![](bg5.png)
X = {x
i
} is a mixture of the form
P
λ
k
g
k
(x). Then formulas of type (2) or (3)
containing estimates of parameters x
k
, c
k
, B
k
, µ
k
obtained on the basis of searching all
the set of initial data, will be more exact, than nonparametric density estimates provided
by restricted fragments situated in layers of scaling A(x) = a, in particular,more exact,
than similar evaluations produced from standard aggregates or other partial histograms.
The framework could be useful in applied tasks concerning to mining and analytical
processing images and other big data sets represented by clusters with described above
features of symmetry.
Acknowledgements
This work was supported by the Russian Foundation for Basic Research (05-01-00332,
05-07-90333,06-01-00492, 06-01-08045, 07-01-12020), and the Grant of Presidium of
RAS ”Scientific Schools” No 5833.2006.1.
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