论文标题
通过公制测量laplacians对随机对象的统计分析
Statistical analysis of random objects via metric measure Laplacians
论文作者
论文摘要
在本文中，我们考虑了一定的卷积拉普拉斯，用于度量度量空间，并研究其对复杂物体的统计分析的潜力。该拉普拉斯人的频谱是所考虑的空间的签名，特征向量提供了形状的主要方向，即谐波。这些概念用于评估对象的相似性或以原则性的方式理解其最重要的特征，并在各种示例中进行了说明。采用统计观点，我们定义了平均光谱量度及其经验措施。引入了相应的限制过程，并讨论了统计应用程序。
In this paper, we consider a certain convolutional Laplacian for metric measure spaces and investigate its potential for the statistical analysis of complex objects. The spectrum of that Laplacian serves as a signature of the space under consideration and the eigenvectors provide the principal directions of the shape, its harmonics. These concepts are used to assess the similarity of objects or understand their most important features in a principled way which is illustrated in various examples. Adopting a statistical point of view, we define a mean spectral measure and its empirical counterpart. The corresponding limiting process of interest is derived and statistical applications are discussed.
