## 6 Description of Tests and Their Procedure
### Classifying Images with RBF Networks  
In this particular section, we are investigating the effectiveness of the RBF neural network in the task of image classification. The training dataset consisted of 90 \(\times\) 240 pixel images of musical notation symbols. The values describing the pixel saturation were converted to binary data with values of \(-1\) for black and 1 for white. The set of symbol matrices was converted into vectors with a size of 1 \(\times\) 21,600 pixels for each pattern. Each symbol was represented as 36 distorted patterns. The total number of symbols was 33. As a result, a matrix with the dimensions of 1188 rows and 21,600 columns was obtained. The target standards were placed in the second matrix of the same dimensions.  
The RBF network available in the Matlab Neural Toolbox package was used as a classifier. The base radial function was the Gaussian distribution, and the network learning process was carried out using the Levenberg-Marquardt algorithm. The initial network parameters were set according to the order:  
(a) target mean square error = 0,  
(b) area of dispersion of the base function = 1,  
(c) initial number of neurons equal to 1.  
Increasing the base of the Gaussian distribution function increases the smoothing of the function.  
During the learning process, the RBF network is formed iteratively by increasing the number of neurons in the hidden layer by one neuron in every cycle. At each iteration, the input vector with the greatest reduction in network error is used to create a new neuron. More neurons are added until the mean square error value assumes the target error value or the maximum number of neurons is reached. A new network is created using the _newbr_ function. It takes the input and target vector matrices, and design parameters such as the target mean square error value and the base function scatter area. The scattering area should be large enough for the neurons to respond to overlapping areas of the input space but not large enough for all neurons to respond in the same way.  
The target mean square error was set to 0. During the learning process, the value was 0.0008196 (Figure 17). On the basis of the obtained results, one may conclude that this method of network training offers very good results but is time-consuming. The process of learning the network took 92,682 s, which is approximately 25 h and 45 min. Tests were carried out on a Dell Latitude E6530 computer with an Intel Core i7 4800 MQ 2.7 GHz CPU and 16 GB RAM memory. The network effectiveness test was carried out on the number of one thousand randomly selected symbol patterns. Details of the results achieved will be included, in detail, in Section 8.  
Figure 16: Simple regression plot. Range of four symbols, reference symbols, 40 learning epochs and 100 neurons in the hidden layer [39].  
In the next part of the research, attempts will be made to identify the form of musical notation using a classical algorithm, which is based on image segmentation as well as morphological operations, as already mentioned. On the basis of methods that do not employ an artificial neural network, a decision is made to determine the note presented in the image.