Tensor Analysis and the Dynamics of Motor Cortex

Jeffrey Scott Seely

Neural data often span multiple indices, such as neuron, experimental condition, trial, and time, resulting in a tensor or multidimensional array. Standard approaches to neural data analysis often rely on matrix factorization techniques, such as principal component analysis or nonnegative matrix factorization. Any inherent tensor structure in the data is lost when flattened into a matrix. Here, we analyze datasets from primary motor cortex from the perspective of tensor analysis, and develop a theory for how tensor structure relates to certain computational properties of the underlying system. Applied to the motor cortex datasets, we reveal that neural activity is best described by condition-independent dynamics as opposed to condition-dependent relations to external movement variables. Motivated by this result, we pursue one further tensor-related analysis, and two further dynamical...