Winning neuron

The neuron for which this distance gives the minimum is called the winning neuron or central neuron c (see Eq. (5)). 

The weights of the winning neuron are funher adapted to the input data. The neurons within a certain distance surrounding the winning neuron are also adapted Their weight adaptation is performed such that the closer a neuron is to the winning neuron the more its weights will be adapted. 

During training the input layer is adapted as in a regular Kohonen network, i.c., the winning neuron is determined only on the basis of the input values. But in contra.st to the training of a Kohonen network, the output layer is also adapted, which gives an opportunity to use the network for prediction. 

Figure 10.2-9. Application of a counterpropagation neural network as a look-up table for IR spectra sinnulation, The winning neuron which contains the RDF code in the upper layer of the network points to the simulated IR spectrum in the lower layer.

The trained counterpvopagation network is then able to predict the spectrum for a new structure when operating as a look-up table (see Figure 10.2-9) the encoded query or th.c input structure is input into the trained network and the winning neuron is determined by considering just the upper part of the network. The neuron points to the corresponding neuron in the lower part of the network, which then provides the simulated IR spectrum. 

The right-hand side of the form gives the network map in the upper part and to its right the simulated IR spectrum is plotted, which can be downloaded as a JCAMP File (cf. Section 2,4.5, Section 4,2,4.2). By clicking on tbe neurons in the map one obtains the RDF code and the spectrum of the corresponding structure in the lower part of the form and compared with those of the winning neuron,... 

Find the winning neuron / It is that neuron that possesses the smallest distance to the input vector among all neurons i = 1, ... 

The preservation of topology results from the introduction of neighborhood relationships of neurons in the learning algorithm. These relationships are described by a neighborhood function with the distance measure d as the independent variable. This function characterizes the distance to the winning neuron ... 

Calculation of the distance between the input vector and each output unit i to evaluate the winning neuron j ... 

Competition in which a competition between all the I neurons for each input vector x is done, with the winning neuron being called the Best Matching Unit (BMU) for which the Euclidean distance x - Wy is minimized. The BMU index for the corresponding input vector X is denoted by i(x). 

Finding the focus. The network is scanned to find the neuron that holds a reference vector closest to that of the T. rex. This winning neuron is called the focus. Figure 4.11 shows the focus for the first presentation of a 71 rex input pattern. In this example, a quick inspection of the nine nodes can provide the reader with the focus. For more complex examples, the focus is found by calculating the Euclidean distance between the input vector, u, and each neuron, z. The neuron with the smallest Euclidean distance is the focus. 

The winning neuron Ws and the neighboring vectors are then modified according to the following formula (Kohonen rule) ... 

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