Multiscale geometric feature extraction for high-dimensional and non-Euclidean data with applications
提出一种从数据云中提取多尺度几何特征的方法，通过将每对数据点映射为实值特征函数，用于分类和异常检测，并探讨与随机集理论、局部深度度量和非线性降维的联系。
A method for extracting multiscale geometric features from a data cloud is proposed and analyzed. Based on geometric considerations, we map each pair of data points into a real-valued feature function defined on the unit interval. Further statistical analysis is then based on the collection of feature functions. The potential of the method is illustrated by different applications, including classification and anomaly detection. Connections to other concepts, such as random set theory, localized depth measures and nonlinear dimension reduction, are also explored.