Cluster analysis of cardiac data - E. Y. Zimina (Статистика и экономика, 2018)
The article includes the observation of the cluster analysis of medicaldata 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.