Training a neural network to identify objects by parameters in non-overlapping spaces

Abstract

The present moment is characterised by the active use of digital information processing technologies in electronic communications systems. An important task in this case is to develop methods and algorithms for deciding whether a certain object O belongs to one or another m-th class: O_m, m =1, 2, ..., M, M ≥ 2 – number of classes. This task can be solved with the use of neural networks that implement the processing of k conditional estimates of physical parameters x_k1/m, x_k2/m, …, x_kn/m, …, x_kN/m objects, k =1, 2, …, K, K – is the maximum number of training steps, n is the current physical parameter that characterises the object and is an input to the neural network), N – is the number of such physical parameters, N ≥ 2. Contingent valuations x_k1/m, x_k2/m, …, x_kn/m, …, x_kN/m are random, depend on the energy characteristics of the impacts and dynamically change over time, and the decision to determine whether an object O belongs to one or another m-th class involves the use of neural networks, which have the properties of learning and self-learning. Suppose that, from the energy point of view, the input influences are powerful enough to assign the object O to one or another m-th class O_m . Thanks to the expert's ability to accurately determine the m-th class after receiving the k-th conditional vector of physical parameter estimates x_k/m, the m neural network will be trained by refining the lower and upper limits of displacements in the first layers of perceptrons for each m-th class Q_{1m min} and Q_{1m max}, after the next estimates of physical parameters are received and the expert provides the real value of the object O belonging to class m. The article solves the inverse problem of finding, Q_{m min}, Q_{m max}, which ensure the specified quality indicators in neural network training for the minimum number of steps K. The article considers the implementation of a three-layer neural network trained by an experienced expert to solve the problem of object identification by several parameters. The solution to the problem of object identification by classes is presented for known distributions of conditional estimates of physical parameters. The problem of object identification by classes at infinite signal-to-noise ratios in the process of estimating physical parameters is solved. The expressions that determine the perceptron displacement for the problem of object identification by classes when the spaces of true values of input parameters do not intersect are found.