2.2. Methods

Individual classes of compost maturation were identified with the SOFM neural classifier, which was generated by means of a specialized Artificial Neural Networks module, implemented in commercial software Statistica ver. 8.1. An SOFM neural network typically consists of an input layer and a square output layer, in which processed data (on input) are presented [15,16].

SOFM neural models are based on topological properties of the cerebral cortex. The postprocessing transformation of the output values resulted in the output variable, which had nominal nature [17]. The SOFM network has the form of a two-dimensional grid, with radial neurons at nodes. Each of the values represents a single class with corresponding neurons located in the output layer of the network. These neurons are characterised by the highest level of activation, which demonstrates the maximum conformity of the weight vector and the vector presented in the input pattern network. This structure showed the input layer of the SOFM network in a two-dimensional topological map, modelling multidimensional collection of input data.

Due to the specific nature of SOFM neural networks, the training process is different than in the classic optimization of pattern balance of neural networks. The iterated training algorithm, known as the Kohonen algorithm [6], is in fact an adapted and modified version (for the needs of SOFM modelling networks) of the well-known k-means method. This parametric algorithm consists of 2 stages: first the centre of concentration is determined, and then the ray of proximity of specific classes is corrected (minimized) in an iterative way. This means, that the optimizing procedure of the SOFM network consists of the two distinctly separated phases. The first depends on proper organisation of neurons, while the other is used to precisely determine the values of balances.

Learned Vector Quantization (LVQ) is a controlled version of the Kohonen algorithm [7]. The standardized Kohonen algorithm iteratively matches the locations of pattern vectors, which are stored in the radial layer of the SOFM network. It examines both the positions of existing vectors and training data. In fact, it is this algorithm that tries to transfer pattern vectors to the positions, which correspond to the centres of concentration occurring in data. In order to achieve the quality of classification, it was desirable for pattern vectors to be arranged within the range of classes so that they could represent natural concentrations inside each of the classes [17,18].

The generated training file, including the chosen representative features in its structure, was then used to create an SOFM neural classifier. The structure of the training file consisted of 30 input variables describing the colour of compost. The traits which were selected to characterise the colour of compost indicated random changes occurring in the composted organic matter. These values were obtained by means of the PIAO ver. 3 beta system. The selected image parameters represented saturation, luminance, red, blue, and green data. The created PIAO ver 3. beta system also enabled the acquisition of information on the average value, median and standard deviation of these parameters. Therefore, they were representative independent variables. The column including the numbers of compost maturation classes did not participate in the balance optimisation process (learning without supervision) and was only used to label 5 quality classes of compost of the generated topological map. The following 5 quality conditions of compost were identified (see Figure 3).

Quality conditions of the compost.

The created file included 3048 cases, which were conventionally divided into a training subset, a validating one and a testing one at a ratio of 2:1:1, respectively [19,20]. Figure 4 shows the structure of the training file.

A fragment of the training file.

Figure 5 shows the procedure applied to identify neurons of compost quality classes.

The pattern of creation of a Self-Organising Feature Map (SOFM) neural classifier.

In order to generate an SOFM neural classifier with the LVQ algorithm, the Statistica Neural Networks was applied. It is an efficient simulating device generating optimal ANN topology based on existing empirical data. The resulting set of networks was verified qualitatively and then the model with the classifying capability was selected.

Root Mean Square Error (RMSE) is the most commonly used measure of neural network performance [21]. It is a total error made by the ANN on a certain set of data, determined by summing the squares of individual errors, dividing the obtained sum by the number of included values and determining the square root of the obtained quotient. The RMSE is usually the most convenient single interpretation value to describe the network error. The determination algorithm of the RMSE was implemented in in commercial software Statistica ver. 8.1 (TIBCO Software Inc., Palo Alto, CA, USA).