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隨波遂流 Riding the Waves and Following the Flow. Norden E. Huang 黄鍔 數據分析研究中心. My life is almost like a random walk. Though I have had a firm plan, I get here almost all by chance. Chance or Luck?. Luck is when an adversity turns to become an advantage. ---- My definition 從建中到竹中
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隨波遂流Riding the Waves and Following the Flow Norden E. Huang 黄鍔 數據分析研究中心
My life is almost like a random walk. Though I have had a firm plan, I get here almost all by chance.
Chance or Luck? • Luck is when an adversity turns to become an advantage. ----My definition • 從建中到竹中 • 從結構到流力 (遂流) • 從流力到海洋 (隨波) • 從海洋到數據分析 • 萬頃波中得自由
The best a scientist can give is the results not his philosophy. I am forced to violate this tenet today.
My assignments today • a.我的研究（與專業）簡介。 • b.如何尋找與訂定研究題目。 • c.研究過程中所遭遇的困難與克服方法。 • d.學習途中最大的幫助從何而來？ • e.學術路途寂寞嗎？如何排解與休閒？ • f.推薦相關領域或個人具代表性著作為延伸閱讀書目。
Science vs. Philosophy Data and Data Analysis are what separate science from philosophy: With data we are talking about sciences; Without data we can only discuss philosophy.
Henri Poincaré Science is built up of facts*, as a house is built of stones; but an accumulation of facts is no more a science than a heap of stones is a house. * Here facts are indeed data.
Data and Data Analysis Data Analysis is the key step in converting the ‘facts’ into the edifice of science. It is also the only means we can find the truth and the connect to the reality: It infuses meanings to the cold numbers, and lets data telling their own stories and singing their own songs. Un-examined facts yield no truth.
Ever since the advance of computer, there is an explosion of data. The situation has changed from a thirsty for data to that of drinking from a fire hydrant.
Data and Data Analysis Data and Data Analysis are crucial for every single scientific and engineering endeavor, For data are the only connects between us and the real world.
Data Processing and Data Analysis • Processing [proces < L. Processus < pp of Procedere = Proceed: pro- forward + cedere, to go] : A particular method of doing something. • Data Processing >>>> Mathematically meaningful parameters • Analysis [Gr. ana, up, throughout + lysis, a loosing] : A separating of any whole into its parts, especially with an examination of the parts to find out their nature, proportion, function, interrelationship etc. • Data Analysis >>>> Physical understandings
Scientific Activities Collecting, analyzing, synthesizing, and theorizing are the core of scientific activities. Theory without data to prove is just hypothesis. Therefore, data analysis is a key link in this continuous loop.
My assignments today • a.我的研究（與專業）簡介。 • b.如何尋找與訂定研究題目。 • c.研究過程中所遭遇的困難與克服方法。 • d.學習途中最大的幫助從何而來？ • e.學術路途寂寞嗎？如何排解與休閒？ • f.推薦相關領域或個人具代表性著作為延伸閱讀書目。
Motivations for alternatives: Problems for Traditional Methods • Physical processes are mostly nonstationary • Physical Processes are mostly nonlinear • Data from observations are invariably too short • Physical processes are mostly non-repeatable. Ensemble mean impossible, and temporal mean might not be meaningful for lack of stationarity and ergodicity. Traditional methods are inadequate.
Traditional Data Analysis All traditional ‘data analysis’ methods are either developed by or established according to mathematician’s rigorous rules. In pursue of mathematic rigor and certainty, however, we are forced to idealize, but also deviate from, the reality.
Traditional Data Analysis As a result, we are forced to live in a pseudo-real world, in which all processes are Linear andStationary Nonlinear: When input and output are not proportional Nonstationary: When the mean does not make sense
削足適履 Trimming the foot to fit the shoe.
Available Data Analysis Methodsfor Nonstationary (but Linear) time series • Spectrogram • Wavelet Analysis • Wigner-Ville Distributions • Empirical Orthogonal Functions aka Singular Spectral Analysis • Moving means • Successive differentiations
Available Data Analysis Methodsfor Nonlinear (but Stationary and Deterministic) time series • Phase space method • Delay reconstruction and embedding • Poincaré surface of section • Self-similarity, attractor geometry & fractals • Nonlinear Prediction • Lyapunov Exponents for stability
Typical Apologia • Assuming the process is stationary …. • Assuming the process is locally stationary …. • As the nonlinearity is weak, we can use perturbation approach …. Though we can assume all we want, but the reality cannot be bent by the assumptions.
掩耳盜鈴 Stealing the bell with muffed ears
Rigor vs. Reality Mathematics are well and good but nature keeps dragging us around by the nose.Quoted in A P French, Einstein: a Centenary Volume Albert Einstein
The Job of a Scientist The job of a scientist is to listen carefully to nature, not to tell nature how to behave. Richard Feynman To listen is to use adaptive method and let the data sing, and not to force the data to fit preconceived modes.
Data Analysis Data analysis is too important to be left to the mathematicians. Why?!
Mathematicians Absolute proofs Logic consistency Mathematical rigor Scientists/Engineers Agreement with observations Physical meaning Working Approximations Different Paradigms IMathematics vs. Science/Engineering
Mathematicians Idealized Spaces Perfect world in which everything is known Inconsistency in the different spaces and the real world Scientists/Engineers Real Space Real world in which knowledge is incomplete and limited Constancy in the real world within allowable approximation Different Paradigms IIMathematics vs. Science/Engineering
An Adaptive Data Analysis Method • No a priori basis, but the basis is based on and derived from the data • Frequency is determined not through integral transform but by differentiation, which gives instantaneous frequency • Nonlinearity and nonstationarity are not represented by the harmonics but by the intra-wave frequency modulation through time variation of the instantaneous frequency
The Empirical Mode Decomposition Method and Hilbert Spectral AnalysisHHT
Definition of Frequency Given the period of a wave as T ; the frequency is defined as
Equivalence : The definition of frequency is equivalent to defining velocity as Velocity = Distance / Time
Equivalence : • The definition of frequency is equivalent to defining velocity as Velocity = Distance / Time • But velocity should be V = dS / dt .
Jean-Baptiste-Joseph Fourier • “On the Propagation of Heat in Solid Bodies” • 1812Grand Prize of Paris Institute • “Théorie analytique de la chaleur” • ‘... the manner in which the author arrives at these equations is not exempt of difficulties and that his analysis to integrate them still leaves something to be desired on the score of generality and even rigor.’ • Elected to Académie des Sciences • Appointed as Secretary of Math Section • paper published Fourier’s work is a great mathematical poem.Lord Kelvin
Speech Analysis Nonlinear and nonstationary data
On Trend A simple but stayed unresolved for a long time.
The State-of-the-Arts“One economist’s trend is another economist’s cycle”Engle, R. F. and Granger, C. W. J. 1991 Long-run Economic Relationships. Cambridge University Press. • Simple trend – straight line • Stochastic trend – straight line for each quarter
PhilosophicalProblem 名不正則言不順 言不順則事不成 ——孔夫子
Definition of the Trend Within the given data span, the trend is an intrinsically determined monotonic function, or a function in which there can be at most one extremum. The trend should be determined by the same mechanisms that generate the data; it should be an intrinsic and local property. Being intrinsic, the method for defining the trend has to be adaptive. The results should be intrinsic (objective); all traditional trend determination methods give extrinsic (subjective) results. Being local, it has to associate with a local length scale, and be valid only within that length span as a part of a full wave cycle.
Global Temperature Anomaly Annual Data from 1856 to 2003
