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 spatialdimension (differences in stimulus tuning across neurons at different locations), in theirtemporal 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 adataset of single-trial population spike trains into spatial firing patterns (combinations ofneurons firing together), temporal firing patterns (temporal activation of these groups ofneurons) and trial-dependent activation coefficients (strength of recruitment of such neuralpatterns on each trial). We validated various factorization methods on simulated data andon populations of ganglion cells simultaneously recorded in the salamander retina. Wefound that single-trial tensor space-by-time decompositions provided low-dimensionaldata-robust representations of spike trains that capture efficiently both their spatial andtemporal information about sensory stimuli. Tensor decompositions with orthogonality constraints were the most efficient in extracting sensory information, whereas non-negativetensor decompositions worked well even on non-independent and overlapping spike patterns, and retrieved informative firing patterns expressed by the same population inresponse 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 ofnatural images. This information could not be recovered from the spike counts of thesecells. First-spike latencies carried the majority of information provided by the whole spiketrain about fine-scale image features, and supplied almost as much information aboutcoarse natural image features as firing rates. Together, these results highlight the importance of spike timing, and particularly of first-spike latencies, in retinal coding.
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