1. An Adaptive Data Analysis Method with Some Biomedical Applications Norden E. Huang Research Center for Adaptive Data Analysis National Central University 2008

2. Data and Data Analysis Data are the our only connection to the reality. We are overwhelmed by the quantity of the data, But underserved by the quality of the analysis.

3. 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

4. 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. * Unexamined facts (data) are useless!

5. Scientific Activities Collecting, analyzing, synthesizing, and theorizing are the core of scientific activities. Data are our only connection to reality; they are also what separate science from philosophy. Therefore, data analysis is a key link in this continuous loop.

6. Data Analysis Data analysis is too important to be left to the mathematicians. Why?!

7. Different Paradigms I Mathematics vs. Science/Engineering Mathematicians Absolute proofs Logic consistency Mathematical rigor Scientists/Engineers Agreement with observations Physical meaning Working Approximations

8. Different Paradigms II Mathematics 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

9. Rigor vs. Reality As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality. Albert Einstein

10. Traditional Data Analysis In pursue of mathematic rigor and certainty, however, we are forced to idealize, but also deviate from, the reality. As a result, we are forced to live in a pseudo- real world, in which all processes are Linear and Stationary

11. 削足適履 Trimming the foot to fit the shoe.

12. Available ‘ Data Analysis ’ Methods for Nonstationary (but Linear) time series Spectrogram Wavelet Analysis Wigner-Ville Distributions Empirical Orthogonal Functions aka Singular Spectral Analysis Moving means Successive differentiations

13. Available ‘ Data Analysis ’ Methods for Nonlinear (but Stationary and Deterministic) time series Phase space method Delay reconstruction and embedding Poincar é surface of section Self-similarity, attractor geometry & fractals Nonlinear Prediction Lyapunov Exponents for stability

14. 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.

15. 掩耳盜鈴 Stealing the bell with muffed ears

16. 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.

17. 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

18. Characteristics of Data from Nonlinear Processes

19. Duffing Pendulum x

20. Duffing Equation : Data

21. Hilbert Transform : Definition

22. Hilbert Transform Fit

23. The Traditional View of the Hilbert Transform for Data Analysis

24. Traditional View a la Hahn (1995) : Data LOD

25. Traditional View a la Hahn (1995) : Hilbert

26. Why the traditional approach does not work?

27. Hilbert Transform a cos  + b : Data

28. Hilbert Transform a cos  + b : Phase Diagram

29. Hilbert Transform a cos  + b : Phase Angle Details

30. Hilbert Transform a cos  + b : Frequency

31. The Empirical Mode Decomposition Method and Hilbert Spectral Analysis Sifting

32. Empirical Mode Decomposition: Methodology : Test Data

33. Empirical Mode Decomposition: Methodology : data and m1

34. Empirical Mode Decomposition: Methodology : data & h1

35. Empirical Mode Decomposition: Methodology : h1 & m2

36. Empirical Mode Decomposition: Methodology : h3 & m4

37. Empirical Mode Decomposition: Methodology : h4 & m5

38. Empirical Mode Decomposition Sifting : to get one IMF component

39. The Stoppage Criteria The Cauchy type criterion: when SD is small than a pre-set value, where

40. Empirical Mode Decomposition: Methodology : IMF c1

41. Definition of the Intrinsic Mode Function (IMF)

42. Empirical Mode Decomposition: Methodology : data, r1 and m1

43. Empirical Mode Decomposition Sifting : to get all the IMF components

44. Definition of Instantaneous Frequency

45. Definition of Frequency Given the period of a wave as T ; the frequency is defined as

46. Instantaneous Frequency

47. The combination of Hilbert Spectral Analysis and Empirical Mode Decomposition is designated as HHT (HHT vs. FFT)

48. 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

49. Comparison between FFT and HHT

50. Comparisons: Fourier, Hilbert & Wavelet

51. Speech Analysis Hello : Data

52. Four comparsions D

53. An Example of Sifting

54. Length Of Day Data

55. LOD : IMF

56. Orthogonality Check Pair-wise % 0.0003 0.0001 0.0215 0.0117 0.0022 0.0031 0.0026 0.0083 0.0042 0.0369 0.0400 Overall % 0.0452

57. LOD : Data & c12

58. LOD : Data & Sum c11-12

59. LOD : Data & sum c10-12

60. LOD : Data & c9 - 12

61. LOD : Data & c8 - 12

62. LOD : Detailed Data and Sum c8-c12

63. LOD : Data & c7 - 12

64. LOD : Detail Data and Sum IMF c7-c12

65. LOD : Difference Data – sum all IMFs

66. Traditional View a la Hahn (1995) : Hilbert

67. Mean Annual Cycle & Envelope: 9 CEI Cases

68. Properties of EMD Basis The Adaptive Basis based on and derived from the data by the empirical method satisfy nearly all the traditional requirements for basis a posteriori: Complete Convergent Orthogonal Unique

69. Hilbert ’ s View on Nonlinear Data

70. Duffing Equation

71. Duffing Equation : Data

72. Duffing Equation : IMFs

73. Duffing Equation : Hilbert Spectrum

74. Duffing Equation : Detailed Hilbert Spectrum

75. Duffing Equation : Wavelet Spectrum

76. Duffing Equation : Hilbert & Wavelet Spectra

77. What This Means Instantaneous Frequency offers a total different view for nonlinear data: instantaneous frequency with no need for harmonics and unlimited by uncertainty. Adaptive basis is indispensable for nonstationary and nonlinear data analysis HHT establishes a new paradigm of data analysis

78. Comparisons FourierWaveletHilbert Basisa priori Adaptive FrequencyIntegral Transform: Global Integral Transform: Regional Differentiation: Local PresentationEnergy-frequencyEnergy-time- frequency Nonlinearno yes Non-stationarynoyes Uncertaintyyes no Harmonicsyes no

79. Application of Hilbert Huang Transform in Cerebral Blood Flow Regulation Multimodal pressure-flow method to assess dynamics of cerebral auto-regulation By Dr. Lo Meng-Yzung of RCADA, NCU and the Harvard Medical School, Division of Inter-disciplinary Medicine.

