Decomposing the time-frequency representation of EEG using non-negative matrix and multi-way factorization
Decomposing the time-frequency representation of EEG using non-negative matrix and multi-way factorization
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发表时间：
2006
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通讯作者：
Morten Mørup;L. K. Hansen;J. Parnas;S. Arnfred
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作者：
Morten Mørup;L. K. Hansen;J. Parnas;S. Arnfred
我们演示了如何使用非负矩阵分解比n （NMF）来分解多通道脑电图的试验间相位相干性（ITPC），以产生记录通道中不同程度存在的时频特征的独特分解。NMF优化可以很容易地推广到并行因子（PARAFAC）模型，从而形成非负多路因子（NMWF）。虽然NMF可以检查受试者特定的活动，但NMWF可以有效地提取跨受试者和/或条件的最相似的活动。这些方法是在一个本体感觉刺激上进行测试的，该刺激由手持负载的重量变化组成。虽然体感伽马振荡以前只被电刺激引起，但我们假设自然的本体感觉刺激也能引起伽马振荡。通过目测确定了ITPC最大值，并与nmmf和NMWF的分解结果进行了比较。视觉模式检查结果与数学分解结果之间的一致性令人满意，显示出两个显著的连贯活动；在刺激开始60 ms后，额顶区与刺激侧对侧的40Hz活动被预测，另外，额中央区域的20Hz活动被预测略微偏侧。因此，本体感觉刺激也能够引起诱发的伽马活动。脑电图分析已发展到两大方向；一个专注于偶极子或源定位，通过详细的统计模型试图解决“逆”静电问题（Koles， Z. J., 1998）；另一种则侧重于数据的数学分解（Dormann， W. U.等，1987;Makeig， S.等，1997;Rogers， L. J., 1991）。最近，人们对在时频域评估事件相关脑电图（EEG）活动的兴趣越来越大（Duzel， E.等，2003;Gruber， T.等，2004;Herrmann， C. S.等，1999;Jansen, b.h.等，2004;Jones， K.等，2002;Lachaux, j.p.等，2005;Tallon-Baudry， C.和Bertrand， O., 1999）。我们的目标是将脑电图的数学合成扩展到小波变换的多通道事件相关脑电图，以产生易于解释的时频图。我们提出应用非负矩阵分解（NMF） （Lee, d.d. and Seung， H. S., 1999; 2001）来分析由信道x时频给出的多通道小波变换脑电信号的试验间相位相干性。这种NMF方法很容易适应于形成非负mu多向分解（NMWF）的并行因子（PARAFAC）分析。NMWF模型能够分析包含更多模式的脑电图数据，如条件和受试者，而不会破坏这些模式（就像目前的多受试者NMF分析的情况一样），给出了跨受试者和条件最相似的活动的加权平均值。PARAFAC模型h先前被用于探索小波变换后的事件相关脑电图(Mørup, M .；， et al., 2006)。然而，这是第一次
We demonstrate how non-negative matrix factorizatio n (NMF) can be used to decompose the inter trial phase coherence (ITPC) of multi-cha nnel EEG to yield a unique decomposition of time-frequency signatures present in various degrees in the recording channels. The NMF optimization is easily generalize d to a parallel factor (PARAFAC) model to form a non-negative multi-way factorizatio n (NMWF). While the NMF can examine subject specific activities the NMWF can ef fectively extract the most similar activities across subjects and or conditions. The m ethods are tested on a proprioceptive stimulus consisting of a weight change in a handhel load. While somatosensory gamma oscillations have previously only been evoked by el ectrical stimuli we hypothesized that a natural proprioceptive stimulus also would be able to voke gamma oscillations. ITPC maxima were determined by visual inspection and the se r sults were compared to the NMF and NMWF decompositions. Agreement between the resu lts of the visual pattern inspection and the mathematical decompositions was satisfactor y showing two significant coherent activities; the predicted 40Hz activity 60 ms after stimulus onset in the frontal-parietal region contralateral to stimulus side and additiona lly n unexpected 20Hz activity slightly lateralized in the frontal central region. Conseque ntly, also proprioceptive stimuli are able to elicit evoked gamma activity. 1 Introduct ion The analysis of EEG has developed in two major dire ctions; one focusing on dipole or source localization through elaborate statistical m odels trying to solve the “inverse” electrostatics problem (Koles, Z. J., 1998); anothe r focusing on mathematical decomposition on the data (Dormann, W. U., et al., 1987; Makeig, S., et al., 1997; Rogers, L. J., 1991). Lately there has been a growing interest in assessm nt of event related electroencephalographic (EEG) activity in the ime-frequency domain (Duzel, E., et al., 2003; Gruber, T., et al., 2004; Herrmann, C. S., et al., 1999; Jansen, B. H., et al., 2004; Jones, K., et al., 2002; Lachaux, J. P., et al., 20 05; Tallon-Baudry, C.and Bertrand, O., 1999). Our aim is here to extend the mathematical d ecompositions of the EEG to the wavelet transformed multi-channel event related EEG to yield easy interpretable timefrequency plots. We propose to apply non-negative matrix factorizati on (NMF) (Lee, D. D.and Seung, H. S., 1999; 2001) to analyze the inter trial phase cohere nce of multi-channel wavelet transformed EEG given by channel x time-frequency . This NMF approach is easily adapted to a paralle l factor (PARAFAC) analysis forming a non-negative mu lti-way factorization (NMWF). The NMWF model enables analysis of EEG data encompassin g more modalities such as condition and subject without collapsing these moda lities (as is the case for the present multi subject NMF analysis) giving a weighted avera ge of the activity the most similar across subjects and conditions. The PARAFAC model h as previously been used to explore the wavelet transformed event related EEG (Mørup, M ., et al., 2006). It is however the first