Abstract: We extend the principal component analysis (PCA) to the investigation of nonlinear dependence among variables, called most informative component analysis (MICA). The most informative components are linear combinations of the variables that capture both linear and nonlinear dependence among the variables. Compared with the existing extensions such as the principal curve and the kernel PCA, MICA is more interpretable and thus more meaningful in statistical analysis. Properties of MICA are investigated, the estimation method is developed, and asymptotics of the estimators are obtained. Data sets are analyzed to illustrate the usefulness of MICA.

Key words and phrases: Dimension reduction, most predictable component, principal component analysis, projection pursuit, unsupervised learning.