Nonlinear principal components I. Absolutely continuous random variables with positive bounded densities
非线性主成分（一）：具有正有界密度的绝对连续随机变量
Nonlinear principal components for an absolutely continuous random vector X with positive bounded density are defined as the solution of a variational problem in a suitable function space. In this way transformations depending on all the components of X are obtained. Some properties of nonlinear principal components are proved: in particular, it is shown that the set of nonlinear principal transformations of X is an orthonormal basis for the function space associated with…