On the Complexity and Dimension of Continuous Finite-Dimensional Maps
Boris Semenovich Darkhovsky · Theory of Probability and Its Applications · 2020
We introduce the concept of $\varepsilon$-complexity of an individual continuous finite-dimensional map. This concept is in good accord with the principle of A.N. Kolmogorov's idea of measuring complexity of objects. It is shown that the $\varepsilon$-complexity of an “almost all” Hölder map can be effectively described. This description can be used as a basis for a model-free technique for segmentation and classification of data of arbitrary nature. A new definition of the dimension of the graph of a map is also proposed.