Among Neural Network methods, the Support Vector Machine (SVM) solutions are attracting increasing attention, mostly because they automatically derive the “optimal” network structure, in respect to generalization error for a given problem. In practice it means, that a lot of decisions that had to be made during the design of a traditional NN (e.g. the number of neurons, the length and type of t...

Least Squares Support Vector Machines (LS-SVM) is a proven method for classification and function approximation. In comparison to the standard Support Vector Machines (SVM) it only requires solving a linear system, but it lacks sparseness in the number of solution terms. Pruning can therefore be applied. Standard ways of pruning the LSSVM consist of recursively solving the approximation problem...

Analysis of Variance (ANOVA) techniques which is based on classical Least Squares (LS) method requires several assumptions, such as normality, constant variances and independency. Those assumptions can be violated due to several causes, such as the presence of an outlying observation. There are many evident in literatures that the LS estimate is easily affected by outliers. To remedy this probl...

The least squares (LS) can be used for nonlinear autoregressive (NAR) and nonlinear autoregressive moving average (NARMA) parameter estimation. However, for nonlinear cases, the LS results in biased parameter estimation due to its assumption that the independent variables are noise free. The total least squares (TLS) is another method that can used for nonlinear parameter estimation to increase...

The impact of reliable estimation of stream flows at highly urbanized areas and the associated receiving waters is very important for water resources analysis and design. We used the least squares support vector machine (LS-SVM) based algorithm to forecast the future streamflow discharge. A Gaussian Radial Basis Function (RBF) kernel framework was built on the data set to optimize the tuning pa...

Real time system parameter estimation from the set of input-output data is usually solved by the quadratic norm minimization of system equations errors known as least squares (LS). But measurement errors are also in the data matrix and so it is necessary to use a modification known as total least squares (TLS) or mixed LS and TLS. Instead of quadratic norm minimization other p-norms are used, f...

Using a recently proposed communication optimal variant of TSQR, weak scalability of the least squares solver (LS) with multiple right hand sides is studied. The communication for TSQR based LS solver for multiple right hand sides remains optimal in the sense that no additional messages are necessary compared to TSQR. However, LS has additional communication volume and flops compared to that fo...