Matrix Factor Analysis: From Least Squares to Iterative Projection

Gradient Projection Iterative Sketch for Large-Scale Constrained Least-Squares

We propose a randomized first order optimization algorithm Gradient Projection Iterative Sketch (GPIS) and an accelerated variant for efficiently solving large scale constrained Least Squares (LS). We provide the first theoretical convergence analysis for both algorithms. An efficient implementation using a tailored linesearch scheme is also proposed. We demonstrate our methods’ computational e...

Iterative Reweighted Least Squares ∗

Describes a powerful optimization algorithm which iteratively solves a weighted least squares approximation problem in order to solve an L_p approximation problem. 1 Approximation Methods of approximating one function by another or of approximating measured data by the output of a mathematical or computer model are extraordinarily useful and ubiquitous. In this note, we present a very powerful ...

Iterative least-squares solutions of coupled Sylvester matrix equations

In this paper, we present a general family of iterative methods to solve linear equations, which includes the well-known Jacobi and Gauss–Seidel iterations as its special cases. The methods are extended to solve coupled Sylvester matrix equations. In our approach, we regard the unknown matrices to be solved as the system parameters to be identified, and propose a least-squares iterative algorit...

​Rank based Least-squares Independent Component Analysis

  In this paper, we propose a nonparametric rank-based alternative to the least-squares independent component analysis algorithm developed. The basic idea is to estimate the squared-loss mutual information, which used as the objective function of the algorithm, based on its copula density version. Therefore, no marginal densities have to be estimated. We provide empirical evaluation of th...

Least Squares Solutions of Inconsistent Fuzzy Linear Matrix Equations