80. Valsalva Maneuver Dynamics I. Expiration - mechanical II. reduced venous return, BP falls III. Inspiration - mechanical IV. increased cardiac output and increased peripheral resistance

81. Valsalva Maneuver Dynamics Blood Pressure Blood Flow Velocity – Right Middle Cerebral Artery Blood Flow Velocity – Left Middle Cerebral Artery

82. Empirical Mode Decomposition Original blood pressure waveform Key mode of blood pressure waveform during Valsalva maneuver

83. Blood pressure versus blood flow velocity Temporal (time) Relationship

84. Blood pressure versus blood flow velocity Phase Relationship Control Stroke

85. EEMD can easily identify blood pressure oscillations induced by the spontaneous breathing (0.4~0.15 Hz, i.e. period 2.5~7 sec)

86. Cerebral Auto-regulation in stroke patients 86 Hu K, Peng CK, Lo MT, Zhao P, LaRose S, Novak P, Selim M, Lipsitz LA, Novak V (2008) Assessment of Cerebral Autoregulation from Spontaneous Blood Pressure and Cerebral Blood Flow Fluctuations. Stroke (abstract, accepted for publication)

87. Cerebral Auto-regulation in diabetes 87 Hu K, Peng CK, Huang NE, et al. (2008) Altered phase interactions between spontaneous blood pressure and flow fluctuations in Type 2 diabetes mellitus: Nonlinear assessment of cerebral autoregulation. Physica A 387 2279– 2292.

88. Compare with Transfer Function Analysis (Fourier based method) for Diabetes with Valsalva maneuver.

89. Identify the epoch with unwanted interference

90. Nonlinear pressure-flow relationship is able to detect asymmetry of brain blood circulation associated with midline shift Dr. Marek Czosnyka, UK neuroscience

91.  Association between the midline shift and left-right difference in BP-BFV phase shift The difference in BP-BFV phase shifts between the right and left hemispheres was positively correlated to midline shift of the brain

92. Image Analysis We have extended HHT to multi-dimensional data; A patent is being filed.

93. Image analysis by bidimensional empirical mode decomposition J.C. Nunes*, Y. Bouaoune, E. Delechelle, O. Niang, Ph. Bunel Image and Vision Computing, 2003

95. Conclusion Adaptive method is the only scientifically meaningful way to analyze data. It is the only way to find out the underlying physical processes; therefore, it is indispensable in scientific research. It is physical, direct, and simple. But, we have only started and what we have done is only a scratch of the surface.

96. Many of the most significant and interesting challenges of the modern world require boundary-crossing collaborations among scientists and scholars with widely different fields of expertise. Allison Richard Vice Chancellor, Cambridge University

97. Current Applications Non-destructive Evaluation for Structural Health Monitoring –(DOT, NSWC, and DFRC/NASA, KSC/NASA Shuttle) Vibration, speech, and acoustic signal analyses –(FBI, MIT, and DARPA) Earthquake Engineering –(DOT) Bio-medical applications –(Harvard, UCSD, Johns Hopkins) Global Primary Productivity Evolution map from LandSat data –(NASA Goddard, NOAA) Cosmological Gravity Wave –(NASA Goddard) Financial market data analysis –(NCU)

98. History of HHT 1998: The Empirical Mode Decomposition Method and the Hilbert Spectrum for Non-stationary Time Series Analysis, Proc. Roy. Soc. London, A454, 903-995. The invention of the basic method of EMD, and Hilbert transform for determining the Instantaneous Frequency and energy. 1999: A New View of Nonlinear Water Waves – The Hilbert Spectrum, Ann. Rev. Fluid Mech. 31, 417-457. Introduction of the intermittence in decomposition. 2003: A confidence Limit for the Empirical mode decomposition and the Hilbert spectral analysis, Proc. of Roy. Soc. London, A459, 2317-2345. Establishment of a confidence limit without the ergodic assumption. 2004: A Study of the Characteristics of White Noise Using the Empirical Mode Decomposition Method, Proc. Roy. Soc. London, A460, 1597-1611 Defined statistical significance and predictability. 2007: On the trend, detrending, and variability of nonlinear and nonstationary time series. Proc. Natl. Acad. Sci., 104, 14,889-14,894. The correct adaptive trend determination method 2009: On Ensemble Empirical Mode Decomposition. Advances in Adaptive Data Analysis 1, 1-41. 2009: On instantaneous Frequency. Advances in Adaptive Data Analysis (Accepted)

99. Advances in Adaptive data Analysis: Theory and Applications A new journal to be published by the World Scientific Under the joint Co-Editor-in-Chief Norden E. Huang, RCADA NCU Thomas Yizhao Hou, CALTECH To be launched in the March 2008