Empirical mode decomposition with missing values.

This paper considers an improvement of empirical mode decomposition (EMD) in the presence of missing data. EMD has been widely used to decompose nonlinear and nonstationary signals into some components according to intrinsic frequency called intrinsic mode functions. However, the conventional EMD may not be efficient when missing values are present. This paper proposes a modified EMD procedure based on a novel combination of empirical mode decomposition and self-consistency concept. The self-consistency provides an effective imputation method of missing data, and hence, the proposed EMD procedure produces stable decomposition results. Simulation studies and the image analysis demonstrate that the proposed method produces substantially effective results.

Comparing patterns of component loadings: principal component analysis (PCA) versus independent component analysis (ICA) in analyzing multivariate non-normal data.

Principal component analysis identifies uncorrelated components from correlated variables, and a few of these uncorrelated components usually account for most of the information in the input variables. Researchers interpret each component as a separate entity representing a latent trait or profile in a population. However, the components are guaranteed to be independent and uncorrelated only when the multivariate normality of the variables is assumed. If the normality assumption does not hold, components are guaranteed to be uncorrelated, but not independent. If the independence assumption is violated, each component cannot be uniquely interpreted because of contamination by other components. Therefore, in the present study, we introduced independent component analysis, whose components are uncorrelated and independent even when the multivariate normality assumption is violated, and each component carries unique information.