulate the optimization…
The orthogonalization process is an essential building block in Krylov space methods, which takes up a large portion of the computational time. Commonly used methods, like the Gram-Schmidt method, consider the projection and normalization…
Composite function minimization captures a wide spectrum of applications in both computer vision and machine learning. It includes bound constrained optimization, $\ell_1$ norm regularized optimization, and $\ell_0$ norm regularized…
Let G be a Lie group, $g = Lie(G)$ - its Lie algebra, $g*$ - the dual vector space and $\widehat G$ - the set of equivalence classes of unitary irreducible representations of $G$. The orbit method [1] establishes a correspondence between…
This paper addresses signal denoising when large-amplitude coefficients form clusters (groups). The L1-norm and other separable sparsity models do not capture the tendency of coefficients to cluster (group sparsity). This work develops an…
Deformable retinal image registration is notoriously difficult due to large homogeneous regions and sparse but critical vascular features, which cause limited gradient signals in standard learning-based frameworks. In this paper, we…
In this paper, we present a novel method for co-clustering, an unsupervised learning approach that aims at discovering homogeneous groups of data instances and features by grouping them simultaneously. The proposed method uses the entropy…
The unit commitment (UC) problem is a nonlinear, high-dimensional, highly constrained, mixed-integer power system optimization problem and is generally solved in the literature considering minimizing the system operation cost as the only…
Group sparse representation has shown promising results in image debulrring and image inpainting in GSR [3] , the main reason that lead to the success is by exploiting Sparsity and Nonlocal self-similarity (NSS) between patches on natural…
A fundamental challenge for machine learning models is generalizing to out-of-distribution (OOD) data, in part due to spurious correlations. To tackle this challenge, we first formalize the OOD generalization problem as constrained…
This paper highlights a formal connection between two families of widely used matrix factorization algorithms in numerical linear algebra. One family consists of the Jacobi eigenvalue algorithm and its variants for computing the Hermitian…