Related papers: An Introduction to Total Least Squares
A new statistical technique for constructing linear latent structure (LLS) models from available data, supported by well established theoretical results and an efficient algorithm, is presented. The method reduces the problem of estimating…
The analysis of a total least square problem (TLS) can be reduced to that of an associated core problem, which typically has lower dimension and improved solubility properties. Nevertheless, even a core problem may remain reducible,…
The problem of biclustering consists of the simultaneous clustering of rows and columns of a matrix such that each of the submatrices induced by a pair of row and column clusters is as uniform as possible. In this paper we approximate the…
The main contribution of this paper is a new submap joining based approach for solving large-scale Simultaneous Localization and Mapping (SLAM) problems. Each local submap is independently built using the local information through solving a…
This survey highlights the recent advances in algorithms for numerical linear algebra that have come from the technique of linear sketching, whereby given a matrix, one first compresses it to a much smaller matrix by multiplying it by a…
This draft concerns the error analysis of a collocation method based on the moving least squares (MLS) approximation for integral equations, which improves the results of [2] in the analysis part. This is mainly a translation from Persian…
Sketch-and-solve (SAS) is a very successful method to efficiently estimate the solution of heavily overdetermined large linear least squares problems. It uses random sketching to reduce the size of the problem, hence reducing the…
This article introduces a novel approach to the mathematical development of Ordinary Least Squares and Neural Network regression models, diverging from traditional methods in current Machine Learning literature. By leveraging Tensor…
This paper is concerned with the low-rank approximation for large-scale nonsymmetric matrices. Inspired by the classical Nystrom method, which is a popular method to find the low-rank approximation for symmetric positive semidefinite…
The optimization problem that arises out of the least median of squared residuals method in linear regression is analyzed. To simplify the analysis, the problem is replaced by an equivalent one of minimizing the median of absolute…
Partial Least Squares (PLS) refer to a class of dimension-reduction techniques aiming at the identification of two sets of components with maximal covariance, to model the relationship between two sets of observed variables…
We are interested in the numerical solution of the tensor least squares problem \[ \min_{\mathcal{X}} \| \mathcal{F} - \sum_{i =1}^{\ell} \mathcal{X} \times_1 A_1^{(i)} \times_2 A_2^{(i)} \cdots \times_d A_d^{(i)} \|_F, \] where…
Least-squares approximation is one of the most important methods for recovering an unknown function from data. While in many applications the data is fixed, in many others there is substantial freedom to choose where to sample. In this…
In this paper, we consider the mixed and componentwise condition numbers for a linear function of the solution to the total least squares (TLS) problem. We derive the explicit expressions of the mixed and componentwise condition numbers…
Modelling real world systems frequently requires the solution of systems of nonlinear equations. A number of approaches have been suggested and developed for this computational problem. However, it is also possible to attempt solutions…
It is well-known that the noise associated with the collection of an astronomical image by a CCD camera is, in large part, Poissonian. One would expect, therefore, that computational approaches that incorporate this a priori information…
Given a linear regression setting, Iterative Least Trimmed Squares (ILTS) involves alternating between (a) selecting the subset of samples with lowest current loss, and (b) re-fitting the linear model only on that subset. Both steps are…
We introduce a probabilistic approach to the LMS filter. By means of an efficient approximation, this approach provides an adaptable step-size LMS algorithm together with a measure of uncertainty about the estimation. In addition, the…
In this paper, we study the problem of finding the least square solutions of over-determined linear algebraic equations over networks in a distributed manner. Each node has access to one of the linear equations and holds a dynamic state. We…
In time series analysis, when fitting an autoregressive model, one must solve a Toeplitz ordinary least squares problem numerous times to find an appropriate model, which can severely affect computational times with large data sets. Two…