Metrization of discrete topological spaces in the context of lattice theory. Part 2. Practical analysis of the consequences
of the theorem on regularity and normality
Abstract:
In the first part, a theorem has been proved that connects the concept of normality of topological spaces and regularity according to Yu. I. Zhuravlev, in the context of the problem of metrization of feature spaces. The consequences of the theorem allow one to systematize the search for the most acceptable problem-oriented metrics. Promising directions for further research have been systematized, including the transition to a lattice of feature values and promising functionals for generating synthetic features. The results of the corresponding computational experiments are presented.
Keywords:topological data analysis, algebraic approach of Yu. I. Zhuravlev and K. V. Rudakov, computational experiment, synthetic features.
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