Localized Cross Spectral Analysis and Pattern Recognition Methods for Non-Stationary Signals

摘要：Hernando Ombao Proposal：0405243 PI开发了一套系统的方法和模型来分析海量非平稳信号。基本工具是SLEX库，它是一个基本集合，每个基本由正交局部化傅立叶波形组成。SLEX方法给出的结果很容易解释，因为它们是平稳信号的傅立叶谱分析的随时间变化的类似物。此外，SLEX方法使用计算效率高的算法，因此，它们将能够处理海量数据集。PI为几个受试者记录的非平稳信号开发了一系列多变量模型。该模型显式地考虑了多变量信号各分量之间随时间演变的相互关系。此外，PI利用时变SLEX谱矩阵的特征值-特征向量分解，开发了将高维多变量信号分解成SLEX分量的自动过程。SLEX分量是非平稳的，并且具有零相干性。因此，它们包含关于时变交叉谱的非冗余信息，这些信息将被用作模型选择以及区分和分类的主要特征。最后，PI发展了一种自动和系统的方法来提取非平稳信号的时变高阶谱特征。PI发展了SLEX高阶谱，它可以解释信号中不同频率分量之间的时间演化相互作用。在这项建议中，SLEX是建立一套连贯和系统的非平稳信号方法的基础。这项建议的动机是神经科学界面临的统计学问题。现在，技术的重大进步使神经科学家能够收集复杂的数据集，以研究人类大脑更复杂的功能。目前有一个主要的兴趣是研究不同的大脑区域如何在精神刺激下相互作用。人们还对探索大脑连接障碍和各种精神障碍之间的联系产生了广泛的兴趣。为了研究大脑的连通性，记录了各种类型的信号(脑电、脑磁图、fMRI)。分析大脑信号相当具有挑战性，因为大脑是一个复杂的器官。此外，采集到的信号既是非平稳的，又是海量的。PI在本提案中开发的SLEX方法解决了这些问题。SLEX方法能够捕获信号的局部时间特征。此外，这些方法能够处理海量数据集，因为它们使用计算效率高的算法。作为这项建议的教育部分的一部分，国际和平研究所与研究生和本科生在这项研究工作中密切合作。

AbstractPI: Hernando Ombaoproposal: 0405243The PI develops a systematic body of methods and models for analyzing massive non-stationary signals. The basic tool is the SLEX library, a collection of bases, each basis consisting of orthogonal localized Fourier waveforms. The SLEX methods give results that are easy to interpret because they are time-dependent analogues of the Fourier spectral analysis of stationary signals. Moreover, the SLEX methods use computationally efficient algorithms, thus, they will be capable of handling massive data sets. The PI develops a family of multivariate models for non-stationary signals recorded from several subjects. The model explicitly takes into account the time-evolving inter-connection between the components of the multivariate signals. In addition, the PI develops an automatic procedure for decomposing the high dimensional multivariate signals into SLEX components using the eigenvalue-eigenvector decomposition of the time-varying SLEX spectral matrix. The SLEX components are non-stationary and have zero-coherency. Thus, they contain non-redundant information on the time-varying cross spectra, which will be used as the primary feature for model selection as well as for discrimination and classification. Finally, the PI develops an automatic and systematic method for extracting time-varying higher order spectral features of non-stationary signals. The PI develops the SLEX higher order spectra, which can account for the time-evolutionary interaction between different frequency components in the signal. In this proposal, the SLEX are the foundation on which the body of coherent and systematic methods for non-stationary signals is built.This proposal is motivated by the statistical problems that confront the neuroscience community. Major advances in technology now enable neuroscientists to collect complex data sets for investigating the more intricate functioning of the human brain. There is currently a major interest to study how different brain areas interact with each other in response to a mental stimulus. There is also a widespread interest in exploring the association between impairment in brain connectivity and various mental disorders. To study brain connectivity, various types of signals (EEGs, MEGs, fMRI) are recorded. Analyzing brain signals is quite challenging because the brain is a complex organ. Moreover, the signals collected are both non-stationary and massive. The SLEX methods that the PI develops in this proposal address these issues. The SLEX methods are able to capture the local temporal features of the signals. Moreover, the methods are able to handle massive data sets, because they use computationally efficient algorithms. As part of the educational component of this proposal, the PI works closely with graduate and undergraduate students in this research undertaking.