By M.M. Poulton
This booklet was once essentially written for an viewers that has heard approximately neural networks or has had a few event with the algorithms, yet want to achieve a deeper realizing of the elemental fabric. for those who have already got a great grab of the way to create a neural community program, this paintings promises quite a lot of examples of nuances in community layout, info set layout, trying out approach, and mistake analysis.Computational, instead of synthetic, modifiers are used for neural networks during this ebook to make a contrast among networks which are carried out in and people who are applied in software program. The time period man made neural community covers any implementation that's inorganic and is the main common time period. Computational neural networks are just carried out in software program yet characterize nearly all of applications.While this publication can't supply a blue print for each feasible geophysics program, it does define a simple strategy that has been used effectively.
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Extra info for Computational Neural Networks for Geophysical Data Processing (Handbook of Geophysical Exploration: Seismic Exploration)
Both the hidden and output layers estimate nearly constant values for the training set before any weight adjustments are made. 8. 5 o. O o" Hidden Layer ..... - , . 5 o c _All__ U.. 5 Desired Angle (Degrees) have duplicated the approximate shape of the sine function while the weights between the hidden and output layer perform a scaling to the desired magnitude. The altemative approach to building the hidden layer from an initial state with no hidden PEs is to start with a large number of hidden PEs and reduce, or prune, the number of nodes or weights over time.
If the error surface we are traversing is highly convoluted, then the weight changes 46 CHAPTER 3. 12). In this case, the addition of a momentum term will tend to dampen the oscillations and again the network can converge faster. The values for the learning rate and momentum terms are often picked by trial and error. The same values are used for all PEs in a particular layer and the values can change with time according to a user-specified schedule. Jacobs (1988) developed an algorithm called the "Delta Bar Delta" or DBD that allows a learning rate to be assigned to each connection weight and updated throughout the training process.
5. RMS test error for the sine function estimation as a function of number of hidden PEs in the first and second hidden layers. 2. 2 - co 0 . 6. The relationship between RMS error on training data as a function of the number of hidden PEs in a single hidden layer for the noisy sine function data set. 38) t where | is the bias connected to each hidden and output PE. 38) can easily be expanded to accommodate it. The value of writing the network output in this form is that once training is complete and the values for the connections weights are set, we can have the output as a function of the input values.