报告人：黄锷院士
9月8日上午10点，知新楼C702报告厅
9月9日上午10点， 知新楼A511第五讲学厅
报告一
An Introduction to Adaptive Data Analysis:
Method for study nonlinear and nonstationary time series
Data analysis is indispensable to every scientificendeavors. The existing data analysis methods are all developed by mathematicians based on their rigorous rules. In pursue of the rigor, we are forced to make idealized assumptions and live in a pseudo-real linear and stationary world, in which data analysis is relegated to data processing. But the world we live in is neither stationary nor linear. As scientific research getting increasingly sophistic, the inadequacy of mere processing data becomes glaringly obvious. In fact, the frequency defined from the traditional Fourier analysis can be proved to lack mathematical and physical meanings. To get the truth containing in the data, we have to break away from these limitations; we should let data speak for themselves so that the results could reveal the full range of consequences of nonlinearity and nonstationarity. To do so, we need new paradigm of data analysis methodology without a priori basis to fully accommodating the variations of the underlying driving mechanisms. The solution lies in adaptive data analysis approach. One example is the Empirical Mode Decomposition method and the associated extensions of time-frequency representation. We will show that, with the adaptive method, we can only define true frequency with adaptive method, which would lead to quantify nonstationarity and nonlinearity.An extra bonus is the ability to define the trend. Examples from classic nonlinear system and recent climate change data will be used to illustrate the prowess of the new approach.
报告二
Recent development of Adaptive Data Analysis:
Holo-spectral analysis
Traditionally, spectral analysis, defined as time to frequency conversion, is achieved through convolutional integral transforms based on additive expansions of a priori determined basis, mostly under linear and stationary assumptions. For nonlinear processes, the data can have both amplitude and frequency modulations generated by two different mechanisms: linear additive or nonlinear multiplicative processes. As all existing spectral analysis methods are based on additive expansions, either a priori or adaptive, none of them could represent the multiplicative processes. While the adaptive Hilbert spectral analysis could accommodate the intra-wave nonlinearity, the inter-wave nonlinear multiplicative mechanisms that include cross-scale coupling and phase lock modulations are left untreated. To resolve the multiplicative processes, we have to use additional dimensions in the spectrum to account for both the variations in frequency and amplitude modulations (FM and AM) simultaneously. For this necessity, we propose a full informationalspectral representation: the Holo-Hilbert Spectral Analysis (HHSA), which would accommodate all the processes: additive and multiplicative, intra-mode and inter-mode, stationary and non-stationary, linear and nonlinear interactions. Applications to wave-turbulence interactions and some biomedical data will be presented to demonstrate the usefulness of this new spectral representation.
黄锷教授简介
黄锷教授，美国工程院院士，中国工程院外籍院士，美国航空太空署（NASA）海洋物理和流体力学首席科学家，台湾国立中央大学特聘教授，自适应数据分析研究中心主任。1998年发表HHT讯号处理法，完全改变以往对于非线性、非稳态讯号几乎束手无策的窘境。后又开发了全息希尔伯特特谱分析（HHSA）和内在的概率分布函数（IPDF），IPDF在光谱和概率领域充分考虑了物理过程中的非线性乘法效应。黄先生在流体力学相关领域于国际著名刊物发表论文一百余篇。
Dr. Norden Huang is the K. T. Lee Chair professor at the National Central University in Taiwan and the funding director of the Research Center for Adaptive Data Analysis. He held a doctoral degree (1967) in Fluid Mechanics and Mathematics from the Johns Hopkins University. Most of his career is in NASA, where he had served as Research Scientist and Senior Fellow at NASA Goddard Space Flight Center (1975-2006) and the Chief Scientist for Ocean Sciences NASA from 2000 to 2006. He had also taken time to serve as a Faculty Associate in the Engineering Division, the California Institute of Technology (1997 to 2003). While working in NASA, he had developed a new adaptive Hilbert-Huang Transform (HHT), specifically designed to analyze nonstationary and nonlinear time series. For this invention, he was awarded the 1998 NASA Special Space Act Award with the citation, ‘[Dr. Huang’s new method] is one of the most important discoveries in the field of applied mathematics in NASA history.’ The details of HHT are covered in many patents by NASA; and his initial paper on HHT has been cited near13,000 times (Google Scholar). “For contributions to the analysis of nonlinear stochastic signals and related mathematical applications in engineering, biology, and other sciences (NAE Citation),” he was elected as members of the US National Academy of Engineering, 2000; Academia Sinica, 2004; and a Foreign Member of the Chinese Academy of Engineering, 2006.
Over the last few years, he has engaged in applications in biomedical areas by establishing a Joint Center for Dynamical Biomarkers and Translational Medicine at NCU with Professor Chung Kang Peng, as the Co-Director, from Margret and H.A.Rey Institute for Nonlinear Dynamics in Physiology & Medicine, Division of Interdisciplinary Medicine, Beth Israel Deaconess Medical Center, Harvard Medical School.
Recently, he has found deficiencies on HHT. As a result, he had developed the Holo-Hilbert Spectral Analysis (HHSA), and intrinsic Probability Distribution Function (iPDF) which give a new view of the data in the spectral and probabilistic representations fully considered nonlinear multiplicative effects of the physical processes. Applications of HHSA and iPDFon EEG and turbulence datais the area of his active research currently. The basic methodology on HHSA has just appeared in a special issue of the Philosophical Transactions, Royal Society of London, co-edited by him and Professors Ingrid Daubechies of Duke University and Thomas Y. Hou of Caltech. Furthermore, the application of the method to EEG and brain science has attracted formal collaborations with Beth Israel Deaconess Medical Center/Harvard Medical School and Oxford University Center for Human Brain Activity for general brain science and mental diseases, and Stanford Medical School on sleep science and medicine.
