Weight Vector Calculation

In general, weights wy, W2, wj,w can be calculated using the following equation  

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Single hierarchical sort (weight vector calculation) and inspection. 

This is done by calculating the Euclidean distance between the input data vector Xc and the weight vectors Wj of all neurons ... 

Calculate a specified similarity measure, D, between each weight vector and a randomly chosen input pattern, x. 

For the next input vector the similarity, p,, with the weight vector, W , of each active unit, k is calculated ... 

Calculate how similar the sample pattern is to the weights vector at each node in turn, by determining the Euclidean distance between the sample pattern and the weights vector. 

Each value in the chosen sample pattern is compared in turn with the corresponding weight at the first node to determine how well the pattern and weights vector match (Figure 3.9). A numerical measure of the quality of the match is essential, so the difference between the two vectors, dpq, generally defined as the squared Euclidean distance between the two, is calculated ... 

Example 6 Calculating the Distances between Sample and Weights Vector... 

The distance between the node weights and the input vector calculated in this way is also known as the node s activation level. This terminology is widespread, but counterintuitive, since a high activation level sounds desirable and might suggest a good match, while the reverse is actually the case. 

Recall equation (4.19) yCaic=Fa. To achieve minimal %2 in a linear regression calculation, all we need to do is to divide each element of y and of the column vectors f-j by its corresponding ayi to result in the weighted vectors yw and fw (... 

PLSR weight vectors. This deflation is carried out by first calculating the a-loading... 

Calculate the first principal component of ZZT and compute the normalized weight vector w from the PCA loading vector p (the first eigenvector of ZZT with eigenvalue A). 

Intermediate Least Squares regression (ILS) is an extension of the Partial Least Squares (PLS) algorithm where the optimal variable subset model is calculated as intermediate to PLS and stepwise regression, by two parameters whose values are estimated by cross-validation [Frank, 1987]. The first parameter is the number of optimal latent variables and the second is the number of elements in the weight vector w set to zero. This last parameter (ALIM) controls the number of selected variables by acting on the weight vector of each mth latent variable as the following ... 

Thus the error is calculated first in the output layer and is then passed back through the network to preceding layers for their weight vector to be adapted in order to reduce the error. A discussion of Equations (63) to (65) is provided by Beale and Jackson, and is derived by Zupan. ... 

Below a Matlab script implementing the tensor-product QMOM for a simple bivariate case described in this section is reported. The required inputs are the number of nodes for the first (Nl) and for the second (N2) internal coordinates. Since in the formulation described above the moments used for the calculation of the quadrature approximation are defined by the method itself, no exponent matrix is needed. The moments used are passed though a matrix variable m, whose elements are defined by two indices. The first one indicates the order of the moments with respect to the first internal coordinates (index 1 for moment 0, index 2 for moment order 1, etc.), whereas the second one is for the order of the moments with respect to the second internal coordinate. The final matrix is very similar to that reported in Table 3.8. The script returns the quadrature approximation in the usual form the weights are stored in the weight vector w of size N = Mi M2, whereas the nodes are stored in a matrix with two rows (corresponding to the first and second internal coordinate) and M = M1M2 columns (corresponding to the different nodes). 

Thus the error is calculated first in the output layer and is then passed back through the network to preceding layers for their weight vector to be adapted... 

Calculate a scaling factor, c, that makes the loading weight vector Wk=, ... 

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