Pouzat Christophe, Delescluse Matthieu, Viot Pascal, Diebolt Jean
Laboratoire de Physiologie Cérébrale, Centre National de la Recherche Scientifique (CNRS) Unité Mixte de Recherche (UMR) 8118, Université René Descartes, 45 rue des Saintes Pères, 75006 Paris, France.
J Neurophysiol. 2004 Jun;91(6):2910-28. doi: 10.1152/jn.00227.2003. Epub 2004 Jan 28.
Spike-sorting techniques attempt to classify a series of noisy electrical waveforms according to the identity of the neurons that generated them. Existing techniques perform this classification ignoring several properties of actual neurons that can ultimately improve classification performance. In this study, we propose a more realistic spike train generation model. It incorporates both a description of "nontrivial" (i.e., non-Poisson) neuronal discharge statistics and a description of spike waveform dynamics (e.g., the events amplitude decays for short interspike intervals). We show that this spike train generation model is analogous to a one-dimensional Potts spin-glass model. We can therefore tailor to our particular case the computational methods that have been developed in fields where Potts models are extensively used, including statistical physics and image restoration. These methods are based on the construction of a Markov chain in the space of model parameters and spike train configurations, where a configuration is defined by specifying a neuron of origin for each spike. This Markov chain is built such that its unique stationary density is the posterior density of model parameters and configurations given the observed data. A Monte Carlo simulation of the Markov chain is then used to estimate the posterior density. We illustrate the way to build the transition matrix of the Markov chain with a simple, but realistic, model for data generation. We use simulated data to illustrate the performance of the method and to show that this approach can easily cope with neurons firing doublets of spikes and/or generating spikes with highly dynamic waveforms. The method cannot automatically find the "correct" number of neurons in the data. User input is required for this important problem and we illustrate how this can be done. We finally discuss further developments of the method.
尖峰排序技术试图根据产生一系列有噪声电波形的神经元的身份对其进行分类。现有技术在进行这种分类时忽略了实际神经元的几个特性，而这些特性最终可以提高分类性能。在本研究中，我们提出了一个更现实的尖峰序列生成模型。它既包含了对“非平凡”（即非泊松）神经元放电统计的描述，也包含了对尖峰波形动态（例如，尖峰间间隔短时事件幅度衰减）的描述。我们表明，这个尖峰序列生成模型类似于一维Potts自旋玻璃模型。因此，我们可以针对我们的特定情况调整在Potts模型被广泛使用的领域（包括统计物理和图像恢复）中开发的计算方法。这些方法基于在模型参数和尖峰序列配置空间中构建马尔可夫链，其中一个配置是通过为每个尖峰指定一个起源神经元来定义的。构建这个马尔可夫链，使得其唯一的平稳密度是给定观测数据时模型参数和配置的后验密度。然后使用马尔可夫链的蒙特卡罗模拟来估计后验密度。我们用一个简单但现实的数据生成模型来说明构建马尔可夫链转移矩阵的方法。我们使用模拟数据来说明该方法的性能，并表明这种方法可以轻松应对神经元发放尖峰对和/或生成具有高度动态波形的尖峰的情况。该方法不能自动找到数据中“正确”的神经元数量。对于这个重要问题需要用户输入，我们说明了如何做到这一点。我们最后讨论了该方法的进一步发展。
