基于流形嵌入的模板曲线估计鲁棒算法
A robust algorithm for template curve estimation based on manifold embedding
摘要：
本文考虑的问题，找到一个有意义的模板函数，代表一个样本的曲线的共同模式。为了解决这个问题，一种新的算法的基础上的等距特征映射（Isomap）算法的鲁棒版本的开发。假设函数数据位于一个具有未知底层结构的内在低维光滑流形上，我们提出了一个测地线距离的近似。这种近似用于计算相应的经验Fréchet中值函数，它提供了模板函数的内在估计。与Isomap方法不同，该算法具有无参数和易于使用的优点。与其他方法的比较，模拟和真实数据集，表明该算法工作良好，优于这些方法。
英文摘要：
This paper considers the problem of finding a meaningful template function that represents the common pattern of a sample of curves. To address this issue, a novel algorithm based on a robust version of the isometric featuring mapping (Isomap) algorithm is developed. Assuming that the functional data lie on an intrinsically low-dimensional smooth manifold with unknown underlying structure, we propose an approximation of the geodesic distance. This approximation is used to compute the corresponding empirical Fréchet median function, which provides an intrinsic estimator of the template function. Unlike the Isomap method, the algorithm has the advantage of being parameter free and easier to use. Comparisons with other methods, with both simulated and real datasets, show that the algorithm works well and outperforms these methods.
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