Training pattern

A network that is too large may require a large number of training patterns in order to avoid memorization and training time, while one that is too small may not train to an acceptable tolerance. Cybenko [30] has shown that one hidden layer with homogenous sigmoidal output functions is sufficient to form an arbitrary close approximation to any decisions boundaries for the outputs. They are also shown to be sufficient for any continuous nonlinear mappings. In practice, one hidden layer was found to be sufficient to solve most problems for the cases considered in this chapter. If discontinuities in the approximated functions are encountered, then more than one hidden layer is necessary. 

ART2 forms clusters from training patterns by first computing a measure of similarity (directional rather than distance) of each pattern vector to a cluster prototype vector, and then comparing this measure to an arbitrarily specified proximity criterion called the vigilance. If the pattern s similarity measure exceeds the vigilance, the cluster prototype or center is updated to incorporate the effect of the pattern, as shown in Fig. 25 for pattern 3. If the pattern fails the similarity test, competition resumes without the node... 

The previously scaled atomic spectrum of a standard (technically, it is called a training pattern) enters the net throughout the input layer (a variable per node). Thus, an input neuron receives, simply, the information corresponding to a predictor variable and transmits it to each neuron of the hidden layer (see Figures 5.1, 5.3 and 5.4). The overall net input at neuron7 of the hidden layer is given by eqn (5.3), which corresponds to eqn (5.1) above ... 

Figure 13.10 SVM training results in the optimal hyperplane separating classes of data. The optimal hyperplane is the one with the maximum distance from the nearest training patterns (support vectors). The three support vectors defining the hyperplane are shown as solid symbols. D(x) is the SVM decision function (classifier function).

The steady-state response of each sensor ( 5 min) was recorded for each substance. A training pattern was formed by converting each set of steady-state sensor responses to a bit pattern. Bit patterns generally consisted of no more than 200 bits. The low resolution of the training pattern maximized process speed for the test in an actual instrument, a small pattern size would also help to... 

Second, neural networks that may store knowledge implicitly and find appropriate answers after presentation of training patterns or structures (cf Section 8.2) are exploited. Neural networks are built at present by using conventional programming languages. In the future, however, parallel operating computers or transputers will be applied. 

The BPNN is based on the use of sample patterns to estimate statistical parameters of each pattern class. The patterns (of known class membership) used to estimate these parameters usually are called training patterns, and a set of such patterns from each class is called a training set. The process by which a training set is used to obtain decision functions is called learning or training. 

The training patterns of each class are used to compute the parameters of the decision function of BPNN corresponding to that class. After the parameters in question have been estimated, the structure of the BPNN is fixed, and its eventual performance will depend on how well the actual pattern populations satisfy the underlying statistical assumptions made in the derivation of the classification method being used. 

For training and validation of the ANN, 29 theoretical and 59 measured input patterns of imperfection with corresponding target outputs - the FEM calculated strength values are available (Sadovsky etal. 2007). AU theoretical and five measured patterns are used for the training set, i.e. number of training patterns np = 34. Amendment by few measured patterns derives from... 

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