• 제목/요약/키워드: the Poincare metric

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AFFINE HOMOGENEOUS DOMAINS IN THE COMPLEX PLANE

  • Kang-Hyurk, Lee
    • Korean Journal of Mathematics
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    • 제30권4호
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    • pp.643-652
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    • 2022
  • In this paper, we will describe affine homogeneous domains in the complex plane. For this study, we deal with the Lie algebra of infinitesimal affine transformations, a structure of the hyperbolic metric involved with affine automorphisms. As a consequence, an affine homogeneous domain is affine equivalent to the complex plane, the punctured plane or the half plane.

평균회귀 심박변이도의 K-평균 군집화 학습을 통한 심실조기수축 부정맥 신호의 특성분석 (Characterization of Premature Ventricular Contraction by K-Means Clustering Learning Algorithm with Mean-Reverting Heart Rate Variability Analysis)

  • 김정환;김동준;이정환;김경섭
    • 전기학회논문지
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    • 제66권7호
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    • pp.1072-1077
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    • 2017
  • Mean-reverting analysis refers to a way of estimating the underlining tendency after new data has evoked the variation in the equilibrium state. In this paper, we propose a new method to interpret the specular portraits of Premature Ventricular Contraction(PVC) arrhythmia by applying K-means unsupervised learning algorithm on electrocardiogram(ECG) data. Aiming at this purpose, we applied a mean-reverting model to analyse Heart Rate Variability(HRV) in terms of the modified poincare plot by considering PVC rhythm as the component of disrupting the homeostasis state. Based on our experimental tests on MIT-BIH ECG database, we can find the fact that the specular patterns portraited by K-means clustering on mean-reverting HRV data can be more clearly visible and the Euclidean metric can be used to identify the discrepancy between the normal sinus rhythm and PVC beats by the relative distance among cluster-centroids.