V.A. Belobrodsky Post-graduate Student, Medical Cybernetics Lab, Faculty of Computer Science, Voronezh State University S.D. Kurgalin Dr.Sc.(Phys.-Math.), Head of the Department of Digital Technologies, Faculty of Computer Science, Voronezh State University Ya.A. Turovsky Ph.D.(Med.), Associate Professor, Head of the Medical Cybernetics Lab, Faculty of Computer Science, Voronezh State University A.A. Vahtin Ph.D.( Phys.-Math.), Associate Professor, Programming and Information Technology Department, Faculty of Computer Science, Voronezh State University

Biomedical signals reflecting the activity of human organs or systems carry information about the state of the in-vestigated morphological and functional structures, important both for basic research and for medical practice. The creation of new and modification of existing methods for comprehensive studies of human organs and systems for recognition, differentiation and analysis of their various states is relevant. One of them is the method based on the use of genetic algorithms conception to create and select digital filters. The digital filters are created by random selection, combination and variation of their values using mechanisms similar to natural selection, such as inheritance, mutation, selection and crossing-over. It is obvious that the proposed method should be tested by using test signals with known parameters, such as, for example, harmonic signals of different frequencies, or an electrocardiogram (ECG), in view of their relatively simple structure. The verification of the named method is performed and presented in this paper. Suppose we have a generation of filter functions Qnm(t), where the superscript n denotes the generation number, subscript m - the index of the filter in the generation, t - discrete time. The filter Qnm(t) has zero mean and unit norm. Each filter of the current generation Qnm has a certain value of Фnm, which we call the \"efficiency\" or \"adap-tation parameter\" (also called \"fitness\"- the term sometimes found in the literature). Obviously the filters that reveal the greatest differences between the studied signals are those that have max-imum values Фnm. They are the ones that should be allowed to \"crossing\". A part of next generation Qn+1 filters is created by «crossing» the previous generation filters. In our experiments it is 50% of the total \"population\" of filters, and the remaining 50% of the \"population\" comprise the best filters from the previous generation without any changes made to them. Thus, the \"good\" filters will be maintained throughout the series of \"population\", thereby avoiding a situation where the filters, giving high values of Фnm in the process of \"crossing\" lose their properties. After forming a new generation in the abovementioned manner the procedure that determines the need for mutations is started by using a special logic function. If the logic function indicates the need for a \"muta-tion\" (returns the value \"true\"), then each filter created in the current generation, and not taken from the previous one, has a certain probability to undergo one of the following \"mutations\": «crossing-over»; «crossing-over» and a random phase shift; flicker noise addition; flicker noise and random phase shift addition; blue-green noise addition; blue-green noise and random phase shift addition; random phase shift. The following work of the genetic algorithm is an iterative process that continues until the given number of generations is achieved or the stopping criterion is met. The above genetic algorithm is implemented in the programming language C # in Visual Studio 2013.The input data for the program are the following: zero \"population\" filters, the signals which represent the state k1, and the signals which represent the state k2. Both states can contain from 1 to 2000 signals, and the minimum amount of the starting population of filters is limited to half of the user-specified amount of filters in each generation. This algorithm requires many resources, but the CUDA technology can increase its productivity. However, this technology is only possible to be applied on computers fitted out with a compatible video card. The software de-veloped on the basis of this algorithm allows making calculations on non-parallel computers, but with a video card compatible with CUDA technology; its operation speed can be increased significantly, for example, by carrying out parallel GPU-computing of mathematical convolution procedure. The results of computational experiments with signals whose properties are known have demonstrated that the use of genetic algorithm to find the ultimate \"population\" of filters allowed to increase the fitness function value up to 2.5-3 times, which indicates that the filters have acquired the positive properties for solving the problem of classification. The distribution of maximum values of convolutions obtained with final generation filters (in this work the final generation is when n = 99 in the first example, and n = 20 in the second example of computational experiments) contrasted to the initial generation filters reveals that the coefficients of the convolutions of the two states are less likely to overlap. Therefore, in the long view the filters obtained in the \"evolution\" allow to perform the task of classifying unknown signals by specific states (which were used in the learning procedure (\"evolution\")). To perform the quality analysis of such binary classification and compare this method with others ROC analysis may be used as well. The results of testing the algorithm on signals generated with known parameters confirm that the use of genetic algorithms is a promising tool for finding digital filters that ensure the certain quality of the binary classification of biomedical signals.

 

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