)
=
=𝑎𝑟𝑔min
𝐷
𝑤
∗
,𝑤
+
1
2
𝐷
𝜂⃗
(∗)
,𝜂⃗
(35)
which in the above entry is literally the criterion of
minimum difference.
4 CONCLUSIONS
The considered case of approximating the shape of
the intensity of objects by mixtures of Gaussian
components and the results of the corresponding
numerical simulation showed the adequacy of the
method of maximum similarity to the problems of
analyzing PCD images. Even in low-quality images
(~ 1000 samples), the algorithm corresponding to the
proposed method gives the correct identification of
objects. Note that the implementation of the
algorithm, like the method of 𝐾‒means segmentation,
is very efficient computationally ‒ for mixtures with
~ 1000 components in the common computation
environment, processing of images with a size of
500×500 pixels by PM algorithm (28) ‒ (29) takes ~
1 sec on a standard PC and it is already clear that these
characteristics can be improved if desired.
As for the maximum similarity method itself, the
simplicity of its interpretation, to which the section 2
is devoted, and the straightforwardness of its
algorithmic implementation, what is the main content
of the section 3, makes it attractive both in theoretical
and practical terms, especially in the context of
modern, oriented to machine learning approaches. In
a sense, for machine learning problems, the proposed
method is an adaptation of the R. Fisher's maximum
likelihood method widely used in traditional statistics
(Efron, 1982). The fruitful use of the latter, as is
known, has led to a huge number of important
statistical results. In this regard, it is hoped that the
proposed maximum similarity method will also be
useful in solving a wide range of modern problems of
statistical (machine) learning.
ACKNOWLEDGEMENTS
The author is grateful to the Russian Foundation for
Basic Research (RFBR), grant N 18-07-01295 А for
the financial support of the work.
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