Neural spiketrains and population vectors entangle neural representations

Neural recordings are usually analyzed by comparing neural spiketrains or comparing time bins (population vectors). If multiple variables drive the neural activity these comparisons will be affected by all of them. Our aim is to disentangle the different latent variables or covariates that drive neural activity and reveal their structure and geometry. The central idea of the paper is that a matrix is disentangled when its rows and columns are local on each other, a condition we call bidirectional locality. In such a matrix, rows and columns encode the same geometry and they respond to only one localized part of it. This suggests finding bidirectional local matrices in a given data matrix, from which we can recover the geometry of the covariates driving it in a straightforward way. We present two ways of doing just this. The first method, coherent projections, works by finding non-negative projections of the neural data matrix (neurons by time bins) that are bidirectionally local. The second method, clumps, works by finding dense submatrices of the neural data matrix, that each identify a local region of one covariate. We apply these methods to two neural datasets, showing that they can separate grid cell modules and reveal a movement-driven low-dimensional structure in the motor cortex.