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，使得可同时监测的神经元数目不断攀升。这带来了一项关键的分析挑战：如何以紧凑的形式完整提取神经群体编码（neural population codes）所承载的全部感官信息——这些信息既存在于空间维度（不同位置神经元的刺激调谐差异）、时间维度（神经元响应的时间动态变化），也存在于二者的协同维度（时间同步的神经群体放电活动）。本研究针对沿空间和时间维度展开的群体锋电位序列（spike train）张量分解（tensor factorization）的应用价值展开探究。这类分解方法可将单次试次群体锋电位序列数据集拆解为三类组分：空间放电模式（同步放电的神经元组合）、时间放电模式（上述神经元集群的时间激活过程），以及试次依赖的激活系数（每一试次中此类神经模式的募集强度）。我们在模拟数据以及同时记录的蝾螈视网膜神经节细胞（ganglion cell）集群数据集上，对多种分解方法进行了验证。研究发现，单次试次张量时空分解可生成锋电位序列的低维数据鲁棒表征，能够高效提取锋电位序列中关于感官刺激的空间与时间信息。带正交约束的张量分解在提取感官信息时效率最优；而非负张量分解则即便在处理非独立且重叠的放电模式时，也能取得良好效果，且可还原出同一神经元集群对新型刺激响应时的功能性放电模式。本研究方法表明，视网膜神经节细胞集群可在10毫秒尺度上通过锋电位时序承载自然图像的空间细节信息，而此类信息无法通过这些细胞的锋电位发放数获取。首峰潜伏期（first-spike latency）承载了整个锋电位序列中关于精细图像特征的绝大多数信息，且其携带的粗糙自然图像特征信息量几乎与放电率相当。综上，本研究结果凸显了锋电位时序，尤其是首峰潜伏期，在视网膜编码中的重要性。