Manifold learning (ML), also known as nonlinear dimension reduction, is a set of methods to find the low-dimensional structure of data. Dimension reduction for large, high-dimensional data is not merely a way to reduce the data; the new representations and descriptors obtained by ML reveal the geometric shape of high-dimensional point clouds and allow one to visualize, denoise, and interpret them. This review presents the underlying principles of ML, its representative methods, and their statistical foundations, all from a practicing statistician's perspective. It describes the trade-offs and what theory tells us about the parameter and algorithmic choices we make in order to obtain reliable conclusions.

中文翻译：

---

多种学习：内容、方式和原因


流形学习 （ML），也称为非线性降维，是一组查找数据低维结构的方法。大型高维数据的降维不仅仅是一种减少数据的方法;ML 获得的新表示和描述符揭示了高维点云的几何形状，并允许人们可视化、降噪和解释它们。这篇综述从实践统计学家的角度介绍了 ML 的基本原理、其代表性方法及其统计基础。它描述了权衡以及理论告诉我们为获得可靠结论而做出的参数和算法选择。