## From a set of parts to an indivisible whole. Part I: Operations in a closed mode

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Andreev, Leonid

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This paper provides a description of a new method for information processing
based on holistic approach wherein analysis is a direct product of synthesis.
The core of the method is iterative averaging of all the elements of a system
according to all the parameters describing the elements. Contrary to common
logic, the iterative averaging of a system's elements does not result in
homogenization of the system; instead, it causes an obligatory subdivision of
the system into two alternative subgroups, leaving no outliers. Within each of
the formed subgroups, similarity coefficients between the elements reach the
value of 1, whereas similarity coefficients between the elements of different
subgroups equal a certain constant value greater than 0 but lower than 1. When
subjected to iterative averaging, any system consisting of three or more
elements of which at least two elements are not completely identical undergo
such a process of bifurcation that occurs non-linearly. Successive iterative
averaging of each of the forming subgroups eventually provides a hierarchical
system that reflects relationships between the elements of an input system
under analysis. We propose a definition of a natural hierarchy that can exist
only in conditions of closeness of a system and can be discovered upon
providing such an effect onto a system which allows its elements interact with
each other based on the principle of self-organization. Self-organization can
be achieved through an overall and total cross-averaging of a system's
elements. We demonstrate the application potentials of the proposed technology
on a number of examples, including a system of scattered points, randomized
datasets, as well as meteorological and demographical datasets.

Comment: 28 pages, 10 figures; typos in equations (4) and (5) corrected

Comment: 28 pages, 10 figures; typos in equations (4) and (5) corrected

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Computer Science - Other Computer Science