The formation of patterns is one of the main stages in logical data analysis. Fuzzy approaches to pattern generation in logical analysis of data allow the pattern to cover not only objects of the target class, but also a certain proportion of objects of the opposite class. In this case, pattern search is an optimization problem with the maximum coverage of the target class as an objective function, and some allowed coverage of the opposite class as a constraint. We propose a more flexible and symmetric optimization model which does not impose a strict restriction on the pattern coverage of the opposite class observations. Instead, our model converts such a restriction (purity restriction) into an additional criterion. Both, coverage of the target class and the opposite class are two objective functions of the optimization problem. The search for a balance of these criteria is the essence of the proposed optimization method. We propose a modified evolutionary algorithm based on the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) to solve this problem. The new algorithm uses pattern formation as an approximation of the Pareto set and considers the solution’s representation in logical analysis of data and the informativeness of patterns. We have tested our approach on two applied medical problems of classification under conditions of sample asymmetry: one class significantly dominated the other. The classification results were comparable and, in some cases, better than the results of commonly used machine learning algorithms in terms of accuracy, without losing the interpretability.
Here are the results of theoretical studies of microstrip multimode resonators with a short-circuited section of a strip conductor and ultra-wideband filter based on five-mode resonators. Electrical characteristics of microwave devices were obtained by means of numerical electrodynamic analysis of their 3D models. Substrates with dielectric constant of ε = 80 and ε = 9.8 were used in calculations. A synthesized filter with a 100% bandwidth has high frequency-selective properties and can be used in radio equipment of tropospheric and space communication with the advanced information transfer.
Microwave electromagnetic devices have been used for many applications in tropospheric communication, navigation, radar systems, and measurement. The development of the signal preprocessing units including frequency-selective devices (bandpass filters) determines the reliability and usability of such systems. In wireless sensor network nodes, filters with microstrip resonators are widely used to improve the out-of-band suppression and frequency selectivity. Filters based on multimode microstrip resonators have an order that determines their frequency-selective properties, which is a multiple of the number of resonators. That enables us to reduce the size of systems without deteriorating their selective properties. Various microstrip multimode resonator topologies can be used for both filters and microwave sensors, however, the quality criteria for them may differ. The development of every resonator topology is time consuming. We propose a technique for the automatic generation of the resonator topology with required frequency characteristics based on the use of evolutionary algorithms. The topology is encoded into a set of real valued parameters, which are varied to achieve the desired features. The differential evolution algorithm and the genetic algorithm with simulated binary crossover and polynomial mutation are applied to solve the formulated problem using the dynamic penalties method. The experimental results show that our technique enables us to find microstrip resonator topologies with desired amplitude-frequency characteristics automatically, and manufactured devices demonstrate characteristics very close to the results of the algorithm. The proposed algorithmic approach may be used for automatically exploring the new perspective topologies of resonators used in microwave filters, radar antennas or sensors, in accordance with the defined criteria and constraints.
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