Composite real principal component analysis of complex signals

Principal component analysis (PCA) is a tool for dimensionality reduction, feature extraction, and data compression, which is applied to both real-valued and complex-valued data sets. For complex data, a modified version of PCA based on widely linear transformations was shown to be beneficial if the considered random variables are improper, i.e., in the case of correlations or power imbalances between real and imaginary parts. This widely linear approach is formulated in an augmented complex representation in the existing literature. In this paper, we propose a composite real PCA, which instead transforms the complex data into a set of real-valued principal components. This alternative approach is superior in dimensionality reduction due to the finer granularity that is possible when counting dimensions in the real-valued representation. Moreover, it can be used to obtain the same results as the augmented complex version at a lower computational complexity.