相关论文: Fr\'echet means of curves for signal averaging and…

To characterize the location (mean, median) of a set of graphs, one needs a notion of centrality that is adapted to metric spaces, since graph sets are not Euclidean spaces. A standard approach is to consider the Fr\'echet mean. In this…

We study the problem of estimating a mean pattern from a set of similar curves in the setting where the variability in the data is due to random geometric deformations and additive noise. We propose an estimator based on the notion of…

Fr\'echet regression extends classical regression methods to non-Euclidean metric spaces, enabling the analysis of data relationships on complex structures such as manifolds and graphs. This work establishes a rigorous theoretical analysis…

To characterize the location (mean, median) of a set of graphs, one needs a notion of centrality that is adapted to metric spaces, since graph sets are not Euclidean spaces. A standard approach is to consider the Frechet mean. In this work,…

Fr\'echet means are a popular type of average for non-Euclidean datasets, defined as those points which minimise the average squared distance to a set of data points. We consider the behaviour of sample Fr\'echet means on normed spaces…

A new class of statistical deformable models is introduced to study high-dimensional curves or images. In addition to the standard measurement error term, these deformable models include an extra error term modeling the individual…

Increasingly, statisticians are faced with the task of analyzing complex data that are non-Euclidean and specifically do not lie in a vector space. To address the need for statistical methods for such data, we introduce the concept of…

Estimating the mean of a random vector from i.i.d. data has received considerable attention, and the optimal accuracy one may achieve with a given confidence is fairly well understood by now. When the data take values in more general metric…

The traditional method of diagnosing heart disease on ECG signal is artificial observation. Some have tried to combine expertise and signal processing to classify ECG signal by heart disease type. However, the currency is not so sufficient…

The human heart is a complex system exhibiting stochastic nature, as reflected in electrocardiogram (ECG) signals. ECG signal is a weak, non-stationary, and nonlinear signal, which indicates the health of a heart in terms of temporal…

The analysis of curves has been routinely dealt with using tools from functional data analysis. However its extension to multi-dimensional curves poses a new challenge due to its inherent geometric features that are difficult to capture…

Fr\'echet mean and variance provide a way of obtaining mean and variance for general metric space valued random variables and can be used for statistical analysis of data objects that lie in abstract spaces devoid of algebraic structure and…

A new algorithm has been developed for delineation of significant points of various electrocardiographic signal (ECG) waves, taking into account information from all available leads and providing similar or higher accuracy in comparison…

Monitoring the electrical pulse of fetal heart through a non-invasive fetal electrocardiogram (fECG) can easily detect abnormalities in the developing heart to significantly reduce the infant mortality rate and post-natal complications. Due…

Fr\'echet means, conceptually appealing, generalize the Euclidean expectation to general metric spaces. We explore how well Fr\'echet means can be estimated from independent and identically distributed samples and uncover a fundamental…

ECG signals appear to be quite complex. In this paper, we present results, which show that a normal ECG signal, which is a function of time can be transformed into a relatively simpler signal by stretching the time in a predetermined way.…

Electrocardiogram (ECG) is one of the non-invasive and low-risk methods to monitor the condition of the human heart. Any abnormal pattern(s) in the ECG signal is an indicative measure of malfunctioning of the heart, termed as arrhythmia.…

Fr\'echet regression extends the principles of linear regression to accommodate responses valued in generic metric spaces. While this approach has primarily focused on exploring relationships between Euclidean predictors and non-Euclidean…

In the present paper we have reported a wavelet based time-frequency multiresolution analysis of an ECG signal. The ECG (electrocardiogram), which records hearts electrical activity, is able to provide with useful information about the type…

It is well known, that Fr\'echet means on non-Euclidean spaces may exhibit nonstandard asymptotic rates depending on curvature. Even for distributions featuring standard asymptotic rates, there are non-Euclidean effects, altering finite…