Measuring Order Parameters Based on Neural Network Technologies

Abstract

We show convergence of a procedure for multiple training of a neural network, when during multiple repetitions of the solution of a binary classifi cation task based on unchanged packets of training samples the neural emulator can initially demonstrate a chaotic set of values for the feature weights, which as the number of iterations increases is reduced to a certain ranked series. Keywords: biosystem, order parameters, neural network, theory of chaos and self-organization.Development of synergetics has been associated with the possibility and need for solving problems involving identifi cation of order parameters and constructing a theory of systems synthesis as a whole. Despite tremendous efforts by scientists over the past 40 years, there have been no substantial achievements in the area of formalization of the procedure for identifi cation of order parameters and total systems synthesis. Identifi cation of order parameters remains a unique procedure for individual selected tasks. Universal formalization of systems synthesis is lacking at the moment for complex systems, which especially include biosystems [1,2].At the same time, there is a certain class of tasks and systems where such formalization is possible by application of neural network technologies. In recent years, neural emulators have been widely used for identifi cation of the most important diagnostic signs (features) in medicine and biology, but the result obtained with their application is not always unambiguous, and so it has not been worthwhile to use neural emulators for practical purposes. Is there a way out of this situation? An answer is presented in this paper, using binary classifi cation as an example, i.e., for attempts to identify order parameters and to rank the weights of diagnostic features: the components x i of the system state vector x = x(t).Nonparametric Distribution of Weighted Features in a Neural Emulator. The binary classifi cation task utilizing a neural computer is very widely used in medicine, since it lets us, without separate analysis of the dynamics of variation in each component x i of the state vector for the human body (the human state vector) x = x(t) = (x 1 , x 2 , ..., x m ) T , to establish in general how one group of patients (for example, an untreated group) differs from another group (with a specifi c type of treatment). Based on binary classifi cation, we can compare groups of patients receiving different types of care (drugs, physical therapy, etc.) [2, 3] and can establish the effi cacy of health-related measures and the effect of environmental factors, and to evaluate coaching in sports.After identifi cation of the differences by the neural emulator, we need to estimate the signifi cance (weight) of a specifi c ith diagnostic feature (i = 1, 2, ..., m, where m is the dimensionality of the phase space), i.e., the components x i of the human state vector, which is especially important when these features characterize the state of different functional systems in the human body. Guidelines for the doctor (wh...

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