4 papers
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…
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…
Iterative Methods for Computing the Moore-Penrose Pseudoinverse of Quaternion Matrices, with Applications
Valentin Leplat, Salman Ahmadi-Asl, JunJun Pan +1
We develop quaternion--native iterative methods for computing the Moore--Penrose (MP) pseudoinverse of quaternion matrices and analyze their convergence. Our starting point is a da…