  ElectroCOrticoGraphy (ECoG) technology measures electrical activity in the
human brain via electrodes placed directly on the cortical surface during
neurosurgery. Through its capability to record activity at a fast temporal
resolution, ECoG experiments have allowed scientists to better understand how
the human brain processes speech. By its nature, ECoG data is difficult for
neuroscientists to directly interpret for two major reasons. Firstly, ECoG data
tends to be large in size, as each individual experiment yields data up to
several gigabytes. Secondly, ECoG data has a complex, higher-order nature.
After signal processing, this type of data may be organized as a 4-way tensor
with dimensions representing trials, electrodes, frequency, and time. In this
paper, we develop an interpretable dimension reduction approach called
Regularized Higher Order Principal Components Analysis, as well as an extension
to Regularized Higher Order Partial Least Squares, that allows neuroscientists
to explore and visualize ECoG data. Our approach employs a sparse and
functional Candecomp-Parafac (CP) decomposition that incorporates sparsity to
select relevant electrodes and frequency bands, as well as smoothness over time
and frequency, yielding directly interpretable factors. We demonstrate the
performance and interpretability of our method with an ECoG case study on audio
and visual processing of human speech.
