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Information × Registration Number 0223U004380, 0121U110611 , R & D reports Title Development of effective mathematical methods and algorithms of machine learning as well as related software tools with applications to cloud-based data analysis popup.stage_title Head Vasylyk Vitalii В., Кандидат фізико-математичних наук Registration Date 24-10-2023 Organization Institute of Mathematics of the National Academy of Sciences of Ukraine popup.description2 MATHEMATICAL MODEL, EXPONENTIALLY CONVERGENT METHOD, METHOD WITHOUT SATURATION OF ACCURACY, PARALLEL COMPUTATIONS, RANKING PROBLEM, NYSTRÖM METHOD, MACHINE LEARNING, PROBLEMS WITH FREE BOUNDARY, FLUID OSCILLATION IN TANKS, DIFFUSION MAPS The object of research is machine learning problems, problems of liquid oscillations in tanks with a free surface, diffusion mapping, parallel calculation methods. The purpose of the second stage of the project is to develop modified methods of diffusion mapping and corresponding algorithms, which are fundamentally more efficient from a computational point of view and, as a result, can be applied to solving machine learning problems with large and extra-large input datasets; development and justification of effective algorithms for ranking problems based on the Nyström method and the regularizers of high quality; establishing the optimal approximation accuracy for the developed algorithms in the case of smooth solutions; minimization of the input data size without the loss of approximation accuracy; Within the framework of the second stage of research work, a wide range of problems arising in the theory of machine learning methods have been solved. In particular, a strategy for solving machine learning problems using the Hilbert space of the reproducible kernel was developed, and machine learning methods for solving domain adaptation problems have been constructed. Diffusion geometry based machine learning methods based for solving handwritten text processing problems were proposed. Participants of the project depeloped a machine learning technique to obtain damping rate functions in the so-called single dominant modal system describing a resonant liquid splashing in a rectangular tank. An exponentially convergent method for solving the problem with a fractional derivative and an unbounded operator coefficient in the Banach space has been also proposed and justified. Product Description popup.authors Vasylyk Vitalii Bogdanovych Semenova Yevgeniya V. Sytnyk Dmytro Oleksiyovych Solodky Sergiy Grygorovych Tymokha Oleksandr Mykolayovych popup.nrat_date 2023-10-24 Close