Abstract:
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.
Keywords:$\varepsilon$-complexity, continuous maps, model-free classification and segmentation of data.
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