Bernat Edward M, Williams William J, Gehring William J
Department of Psychology, University of Minnesota, 75 East River Road, Elliot Hall, Minneapolis, MN 55455, USA.
Clin Neurophysiol. 2005 Jun;116(6):1314-34. doi: 10.1016/j.clinph.2005.01.019. Epub 2005 Apr 2.
Time-frequency transforms (TFTs) offer rich representations of event-related potential (ERP) activity, and thus add complexity. Data reduction techniques for TFTs have been slow to develop beyond time analysis of detail functions from wavelet transforms. Cohen's class of TFTs based on the reduced interference distribution (RID) offer some benefits over wavelet TFTs, but do not offer the simplicity of detail functions from wavelet decomposition. The objective of the current approach is a data reduction method to extract succinct and meaningful events from both RID and wavelet TFTs.
A general energy-based principal components analysis (PCA) approach to reducing TFTs is detailed. TFT surfaces are first restructured into vectors, recasting the data as a two-dimensional matrix amenable to PCA. PCA decomposition is performed on the two-dimensional matrix, and surfaces are then reconstructed. The PCA decomposition method is conducted with RID and Morlet wavelet TFTs, as well as with PCA for time and frequency domains separately.
Three simulated datasets were decomposed. These included Gabor logons and chirped signals. All simulated events were appropriately extracted from the TFTs using both wavelet and RID TFTs. Varying levels of noise were then added to the simulated data, as well as a simulated condition difference. The PCA-TFT method, particularly when used with RID TFTs, appropriately extracted the components and detected condition differences for signals where time or frequency domain analysis alone failed. Response-locked ERP data from a reaction time experiment was also decomposed. Meaningful components representing distinct neurophysiological activity were extracted from the ERP TFT data, including the error-related negativity (ERN).
Effective TFT data reduction was achieved. Activity that overlapped in time, frequency, and topography were effectively separated and extracted. Methodological issues involved in the application of PCA to TFTs are detailed, and directions for further development are discussed.
The reported decomposition method represents a natural but significant extension of PCA into the TFT domain from the time and frequency domains alone. Evaluation of many aspects of this extension could now be conducted, using the PCA-TFT decomposition as a basis.
时频变换（TFT）能够丰富地呈现事件相关电位（ERP）活动，因而增加了复杂性。除了对小波变换的细节函数进行时间分析之外，TFT的数据约简技术发展缓慢。基于减少干扰分布（RID）的科恩类TFT相比小波TFT具有一些优势，但不具备小波分解中细节函数的简单性。当前方法的目标是一种数据约简方法，用于从RID和小波TFT中提取简洁且有意义的事件。
详细介绍了一种基于能量的通用主成分分析（PCA）方法来约简TFT。首先将TFT表面重构为向量，把数据重铸为适合PCA的二维矩阵。对二维矩阵进行PCA分解，然后重构表面。使用RID和Morlet小波TFT进行PCA分解方法，同时也分别对时域和频域进行PCA。
对三个模拟数据集进行了分解。这些数据集包括Gabor登录信号和啁啾信号。使用小波和RID TFT均能从TFT中适当地提取所有模拟事件。然后向模拟数据中添加不同程度的噪声以及模拟的条件差异。PCA-TFT方法，特别是与RID TFT一起使用时，能够适当地提取成分并检测出仅通过时域或频域分析无法检测到的信号条件差异。还对来自反应时间实验的反应锁定ERP数据进行了分解。从ERP TFT数据中提取了代表不同神经生理活动的有意义成分，包括错误相关负波（ERN）。
实现了有效的TFT数据约简。在时间上、频率上和地形上重叠的活动被有效地分离和提取。详细阐述了将PCA应用于TFT所涉及的方法学问题，并讨论了进一步发展的方向。
所报道的分解方法代表了PCA仅从时域和频域自然但重要地扩展到时频变换领域。现在可以以PCA-TFT分解为基础，对这一扩展的许多方面进行评估。
