Using Matrix and Tensor Factorizations for the Single-Trial Analysis of Population Spike Trains

Advances in neuronal recording techniques are leading to ever larger numbers of simultaneously monitored neurons. This poses the important analytical challenge of how to capture compactly all sensory information that neural population codes carry in their spatial dimension (differences in stimulus tuning across neurons at different locations), in their temporal dimension (temporal neural response variations), or in their combination (temporally coordinated neural population firing). Here we investigate the utility of tensor factorizations of population spike trains along space and time. These factorizations decompose a dataset of single-trial population spike trains into spatial firing patterns (combinations of neurons firing together), temporal firing patterns (temporal activation of these groups of neurons) and trial-dependent activation coefficients (strength of recruitment of such neural patterns on each trial). We validated various factorization methods on simulated data and on populations of ganglion cells simultaneously recorded in the salamander retina. We found that single-trial tensor space-by-time decompositions provided low-dimensional data-robust representations of spike trains that capture efficiently both their spatial and temporal information about sensory stimuli. Tensor decompositions with orthogonality constraints were the most efficient in extracting sensory information, whereas non-negative tensor decompositions worked well even on non-independent and overlapping spike patterns, and retrieved informative firing patterns expressed by the same population in response to novel stimuli. Our method showed that populations of retinal ganglion cells carried information in their spike timing on the ten-milliseconds-scale about spatial details of natural images. This information could not be recovered from the spike counts of these cells. First-spike latencies carried the majority of information provided by the whole spike train about fine-scale image features, and supplied almost as much information about coarse natural image features as firing rates. Together, these results highlight the importance of spike timing, and particularly of first-spike latencies, in retinal coding.Author Summary: The ever growing size of neural populations simultaneously recorded in electrophysiological experiments calls for urgent analytical progress in understanding how to compactly describe all sensory information present both in the spatial and temporal structure of single-trial neural population activity. Here we show the power of analytical methods, termed space-by-time tensor factorizations, which detect groups of simultaneously coactive neurons and the temporal profiles of their coactivation. By validation on simulated data and on retinal recordings, we show that the tensor decomposition performs competitively compared to other techniques both in terms of data robustness and ability to find informative patterns across diverse stimuli. We show that this method can determine the spatial and temporal resolution of neural population codes, and find which spatial or temporal components of neural responses carry information not available in other aspects of the population code. When applied to experimental data, the method demonstrates the importance of first-spike latencies in retinal population coding of visual images, particularly for decoding fine spatial details of natural images from population activity. This work shows that this methodology can improve our knowledge of population coding by allowing the discovery of informative spatial and temporal firing patterns in populations of simultaneously recorded neurons.