Frechet Means for Distributions of Persistence Diagrams
Frechet Means for Distributions of Persistence Diagrams
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DOI：
10.1007/s00454-014-9604-7
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发表时间：
2014-07-01
影响因子：
0.8
通讯作者：
Harer, John
中科院分区：
文献类型：
--
作者：
Turner, Katharine;Mileyko, Yuriy;Harer, John
给定一个分布。关于持续图和观测值x-1，...，x-N类似于（IID）Rho，我们在本文中引入了一种算法，该算法从图表x-1，...，x-n的集合中估算出frechet均值。如果基本措施RHO是Dirac Masses rho = 1/m Sigma（m）（i = 1）delta（Zi）的组合由从Rho绘制的观察结果计算得出的算法。我们说明了算法通过高斯随机场的模拟计算出的经验平均值与人群平均值的收敛性。
Given a distribution. on persistence diagrams and observations X-1, ... , X-n similar to(iid) rho we introduce an algorithm in this paper that estimates a Frechet mean from the set of diagrams X-1, ... , X-n. If the underlying measure rho is a combination of Dirac masses rho = 1/m Sigma(m)(i=1) delta(Zi) then we prove the algorithm converges to a local minimum and a law of large numbers result for a Frechet mean computed by the algorithm given observations drawn iid from rho. We illustrate the convergence of an empirical mean computed by the algorithm to a population mean by simulations from Gaussian random fields.