On the (Apparently) Paradoxical Role of Noise in the Recognition of Signal Character of Minor Principal Components

Abstract

The usual method of separating signal and noise principal components on the sole basis of their eigenvalues has evident drawbacks when semantically relevant information ‘hides’ in minor components, explaining a very small part of the total variance. This situation is common in biomedical experimentation when PCA is used for hypothesis generation: the multi-scale character of biological regulation typically generates a main mode explaining the major part of variance (size component), squashing potentially interesting (shape) components into the noise floor. These minor components should be erroneously discarded as noisy by the usual selection methods. Here, we propose a computational method, tailored for the chemical concept of ‘titration’, allowing for the unsupervised recognition of the potential signal character of minor components by the analysis of the presence of a negative linear relation between added noise and component invariance.