Suppose that we have hidden a number of the branch currents, and we now wish to display one of the hidden currents. Displaying hidden branch currents is a little different than displaying hidden node voltages. Node voltages are [Pg.166]

The output of hidden nodes in the immediately preceeding layer that generated the input signals into the node. [Pg.30]

The output of these hidden nodes, o, is then forwarded to all output nodes through weighted connections. The output yj of these nodes consists of a linear combination of the kernel functions [Pg.682]

The number of middle layers (hidden nodes) in a NN must be identified either through a particular choice or through an optimization procedure with careful monitoring of the predictive behavior of the derived model (see point 2). [Pg.400]

To determine the error at the hidden nodes, we backpropagate the error from the output nodes. We can expand this error in terms of the posterior nodes [Pg.34]

The PPR model usually has fewer hidden nodes than a BPN model and is easier and faster to train (Hwang et al, 1994). The PPR basis functions [Pg.39]

Radial basis function networks with more than one input unit have more parameters for each hidden node e.g.,. if there are two input units, then the basis function for each hidden unit j needs two location parameters, pij and p2j, for the center, and, optionally, two parameters, Oij and a2j, for variability. The dimension of the centers for each of the hidden units matches the dimension of the input vector. [Pg.43]

One layer of input nodes and another of output nodes form the bookends to one or more layers of hidden nodes Signals flow from the input layer to the hidden nodes, where they are processed, and then on to the output nodes, which feed the response of the network out to the user. There are no recursive links in the network that could feed signals from a "later" node to an "earlier" one or return the output from a node to itself. Because the messages in this type of layered network move only in the forward direction when input data are processed, this is known as a feedforward network. [Pg.27]

The lack of a recipe for adjusting the weights of connections into hidden nodes brought research in neural networks to a virtual standstill until the publication by Rumelhart, Hinton, and Williams2 of a technique now known as backpropagation (BP). This offered a way out of the difficulty. [Pg.30]

Table 1 Blind test results for "Lower wing skin" using network with 2 hidden nodes and training for 2000 iterations |

Figure6.25 Schematicdrawingofan artificial neural network with a multilayer perceptron topology, showing the pathways from the input Xj to the output y , and the visible and hidden node layers. |

For the styrene-butadiene copolymer application, fit results of ANN models using one to six hidden nodes are shown in Table 12.7. Based on these results, it appears that only three, or perhaps four, hidden nodes are required in the model, and the addition of more hidden nodes does not greatly improve the fit of the [Pg.388]

Fig. 2. Structure of an artificial neural network. The network consists of three layers the input layer, the hidden layer, and the output layer. The input nodes take the values of the normalized QSAR descriptors. Each node in the hidden layer takes the weighted sum of the input nodes (represented as lines) and transforms the sum into an output value. The output node takes the weighted sum of these hidden node values and transforms the sum into an output value between 0 and 1. |

In the styrene—butadiene copolymer application, a series of quantitative ANN models for the as-butadiene content was developed. For each of these models, all of the 141 X-variables were used as inputs, and the sigmoid function (Equation 8.39) was used as the transfer function in the hidden layer. The X-data and Y-data were both mean-centered before being used to train the networks. A total of six different models were built, using one to six nodes in the hidden layer. The model fit results are shown in Table 8.7. Based on these results, it appears that only three, or perhaps four, hidden nodes are required in the model, and the addition of more hidden nodes does not greatly improve the fit of the model. Also, note that the model fit (RMSEE) is slightly less for the ANN model that uses three hidden nodes (1.13) than for the PLS model that uses four latent variables (1.25). [Pg.266]

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