The canonical polyadic decomposition (CPD) allows one to extract compact and interpretable representations of tensors. Several optimization-based methods exist fit the CPD a tensor for standard least-squares (LS) cost function. Extensions have been proposed more general functions such as β-divergences well. For these non-LS functions, generalized Gauss-Newton (GGN) method has developed. This is...

We present a new algorithm for the solution of nonlinear least squares problems arising from parameterized imaging problems with diffuse optical tomographic data [D. Boas et al., IEEE Signal Process. Mag., 18 (2001), pp. 57–75]. The parameterization arises from the use of parametric level sets for regularization [M. E. Kilmer et al., Proc. SPIE, 5559 (2004), pp. 381– 391], [A. Aghasi, M. E. Kil...

This paper studies adaptive regularized methods for nonlinear least-squares problems where the model of the objective function used at each iteration is either the Euclidean residual regularized by a quadratic term or the Gauss-Newton model regularized by a cubic term. For suitable choices of the regularization parameter the role of the regularization term is to provide global convergence. In t...

A unifying theoretical and algorithmic framework for diffusion tensor estimation is presented. Theoretical connections among the least squares (LS) methods, (linear least squares (LLS), weighted linear least squares (WLLS), nonlinear least squares (NLS) and their constrained counterparts), are established through their respective objective functions, and higher order derivatives of these object...

We begin by considering the problem of fitting a single Bézier curve segment to a set of ordered data so that the error is minimized in the total least squares sense. We develop an algorithm for applying the Gauss–Newton method to this problem with a direct method for evaluating the Jacobian based on implicitly differentiating a pseudo-inverse. We then demonstrate the simple extension of this a...

The subproblem is in a form of L1-regularized least squares. To perform a coordinate update in the CD subroutine, the training data is accessed/used in a feature-wise manner, which is the same as how data is used in CDN for problem (3.2). Thus, the applicability of the naive parallelization to the CD subroutine should hold here and the speedup is predicted to be at a comparable level. In additi...

In this paper we point out an overlooked structure of SLAM that distinguishes it from a generic nonlinear least squares problem. The measurement function in most common forms of SLAM is linear with respect to robot and features’ positions. Therefore, given an estimate for robot orientation, the conditionally optimal estimate for the rest of state variables can be easily obtained by solving a sp...

In this paper we propose and analyze nonlinear least squares methods, which process the data incrementally, one data block at a time. Such methods are well suited for large data sets and real time operation, and have received much attention in the context of neural network training problems. We focus on the Extended Kalman Filter, which may be viewed as an incremental version of the Gauss-Newto...