Multi-Linear Population Analysis (MLPA) of LFP Data Using Tensor Decompositions

The local field potential (LFP) is the low frequency part of the extracellular electrical potential in the brain and reflects synaptic activity onto thousands of neurons around each recording contact. Nowadays, LFPs can be measured at several hundred locations simultaneously. The measured LFP is in general a superposition of contributions from many underlying neural populations which makes interpretation of LFP measurements in terms of the underlying neural activity challenging. Classical statistical analyses of LFPs rely on matrix decomposition-based methods such as PCA (Principal Component Analysis) and ICA (Independent Component Analysis), which require additional constraints on spatial and/or temporal patterns of populations. In this work, we instead explore the multi-fold data structure of LFP recordings, e.g., multiple trials, multi-channel time series, arrange the signals as a higher-order tensor (i.e., multiway array), and study how a specific tensor decomposition approach, namely canonical polyadic (CP) decomposition, can be used to reveal the underlying neural populations. Essential for interpretation, the CP model provides uniqueness without imposing constraints on patterns of underlying populations. Here, we first define a neural network model and based on its dynamics, compute LFPs. We run multiple trials with this network, and LFPs are then analysed simultaneously using the CP model. More specifically, we design \Note{feed-forward population rate neuron models} to match the structure of state-of-the-art, large-scale LFP simulations, but downscale them to allow easy inspection and interpretation. We demonstrate that our feed-forward model matches the mathematical structure assumed in the CP model, and CP successfully reveals temporal and spatial patterns as well as variations over trials of underlying populations when compared with the ground truth from the model. We also discuss the use of diagnostic approaches for CP to guide the analysis when there is no ground truth information. In comparison with classical methods, we discuss the advantages of using tensor decompositions for analyzing LFP recordings as well as their limitations.