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 and Stationary

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 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.

The Job of a Scientist

Data Analysis

Data analysis is too important to be left to the mathematicians.

Why?!

Different Paradigms IMathematics vs. Science/Engineering

• Mathematicians

• Absolute proofs

• Logic consistency

• Mathematical rigor

• Scientists/Engineers

• Agreement with observations

• Physical meaning

• Working Approximations

Different Paradigms IIMathematics 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

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 Analysis

HHT

Empirical Mode Decomposition: Methodology : Test Data

Empirical Mode Decomposition: Methodology : data and m1

Empirical Mode Decomposition: Methodology : IMF c1

Empirical Mode Decomposition: Methodology : data & r1

Definition of Frequency

Given the period of a wave as T ; the frequency is defined as

1.

T

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 .

Instantaneous Frequency

distanceVelocity ; mean velocity

time

dxNewton v

dt

1Frequency ; mean frequency

period

dHH

So that both v and

T defines the p

can appear in differential equations.

hase functiondt

Jean-Baptiste-Joseph Fourier

1807 “On the Propagation of Heat in Solid Bodies”

1812 Grand 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.’

1817 Elected to Académie des Sciences

1822 Appointed as Secretary of Math Section

paper published

Fourier’s work is a great mathematical poem. Lord Kelvin

Comparison between FFT and HHT

j

j

t

i t

jj

i ( )d

jj

1. FFT :

x( t ) a e .

2. HHT :

x( t ) a ( t ) e .

Comparisons: Fourier, Hilbert & Wavelet

Speech Analysis

Nonlinear and nonstationary data

Speech Analysis Hello : Data

Four comparsions D

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

Philosophical Problem

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

Global Temperature Anomaly 1856 to 2003

IMF Mean of 10 Sifts : CC(1000, I)

Mean IMF

Data and Trend C6

Data and Overall Trends : EMD and Linear

Rate of Change Overall Trends : EMD and Linear

Variability with Respect to Overall trend

Data and Trend C5:6

Data and Trends: C5:6

Variability with Respect to 65-Year trend

Climate Change &

Global Warming

Is it natural or man made?

Milankovitch Theory

Astronomical theory of climate change

A Truly Nonlinear World

Milutin Milankovitch 1879-1958

Milankovitch Cycles

Precession : 21 – 26 Kyrs

Obliquity : 40 Kyrs

Eccentricity : 100 Kyrs

Eccentricity = 0

Eccentricity = 0.5

European Project for Ice Coring in Antarctica: (800,000 years of

climate and) 650,000 years of CO2 from ice cores

Eric Wolff

(ewwo@bas.ac.uk)

On behalf of the EPICA community

European Project for Ice Coring in Antarctica (EPICA)

Dome C75ºS

3233 m asl~25 kg m-2 yr-1

0km 1 ,000km 2 ,000km

80S°

70S°

60S°

Vo sto k

Do m e F

Ta ylo rDo m e

Byrd

Dro nn ingM a ud La nd

Sip le Do m e

Do m e CLa w Do m e

Be rkne rIsla nd

Dome C

Comparison between Dome C with Vostok

-480

-440

-400

-360

0 200 400 600 800

EPICADome C

Vostok

Age / kyr BP

D /

‰

Deuterium Data vs. Age

Deuterium Data IMF

Deuterium Data and IMF(5:7)

Deuterium Data and IMF(4:7)

Deuterium Data and IMF(3:7)

Deuterium Data and IMF(2:7)

Deuterium Data IMF(1) and IMF(2:7)

A Truly Nonlinear World

Current Applications

• Non-destructive Evaluation for Structural Health Monitoring – (DOT, NSWC, and DRC/NASA, KSC Shuttle, ITRI)

• Bio-medical applications– (Harvard, UCSD, Johns Hopkins, Tai-Da, VAGH Taiwan, and Cathy Hospital,

