2020/01/14 by Andrew Polar, Michael Poluektov, Polar, Andrew +1
Computer Science · Engineering · #Advanced Computational Techniques in Science and Engineering #Advanced Research in Systems and Signal Processing #FOS: Electrical engineering #FOS: Mathematics #Mathematical Control Systems and Analysis #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2001.04652
openalex publication_date 2020/01/14 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
The Kolmogorov-Arnold representation is a proven adequate replacement of a\ncontinuous multivariate function by an hierarchical structure of multiple\nfunctions of one variable. The proven existence of such representation inspired\nmany researchers to search for a practical way of its construction, since such\nmodel answers the needs of machine learning. This article shows that the\nKolmogorov-Arnold representation is not only a composition of functions but\nalso a particular case of a tree of the discrete Urysohn operators. The article\nintroduces new, quick and computationally stable algorithm for constructing of\nsuch Urysohn trees. Besides continuous multivariate functions, the suggested\nalgorithm covers the cases with quantised inputs and combination of quantised\nand continuous inputs. The article also contains multiple results of testing of\nthe suggested algorithm on publicly available datasets, used also by other\nresearchers for benchmarking.\n