Data from: 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.神经元记录技术的持续迭代，使得可同时记录的神经元数目不断攀升。这带来了一项核心分析挑战：如何高效凝练地提取神经群体编码在空间维度（不同位置神经元的刺激调谐差异）、时间维度（神经元响应的时序动态变化），以及二者结合维度（神经群体的协同时序放电）中所承载的全部感官信息。本研究针对神经群体锋电位序列（spike train）沿空间与时间维度的张量分解（tensor factorization）展开应用探究。此类分解可将单次实验的神经群体锋电位序列数据集拆解为三类组分：空间放电模式（协同放电的神经元组合）、时间放电模式（此类神经元集群的时序激活模式），以及实验依赖的激活系数（单次实验中该类神经模式的招募强度）。我们通过模拟数据，以及同时记录的蝾螈视网膜神经节细胞群体数据，对多种分解方法进行了验证。研究发现，单次实验的时空张量分解能够为锋电位序列构建低维度且数据鲁棒的表征，可高效提取锋电位序列中与感官刺激相关的空间与时间维度信息。带有正交约束的张量分解在提取感官信息时效率最优；而非负张量分解（non-negative tensor decomposition）即便面对非独立且存在重叠的锋电位模式，仍可取得良好效果，且能提取同一神经群体对新型刺激产生的具有信息价值的放电模式。本研究方法表明，蝾螈视网膜神经节细胞群体可在10毫秒量级的锋电位时序中，承载自然图像空间细节相关的信息。此类信息无法通过这些细胞的锋电位发放总数（spike count）提取得到。首锋潜伏期（first-spike latency）携带了完整锋电位序列中关于精细图像特征的绝大多数信息，且其携带的自然图像粗尺度特征信息量，几乎与发放速率（firing rate）相当。综上，本研究结果凸显了锋电位时序，尤其是首锋潜伏期，在视网膜编码中的重要性。