scholarly journals Least squares formulations for some elliptic second order problems, feedforward neural network solutions and convergence results

2022 ◽  
pp. 100023
Author(s):  
Jerome Pousin
Keyword(s):  
Neural Network ◽  
Least Squares ◽  
Second Order ◽  
Feedforward Neural Network ◽  
Convergence Results

Information Theoretic Learning

2011 ◽  
pp. 902-909 ◽  
Author(s):  
Deniz Erdogmus ◽  
Jose C. Principe
Keyword(s):  
Neural Network ◽  
Least Squares ◽  
Adaptive Systems ◽  
Mean Squared Error ◽  
Learning Algorithms ◽  
Optimal Solution ◽  
Principal Component ◽  
Second Order ◽  
Linear Discriminant ◽  
Non Gaussian

Learning systems depend on three interrelated components: topologies, cost/performance functions, and learning algorithms. Topologies provide the constraints for the mapping, and the learning algorithms offer the means to find an optimal solution; but the solution is optimal with respect to what? Optimality is characterized by the criterion and in neural network literature, this is the least addressed component, yet it has a decisive influence in generalization performance. Certainly, the assumptions behind the selection of a criterion should be better understood and investigated. Traditionally, least squares has been the benchmark criterion for regression problems; considering classification as a regression problem towards estimating class posterior probabilities, least squares has been employed to train neural network and other classifier topologies to approximate correct labels. The main motivation to utilize least squares in regression simply comes from the intellectual comfort this criterion provides due to its success in traditional linear least squares regression applications – which can be reduced to solving a system of linear equations. For nonlinear regression, the assumption of Gaussianity for the measurement error combined with the maximum likelihood principle could be emphasized to promote this criterion. In nonparametric regression, least squares principle leads to the conditional expectation solution, which is intuitively appealing. Although these are good reasons to use the mean squared error as the cost, it is inherently linked to the assumptions and habits stated above. Consequently, there is information in the error signal that is not captured during the training of nonlinear adaptive systems under non-Gaussian distribution conditions when one insists on second-order statistical criteria. This argument extends to other linear-second-order techniques such as principal component analysis (PCA), linear discriminant analysis (LDA), and canonical correlation analysis (CCA). Recent work tries to generalize these techniques to nonlinear scenarios by utilizing kernel techniques or other heuristics. This begs the question: what other alternative cost functions could be used to train adaptive systems and how could we establish rigorous techniques for extending useful concepts from linear and second-order statistical techniques to nonlinear and higher-order statistical learning methodologies?

Objects Centroid Correlation Using MATLAB's Neural Network Toolbox for Visually-Guided Object Manipulation

2014 ◽  
Vol 931-932 ◽  
pp. 1417-1421
Author(s):  
Sujin Wanchat ◽  
Supattra Plermkamon ◽  
Danaipong Chetchotsak
Keyword(s):  
Neural Network ◽  
Least Squares ◽  
Feedforward Neural Network ◽  
Automatic Process ◽  
Visually Guided ◽  
Linear Least Squares ◽  
Pick And Place ◽  
Place Task ◽  
Neural Network Toolbox ◽  
Practicable Method

Since a pick-and-place task plays an important role in an automatic process, it normally requires machine vision to locate an object for grasping. This paper presents a practicable method used to visually guide an object grasping a group of small, 1.1 mm diameter, screws by using an inexpensive webcam with a resolution of 640 x 480. A basic feedforward neural network is utilized to make a fitting function which associates pixel coordinates of the camera to the physical coordinates of the robot while the method of linear least squares is used for comparison in parallel. The result from the feedforward neural network shows that fifty screws can be completely manipulated from a tray after their physical coordinates are loaded into the robot while the result from the method of linear least squares shows failure when picking two of the samples.

Operational Determination of the Activated Sludge Process Using Neural Networks

1992 ◽  
Vol 26 (9-11) ◽  
pp. 2461-2464 ◽  
Author(s):  
R. D. Tyagi ◽  
Y. G. Du
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Steady State ◽  
Activated Sludge ◽  
Feedforward Neural Network ◽  
Training Data ◽  
Activated Sludge Process

A steady-statemathematical model of an activated sludgeprocess with a secondary settler was developed. With a limited number of training data samples obtained from the simulation at steady state, a feedforward neural network was established which exhibits an excellent capability for the operational prediction and determination.

scholarly journals Testing the Youth Physical Activity Promotion Model during the COVID-19 Pandemic, with Partial Least Squares Second-Order Latent Constructs

2021 ◽  
Vol 18 (12) ◽  
pp. 6398
Author(s):  
Elena Druică ◽  
Rodica Ianole-Călin ◽  
Monica Sakizlian ◽  
Daniela Aducovschi ◽  
Remus Dumitrescu ◽  
...  
Keyword(s):  
Physical Activity ◽  
Least Squares ◽  
Partial Least Squares ◽  
Online Survey ◽  
Physical Activity Promotion ◽  
Second Order ◽  
Latent Constructs ◽  
Activity Promotion ◽  
Youth Physical Activity ◽  
Mediating Mechanisms

We tested the Youth Physical Activity Promotion (YPAP) framework on Romanian students in order to identify actionable determinants to support participation in physical activity. Our sample consisted of 665 responses to an online survey, with participants aged 18–23 (mean = 19 years); 70% were women. We used the partial least squares algorithm to estimate the relationships between students’ behavior and possible predictors during the COVID-19 pandemic. Our results indicate that all the theoretical dimensions of YPAP (predisposing, enabling and reinforcing) have a positive and significant impact on physical activity, with two mediating mechanisms expressed as predisposing factors: able and worth. Unlike previous research, we used second-order latent constructs, unveiling a particular structure for the enabling dimension that only includes sport competence, fitness and skills, but not the environmental factors.

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