Ernst Strüngmann Institute (ESI) for Neuroscience in Cooperation with Max Planck Society, 60528 Frankfurt, Germany; Laboratoire de Neurosciences Cognitives, École Normale Supérieure, 75005 Paris, France.
Ernst Strüngmann Institute (ESI) for Neuroscience in Cooperation with Max Planck Society, 60528 Frankfurt, Germany; Department of Clinical Neuroscience, Karolinska Institute, 171 76 Stockholm, Sweden.
Neuroimage. 2015 Jul 1;114:57-70. doi: 10.1016/j.neuroimage.2015.04.040. Epub 2015 Apr 24.
The quantification of covariance between neuronal activities (functional connectivity) requires the observation of correlated changes and therefore multiple observations. The strength of such neuronal correlations may itself undergo moment-by-moment fluctuations, which might e.g. lead to fluctuations in single-trial metrics such as reaction time (RT), or may co-fluctuate with the correlation between activity in other brain areas. Yet, quantifying the relation between moment-by-moment co-fluctuations in neuronal correlations is precluded by the fact that neuronal correlations are not defined per single observation. The proposed solution quantifies this relation by first calculating neuronal correlations for all leave-one-out subsamples (i.e. the jackknife replications of all observations) and then correlating these values. Because the correlation is calculated between jackknife replications, we address this approach as jackknife correlation (JC). First, we demonstrate the equivalence of JC to conventional correlation for simulated paired data that are defined per observation and therefore allow the calculation of conventional correlation. While the JC recovers the conventional correlation precisely, alternative approaches, like sorting-and-binning, result in detrimental effects of the analysis parameters. We then explore the case of relating two spectral correlation metrics, like coherence, that require multiple observation epochs, where the only viable alternative analysis approaches are based on some form of epoch subdivision, which results in reduced spectral resolution and poor spectral estimators. We show that JC outperforms these approaches, particularly for short epoch lengths, without sacrificing any spectral resolution. Finally, we note that the JC can be applied to relate fluctuations in any smooth metric that is not defined on single observations.
神经元活动（功能连接）协方差的量化需要观察相关变化，因此需要多次观察。这种神经元相关性的强度本身可能会经历瞬息万变，这可能会导致例如反应时间（RT）等单试指标的波动，或者可能与大脑其他区域活动之间的相关性共同波动。然而，由于神经元相关性不是针对单个观察定义的，因此量化神经元相关性的瞬间波动之间的关系是不可能的。该方法通过首先为所有排除一个样本的子样本（即所有观察的 jackknife 复制）计算神经元相关性，然后对这些值进行相关性计算，从而解决了这个问题。由于相关性是在 jackknife 复制之间计算的，因此我们将这种方法称为 jackknife 相关性（JC）。首先，我们证明了 JC 与针对每个观察定义的模拟成对数据的传统相关性的等价性，因此允许计算传统相关性。虽然 JC 精确地恢复了传统相关性，但替代方法，如排序和分箱，会对分析参数产生不利影响。然后，我们探讨了将两个光谱相关度量（如相干性）相关联的情况，这需要多个观察时期，唯一可行的替代分析方法是基于某种形式的时期细分，这会导致光谱分辨率降低和光谱估计器不佳。我们表明，JC 优于这些方法，尤其是对于短时期长度，而不会牺牲任何光谱分辨率。最后，我们注意到 JC 可以应用于任何不是基于单个观察定义的平滑度量的波动关系。
