Most informative component analysis
Yaping Jing, Yingcun Xia · Statistica Sinica · 2013
In this paper, we extend the popular principal component analysis (PCA) to the investigation of nonlinear dependence among variables, called most informative component analysis (MICA). The most informative components are a few 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; estimation method is developed; and asymptotics of the estimators are obtained. Real data sets are analyzed to illustrate the usefulness of MICA.