Deep Ll-PCA of Time-Variant Data with Application to Brain Connectivity Measurements

Ll-Principal Component Analysis (LI-PCA) is a powerful computational tool to identify relevant components in data affected by noise, outliers, partial disruption and so on. Relevant efforts have been made to adapt its powerful summarization capacity to time variant data, e.g. in tracking the evolution of LI-PCA components. Here, we analyze a layered version of LI-PCA, to which we refer to as Deep LI-PCA. Deep LI-PCA is obtained by recursive application of two stages: estimation of LI-PCA basis and extraction of the first rank projector. The Deep LI-PCA is applied to repeated EEG connectivity measures and it proves relevant for identifying outliers, changes, and stable components. Moreover, at each layer, an in-depth analysis of the mean square error between the data applied at the input layer and the output projector is provided. The Deep LI-PCA allows to cope with outliers of different temporal extent as well as to extract the relevant common component at a reduced computational cost.