Error, neural network output

In all figures, the solutions marked with a black square indicate neural networks reaching a full accuracy of 100%. We should note that, while validation and test error are calculated as Mean Squared Error (MSE) between the expected classification value (0/1) and actual neural network output (ranging in [0,1], and depending on the output activation function), the accuracy is calculated based on the confusion matrix (True Positives- -True Negatives)/(Total sample size). 

All elosed-loop eontrol systems operate by measuring the error between desired inputs and aetual outputs. This does not, in itself, generate eontrol aetion errors that may be baek-propagated to train a neural network eontroller. If, however, a neural network of the plant exists, baek-propagation through this network of the system error (r(lcT) — y(lcT)) will provide the neeessary eontrol aetion errors to train the neural network eontroller as shown in Figure 10.29. 

In a standard back-propagation scheme, updating the weights is done iteratively. The weights for each connection are initially randomized when the neural network undergoes training. Then the error between the target output and the network predicted output are back-propa-... 

Here, neural network techniques are used to model these process-model mismatches. The neural network is fed with various input data to predict the process-model mismatch (for each state variable) at the present discrete time. The general input-output map for the neural network training can be seen in Figure 12.2. The data are fed in a moving window scheme. In this scheme, all the data are moved forward at one discrete-time interval until all of them are fed into the network. The whole batch of data is fed into the network repeatedly until the required error criterion is achieved. 

The four experiments done previously with Rnp (= 0.5, 1, 3, 4) were used to train the neural network and the experiment with / exp = 2 was used to validate the system. Dynamic models of process-model mismatches for three state variables (i.e. X) of the system are considered here. They are the instant distillate composition (xD), accumulated distillate composition (xa) and the amount of distillate (Ha). The inputs and outputs of the network are as in Figure 12.2. A multilayered feed forward network, which is trained with the back propagation method using a momentum term as well as an adaptive learning rate to speed up the rate of convergence, is used in this work. The error between the actual mismatch (obtained from simulation and experiments) and that predicted by the network is used as the error signal to train the network as described earlier. 

The characters are first normalized by rotating the original scanned image to correct for scanning error and by combinations of scaling under sampling and contrast and density adjustments of the scanned characters. In operation, the normalized characters are then presented to a multilayer perceptron neural network for recognition the network was trained on exemplars of characters form numerous serif and sans serif fonts to achieve font invariance. Where the output from the neural network indicates more than one option, for example 5 and s, the correct interpretation is determined from context. 

Predictive models are built with ANN s in much the same way as they are with MLR and PLS methods descriptors and experimental data are used to fit (or train in machine-learning nomenclature) the parameters of the functions until the performance error is minimized. Neural networks differ from the previous two methods in that (1) the sigmoidal shapes of the neurons output equations better allow them to model non-linear systems and (2) they are subsymbolic , which is to say that the information in the descriptors is effectively scrambled once the internal weights and thresholds of the neurons are trained, making it difficult to examine the final equations to interpret the influences of the descriptors on the property of interest. 

The weightings w, in the neural network are determined by an optimisation algorithm using the error between the measured outputs and the outputs predicted by the neural network. The work of Rumelhart et.al. (1985) is recommended for more details about this type of neural networks and examples. 

There are two learning paradigms that determine how a network relates to its environment. In supervised learning (learning with teacher), a teacher provides output targets for each input pattern, and corrects the network s errors explicitly. The teacher has knowledge of the environment (in the form of a historical set of input-output data) so that the neural network is provided with desired response when a training vector is available. The... 

Another application of GAs was published by Aires de Sousa et al. they used genetic algorithms to select the appropriate descriptors for representing structure-chemical shift correlations in the computer [69]. Each chromosome was represented by a subset of 486 potentially useful descriptors for predicting H-NMR chemical shifts. The task of a fitness function was performed by a CPG neural network that used the subset of descriptors encoded in the chromosome for predicting chemical shifts. Each proton of a compound is presented to the neural network as a set of descriptors obtaining a chemical shift as output. The fitness function was the RMS error for the chemical shifts obtained from the neural network and was verified with a cross-validation data set. 

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