Penalized PARAFAC analysis of spontaneous EEG recordings
Eduardo Martínez‐Montes, Jose Miguel Sanchez-Bornot, Pedro Antonio Valdes-Sosa · Statistica Sinica · 2008
The multidimensional nature of neuroscience data has made the use of multi-way statistical analysis suitable in this field. Parallel Factor Analysis (PARAFAC) is a multidimensional generalization of PCA with the advantage of offering unique solutions. However, imposing physiologically acceptable constraints would improve the interpretation of this type of analysis. In this work we propose a new algorithm called Alternating Penalized Least Squares to estimate PARAFAC solutions using different kinds of soft penalization. The algorithm relies on the re- cent generalization of modified Newton-Raphson techniques to estimate a multiple penalized least squares model. Applied to semi-synthetic and real spontaneous EEG time-varying spectra, we show that a wide range of sparse and smooth solutions can be found separately, as well as with these two properties combined. Smooth- ness is usually desired in spectra, and different sparse scenarios are observed in the temporal evolution of physiological intermittent phenomena. The degree of con- straints can be tuned through the weighting parameters, whose optimal values can be chosen by means of the cross-validation and Corcondia measures.