9 papers · 1 filter
Iterative Methods for Computing the Moore--Penrose Inverse of Split-Quaternion Matrices with Applications
Salman Ahmadi-Asl, Valentin Leplat, Mohammad S. Alkousa
We study iterative methods for computing the Moore--Penrose inverse of split-quaternion matrices. We first establish a consistent framework based on a \(2\times2\) real representat…
A Provably-Correct and Robust Convex Model for Smooth Separable NMF
Junjun Pan, Valentin Leplat, Michael Ng +1
Nonnegative matrix factorization (NMF) is a linear dimensionality reduction technique for nonnegative data, with applications such as hyperspectral unmixing and topic modeling. NMF…
Adaptive Randomized Pivoting for Tensor Singular Value Decomposition Model
Ahmadsho Akdodshoev, Valentin Leplat, Salman Ahmadi-Asl
This paper studies how adaptive randomized pivoting (ARP), recently introduced for matrix column subset selection, can be extended to tensors in the t-product framework. We propose…
Quaternion Maximum-Volume Submatrix Selection with Applications to Multichannel Imaging and Visual Data
Vsevolod Kliushev, Junjun Pan, Valentin Leplat
Low-rank approximation based on selected rows and columns is a useful alternative to singular value decompositions when the goal is an interpretable and compact matrix representati…
QuatIca: Advanced Numerical Linear Algebra and Optimization for Quaternionic Matrices in Python
Valentin Leplat, Salman Ahmadi-Asl, Junjun Pan +2
Quaternion-valued representations provide a convenient way to model coupled multi-channel signals (e.g., RGB imagery, polarization data, vector fields, and multi-detector time seri…
Pass-efficient Randomized Algorithms for Low-rank Approximation of Quaternion Matrices
Salman Ahmadi-Asl, Malihe Nobakht Kooshkghazi, Valentin Leplat
Randomized algorithms for low-rank approximation of quaternion matrices have gained increasing attention in recent years. However, existing methods overlook pass efficiency, the ab…