NIH)• Vibration, speech, and acoustic signal analyses

– (FBI, MIT, and DARPA)• Earthquake Engineering

– (DOT)• Global Primary Productivity Evolution map from LandSat data

– (NASA Goddard)• Cosmological Gravity Wave and Planets hunting

– (NASA Goddard )• Financial market data analysis

– (NCU)• Climate, Global Warming

– (NCU, NASA)• Biomedical signal and HHT Chip

– (ITRI)• Wind and Ocean Energy

– (ITRI, INER)

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。

My Approach

• I do not like to be bounded by rules and traditions

• I draw strength from the mixture of my Science and Engineering ground

• Science is to explain what is;• Engineering is to build what is not.

• How to build what is not?• Looking for working approximations• Challenge the tradition• Think the unthinkable

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。

My variable background

• Reading widely and thinking practically

• My firm believe in fundamentals

• Talking with smart people around you

• By Luck and be adaptive:– Luck is when an adversity turns to become an a

dvantage. ----My definition

– 從建中到竹中– 從結構到流力– 從流力到海洋– 從海洋到數據分析

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。

Loneliness

• Any time one engaged in changing the traditions, he will be lonely: just like any revolutionary.

• In science, we are luckier than in any other field, for there is an objective view and references: the evidences, the data.

• Even though, there are plenty of examples when a new idea had been attacked mercilessly.

• Loneliness comes mostly from the lack of understanding and appreciation!

Who is this?

Charles Darwin (1809-1882)

Oliver Heaviside (1850-1925)

Why should I refuse a good dinner simply because I don't understand the digestive processes involved.

Whenever I do feel lonely, mostly from the lack of understanding, I would think of van Gogh. Then, I would feel

how lucky I am.

And, I asking bigger Questions to keep me mind occupied:

How to be an educated person?

This is also a way to educate myself,

a process I have kept all my life.

Necessary Conditions

An educated person should know himself; therefore, he should be able to

answer the following questions:

– Who am I?– Where am I?– How do I get here?

Who am I?

• I think, therefore I am.– Rene Descartes 1569-1650

Discourse on the Method Principles of Philosophy

• To be able to think

• The material forms the thoughts is knowledge

Where am I?• The Universe:

Where am I?• There are 125 Billions of Galaxies in the Universe

Where am I?

• How do we find out this?

• It is an amazing achievement that we figure out the way the universe evolves to the present.

• 200~400 Billion stars

• Scale to 130 km in diameter, solar system would be only 2 mm wide.

A Pale Blue Dot:

Seen from 6 billion kilometers away, at the edge of the solar system, Earth is a pale blue dot obscured in a beam of scattered sunlight.

Carl Sagan (1934-1996) That's here. That's home. That's us. On it, everyone

you ever heard of, every human being who ever lived, lived out their lives. The aggregate of all our joys and sufferings, thousands of confident religions, ideologies and economic doctrines, every hunter and forager, every hero and coward, every creator and destroyer of civilizations, every king and peasant, every young couple in love, every hopeful child, every mother and father, every inventor and explorer, every teacher of morals, every corrupt politician, every superstar, every supreme leader, every saint and sinner in the history of our species, lived there on a mote of dust, suspended in a sunbeam.

May 11, 1996

How do I get here?

• We are all made of star dust.

• We get here through billions of years of changes. The odds against me to be here are enormous.

• Treasure the chance of my live. 莫等閒白了少年頭

I want to know the history of everything, including myself. I have the whole Universe to explore; then I would hardly find time to be lonely.

The way to lead a live as an Educated Person

• Keep healthy Curiosity– Always ask why?

• Quest for Truth constantly – Veritas; Veritas vos Liberatib

• Pursuit of Happiness– You can be happy only when all around you are happy.

• Maintain your Health– Keep a healthy habit

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。

Read more biographies of famous scientists, the iconoclastic kind, to find out how they had made new discoveries.

And be ready when Luck knocks at your door.

Thank you!