Maintaining the Integrity of Sources in Complex Learning Systems: Intraference and the Correlation Preserving Transform

The correlation preserving transform (CPT) is introduced to perform bivariate component analysis via decorrelating matrix decompositions, while at the same time preserving the integrity of original bivariate sources. Specifically, unlike existing bivariate uncorrelating matrix decomposition techniques, CPT is designed to preserve both the order of the data channels within every bivariate source and their mutual correlation properties. We introduce the notion of intraference to quantify the effects of interchannel mixing artifacts within recovered bivariate sources, and show that the integrity of separated sources is compromised when not accounting for the intrinsic correlations within bivariate sources, as is the case with current bivariate matrix decompositions. The CPT is based on augmented complex statistics and involves finding the correct conjugate eigenvectors associated with the pseudocovariance matrix, making it possible to maintain the physical meaning of the separated sources. The benefits of CPT are illustrated in the source separation and clustering scenarios, for both synthetic and real-world data.