CNRS and DMA, Ecole Normale Supérieure - PSL University, Paris, France; Inria Saclay, Université Paris-Saclay, Palaiseau, France.
Institut d'Astrophysique de Paris, CNRS (UMR7095), Paris, France.
J Neurosci Methods. 2021 May 15;356:109144. doi: 10.1016/j.jneumeth.2021.109144. Epub 2021 Mar 23.
Independent Component Analysis (ICA) is a widespread tool for exploration and denoising of electroencephalography (EEG) or magnetoencephalography (MEG) signals. In its most common formulation, ICA assumes that the signal matrix is a noiseless linear mixture of independent sources that are assumed non-Gaussian. A limitation is that it enforces to estimate as many sources as sensors or to rely on a detrimental PCA step.
We present the Spectral Matching ICA (SMICA) model. Signals are modelled as a linear mixing of independent sources corrupted by additive noise, where sources and the noise are stationary Gaussian time series. Thanks to the Gaussian assumption, the negative log-likelihood has a simple expression as a sum of 'divergences' between the empirical spectral covariance matrices of the signals and those predicted by the model. The model parameters can then be estimated by the expectation-maximization (EM) algorithm.
On phantom MEG datasets with low amplitude dipole sources (20 nAm), SMICA makes a median dipole localization error of 1.5 mm while competing methods make an error ≥7 mm. Experiments on EEG datasets show that SMICA identifies a source subspace which contains sources that have less pairwise mutual information, and are better explained by the projection of a single dipole on the scalp. With 10 sources, the number of strongly dipolar sources (dipolarity >90%) is more than 80% for SMICA while competing methods do not exceed 65%.
With the noisy model of SMICA, the number of sources to be recovered is controlled by choosing the size of the mixing matrix to be fitted rather than by a preprocessing step of dimension reduction which is required in traditional noise-free ICA methods.
SMICA is a promising alternative to other noiseless ICA models based on non-Gaussian assumptions.
独立成分分析（ICA）是一种广泛用于探索和去噪脑电图（EEG）或脑磁图（MEG）信号的工具。在其最常见的形式中，ICA 假设信号矩阵是独立源的无噪声线性混合，这些源被假设为非高斯分布。其局限性在于，它需要估计与传感器一样多的源，或者依赖于有害的 PCA 步骤。
我们提出了谱匹配 ICA（SMICA）模型。信号被建模为独立源的线性混合，受到加性噪声的干扰，其中源和噪声是平稳的高斯时间序列。由于高斯假设，负对数似然具有一个简单的表达式，即信号的经验谱协方差矩阵与模型预测的谱协方差矩阵之间的“散度”之和。然后可以通过期望最大化（EM）算法来估计模型参数。
在具有低幅度偶极子源（20nAm）的幻影 MEG 数据集上，SMICA 的中值偶极子定位误差为 1.5mm，而竞争方法的误差≥7mm。在 EEG 数据集上的实验表明，SMICA 确定了一个源子空间，其中包含互信息量较小的源，并且可以通过头皮上单个偶极子的投影更好地解释。对于 10 个源，SMICA 的强偶极子（偶极性>90%）数量超过 80%，而竞争方法不超过 65%。
对于 SMICA 的噪声模型，可以通过选择要拟合的混合矩阵的大小来控制要恢复的源的数量，而不是通过传统无噪声 ICA 方法所需的降维预处理步骤来控制。
SMICA 是其他基于非高斯假设的无噪声 ICA 模型的一种有前途的替代方法。
