Here we propose a novel machine learning method for time series forecasting which is based on the widelyused Least Squares Support Vector Machine (LS-SVM) approach. The objective function of our method contains a weighted variance minimization part as well. This modification makes the method more efficient in time series forecasting as this paper will show. The proposed method is a generalizati...

The standard approaches to solving overdetermined linear systems Ax ≈ b construct minimal corrections to the data to make the corrected system compatible. In ordinary least squares (LS) the correction is restricted to the right hand side b, while in scaled total least squares (Scaled TLS) [10; 7] corrections to both b and A are allowed, and their relative sizes are determined by a real positive...

In this talk, starting with some earlier results, we propose and analyze an alternate approach of optimal L2error estimates for semidiscrete Galerkin approximations to a second order linear parabolic initial and boundary value problem with rough initial data. Our analysis is based on energy arguments without using parabolic duality. Further, it follows the spirit of the proof technique used for...

A new data-aided frequency estimator for frequencyselective fading channels is introduced. The proposed estimator is developed based on a least squares (LS) error criterion and can estimate frequency offsets without the need for channel information. Statistical analysis indicates that the resulting estimate is unbiased and tends to approach the Cramér–Rao lower bound (CRLB). Simulation shows th...

We define texture mapping as an optimization problem for which the goal is to preserve the maximum amount of information in the mapped texture. We derive a solution that is optimal in the least-squares sense and that corresponds to the pseudo-inverse of the texturemapping transformation. In practice, a first-order approximation of the least-squares solution is used as an initial estimate for th...

Weconsider a special class of quadraticmatrix optimizationproblemswhich often arise in applications. By exploiting the special structure of these problems, we derive a new semidefinite relaxation which, under mild assumptions, is proven to be tight for a larger number of constraints than could be achieved via a direct approach. We show the potential usefulness of these results when applied to r...

A curve fitting technique for optical spectra based on a robust estimator, least median squares (LMedS), is introduced in this study. For the effective calculation of LMedS, particle swarm optimization (PSO) is also introduced. Unlike a standard curve fitting method using least squares (LS) estimator, the method based on LMedS estimator is less influenced by outliers in experimental data. Two k...

In this research, we introduce a reasonable noise model for range data which is obtained by a laser radar range jnder, and derive two simple approximate solutions of the optimal local planejtting the range data under the noise model. Then we compare our methods with the general least-squares based methods, such as Z-function fitting, the eigenvalue method, and the maximum likelihood estimation ...

Blood flow in large vessels is typically modeled using the Navier-Stokes equations for the fluid domain and elasticity equations for the vessel wall. As the wall deforms, additional complications are introduced because the shape of the fluid domain changes, necessitating the use of a re-mapping or re-griding process for the fluid region. Typically, this system (fluid, solid, mapping) is solved ...

Neural networks such as multilayer perceptrons and radial basis function networks have been very successful in a wide range of problems. In this paper we give a short introduction to some new developments related to support vector machines (SVM), a new class of kernelbased techniques introduced within statistical learning theory and structural risk minimization. This new approach leads to solvi...