Search results for " Least squares"
showing 10 items of 223 documents
Algorithms for Rational Discrete Least Squares Approximation Part I: Unconstrained Optimization
1976
In this paper a modification of L. Wittmeyer’s method ([1], [14]) for rational discrete least squares approximation is given which corrects for its failure to converge to a non-optimal point in general. The modification makes necessary very little additional computing effort only. It is analysed thoroughly with respect to its conditions for convergence and its numerical properties. A suitable implementation is shown to be benign in the sense of F. L. Bauer [2]. The algorithm has proven successful even in adverse situations.
Moving Least Squares Innovative Strategies For Sheet Forming Design
2011
In the last years a great interest in optimization algorithms aimed to design forming processes was demonstrated by many researches. Proper design methodologies to reduce times and costs have to be developed mostly based on computer aided procedures. Response surface methods (RSM) proved their effectiveness in the recent years also for the application in sheet metal forming aiming to reduce the number of numerical simulations. Actually, the main drawback of such method is the number of direct problem to be solved in order to reach good function approximations. A very interesting aspect in RSM application regards the possibility to build response surfaces basing on moving least squares appro…
A contribution on the optimization strategies based on moving least squares approximation for sheet metal forming design
2012
Computer-aided procedures to design and optimize forming processes are, nowadays, crucial research topics since industrial interest in costs and times reduction is always increasing. Many researchers have faced this research challenge with various approaches. Response surface methods (RSM) are probably the most known approaches since they proved their effectiveness in the recent years. With a peculiar attention to sheet metal forming process design, RSM should offer the possibility to reduce the number of numerical simulations which in many cases means to reduce design times and complexity. Actually, the number of direct problems (FEM simulations) to be solved in order to reach good functio…
A generalization of the orthogonal regression technique for life cycle inventory
2012
Life cycle assessment (LCA) is a method used to quantify the environmental impacts of a product, process, or service across its whole life cycle. One of the problems occurring when the system at hand involves processes delivering more than one valuable output is the apportionment of resource consumption and environmental burdens in the correct proportion amongst the products. The mathematical formulation of the problem is represented by the solution of an over-determined system of linear equations. The paper describes the application of an iterative algorithm for the implementation of least square regression to solve this over-determined system directly in its rectangular form. The applied …
TOWARD A SOLUTION OF ALLOCATION IN LIFE CYCLE INVENTORIES: THE USE OF LEAST SQUARES TECHNIQUES
2010
Purpose: The matrix method for the solution of the so-called inventory problem in LCA generally determines the inventory vector related to a specific system of processes by solving a system of linear equations. The paper proposes a new approach to deal with systems characterized by a rectangular (and thus non-invertible) coefficients matrix. The approach, based on the application of regression techniques, allows solving the system without using computational expedients such as the allocation procedure. Methods: The regression techniques used in the paper are (besides the ordinary least squares, OLS) total least squares (TLS) and data least squares (DLS). In this paper, the authors present t…
Bayesian model averaging and weighted-average least squares: Equivariance, stability, and numerical issues
2011
In this article, we describe the estimation of linear regression models with uncertainty about the choice of the explanatory variables. We introduce the Stata commands bma and wals, which implement, respectively, the exact Bayesian model-averaging estimator and the weighted-average least-squares estimator developed by Magnus, Powell, and Prüfer (2010, Journal of Econometrics 154: 139–153). Unlike standard pretest estimators that are based on some preliminary diagnostic test, these model-averaging estimators provide a coherent way of making inference on the regression parameters of interest by taking into account the uncertainty due to both the estimation and the model selection steps. Spec…
Comparison of near and mid infrared spectroscopy as green analytical tools for the determination of total polar materials in fried oils
2017
Abstract Total polar materials (TPM) are used as an indicator of the quality in the frying oil because of high values may be harmful for human health. Spanish legislation establishes the maximum level of total polar materials for frying fats and oils for human consumption around 25% (w/w). Official methods to monitor oil quality are time consuming and use a lot of chemicals; therefore it is necessary a simple and quick analytical technique to evaluate fried oils. Transmittance near-infrared (NIR) and attenuated total reflection mid-infrared (ATR-MIR) spectroscopy measurements, combined with partial least squares (PLS) regression, offer alternatives to determine TPM in fried oils with relati…
Model performance of partial least squares in utilizing the visible spectroscopy data for estimation of algal biomass in a photobioreactor
2018
[EN] Spectroscopy technology and statistical methods (Partial Least Squares) have been integrated to develop a model that allows estimating the microalgal biomass in a photobioreactor. The model employing PLS combines the absorption spectrum measurements in the visible range (400-750 nm) with a microalgae cell density in a water sample. First, a calibration model was constructed using a calibration data set, and then, the predictive capacity of the model was determined by cross validation. Finally, an external validation of the predictive performance of the model was carried out with an independent data set. To test the accuracy of the model it was applied to different culture conditions yi…
OnMLM: An Online Formulation for the Minimal Learning Machine
2019
Minimal Learning Machine (MLM) is a nonlinear learning algorithm designed to work on both classification and regression tasks. In its original formulation, MLM builds a linear mapping between distance matrices in the input and output spaces using the Ordinary Least Squares (OLS) algorithm. Although the OLS algorithm is a very efficient choice, when it comes to applications in big data and streams of data, online learning is more scalable and thus applicable. In that regard, our objective of this work is to propose an online version of the MLM. The Online Minimal Learning Machine (OnMLM), a new MLM-based formulation capable of online and incremental learning. The achievements of OnMLM in our…
An Embedded Solution for Multispectral Palmprint Recognition
2018
Palmprint based identification has attracted much attention in the past decades. In some real-life applications, portable personal authentication systems with high accuracy and speed efficiency are required. This paper presents an embedded palmprint recognition solution based on the multispectral image modality. We first develop an effective recognition algorithm by using partial least squares regression, then a FPGA prototype is implemented and optimized through high-level synthesis technique. The evaluation experiments demonstrate that the proposed system can achieve a higher recognition rate at a lower running cost comparing to the reference implementations.