Diffusion maps for changing data
Diffusion maps for changing data
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DOI：
10.1016/j.acha.2013.03.001
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发表时间：
2014-01-01
影响因子：
2.5
通讯作者：
Hirn, Matthew J.
中科院分区：
文献类型：
--
作者：
Coifman, Ronald R.;Hirn, Matthew J.
图拉普拉斯和相关的到低维空间的非线性映射已被证明是组织高维数据的强大工具。在这里，我们考虑一个数据集X，其中与其关联的图根据某一组参数而改变。我们根据扩散距离和相应的扩散图来分析这类数据。随着数据在参数空间上的变化，低维嵌入也会发生变化。我们给出了一种在这些嵌入之间移动的方法，并且进一步将它们都映射到一个公共空间，允许人们跟踪X在其固有几何中的演变。还定义了全局扩散距离，它给出了数据在参数空间上的全局行为的度量。给出了随机抽样数据的逼近定理及其潜在的应用。(C)2013 Elsevier Inc.保留所有权利。
Graph Laplacians and related nonlinear mappings into low dimensional spaces have been shown to be powerful tools for organizing high dimensional data. Here we consider a data set X in which the graph associated with it changes depending on some set of parameters. We analyze this type of data in terms of the diffusion distance and the corresponding diffusion map. As the data changes over the parameter space, the low dimensional embedding changes as well. We give a way to go between these embeddings, and furthermore, map them all into a common space, allowing one to track the evolution of X in its intrinsic geometry. A global diffusion distance is also defined, which gives a measure of the global behavior of the data over the parameter space. Approximation theorems in terms of randomly sampled data are presented, as are potential applications. (C) 2013 Elsevier Inc. All rights reserved.