Кластерный анализ кардиологических данных

Статистика и Экономика. 2018. Т. 15. № 2. С. 30–37.

Зимина Е. Ю.

The article includes the observation of the cluster analysis of medical
data on the example of the cardiac data. One of the main effective
and commonly used Data Mining methods that applied to the large
amounts of information (for example, mathematical economics) are
clustering methods: the search for signs of similarity between objects
in the study of the subject area and the subsequent merger of objects
into subsets (clusters) according to the established affinity.
The main purpose of the investigation is to examine the hypothesis
of the possibility of diagnosing the patient health status, as well as
identifying his pathologies, using the analysis of electrocardiogram
(ECG) series and the allocation of similar clusters based on the
results of this analysis.
However, the subject of clustering techniques implementation to the
ECG on the grounds of similarity of forms have not previously been
extensively investigated.
In the model of the heart, which is used in this study, the state of
the heart is taken as a fixed oscillatory process of the phenomenon
of the FPU auto-return. But, on the other hand, since the heart is
an self-oscillating system and it has no need to start the oscillations
by obtaining the energy of “perturbation”, the concept of FPU autoreturn
is introduced in the study of the heart.
The mathematical modeling of the heart work by using a decomposition
of the Fermi-Pasta-Ulam (FPU) was investigated. The
formal description of the mathematical model of the heart as a
system of connected cells myocytes is presented. This represents
a single oscillatory degree of freedom described by a system of
coupled nonlinear differential equations of the second order equation
of Van der Pol.
Cluster analysis bases on the search of similar clusters of Fourier
spectrum which are received by FPU recurrence.
The current results that are obtained show that the hypothesis is
confirmed. In mathematical modeling of the FPU heart modeling,
which is based on the forms of Fourier spectra, were identified.
Subsets were identified, among which various subsets of both
forms of Fourier spectra with pathologies and forms of the Fourier
spectrum of healthy people were formed. From this study it follows
that the cluster analysis of the electrocardiogram may refer
this ECG to any cluster and thereby diagnose the state of cardiac
health of the patient.

Keywords: математическое моделирование, кластеризация, mathematical modeling, clustering, большие данные, цифровая экономика, big data, cardiology, кардиология, digital economy