Interpretable Visualization and Higher-Order Dimension Reduction for ECoG Data

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 an extremely fast temporal resolution, ECoG experiments have allowed scientists to better understand how the human brain processes speech. By its nature, ECoG data is extremely difficult for neuroscientists to directly interpret for two major reasons. Firstly, ECoG data tends to be extremely large in size, as each individual experiment yields data up to several GB. Secondly, ECoG data has a complex, higher-order nature; after signal processing, this type of data is typically organized as a 4-way tensor consisting of trials by electrodes by frequency by 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 both the performance and interpretability of our method with an ECoG case study on audio and visual processing of human speech.