1. National Chiao Tung University MVEMD vs. MDEMD + Applications in EEG & Gait Analyses John K. Zao Computer Science Dept. & Brain Research Center National Chiao Tung University, Taiwan 2013/08/29 1 2013/8/29 MEMD Improvement & Apps

2. National Chiao Tung UniversityAgenda  EMD vs. MVEMD vs. MDEMD  MVEMD with PCA  Application in Gait & EEG Analysis  On-line & Light-weight Enhancements 2 2013/8/29 MEMD Improvement & Apps

3. National Chiao Tung University Empirical Mode Decomposition (EMD)  Proposed by Dr. Norden E. Huang (1998)  Useful for non-linear non-stationary signal analysis  Decompose signals into Intrinsic Mode Functions (IMFs) using sifting processing  IMFs capture oscillations at different speeds 3

4. National Chiao Tung University Empirical Mode Decomposition Methodology : Original Signal Source: NCU Lecture Slides 4

5. National Chiao Tung University Empirical Mode Decomposition Methodology : Original & m1 Signal 5 Source: NCU Lecture Slides

6. National Chiao Tung University Empirical Mode Decomposition: Methodology : Original & h1 Signal 6 Source: NCU Lecture Slides

7. National Chiao Tung University M(V)EMD vs. MDEMD 2013/8/29 MEMD Improvement & Apps 7

8. National Chiao Tung University Multivariate Empirical Mode Decomposition (MVEMD)  Decompose the trajectory of a vector into rotations at different speeds  Find the envelop of trajectory  Find the “center” of envelop  Obtain the rotating component by removing the trajectory of the center Questions:  How to find the envelop?  How to find its “center”? 2013/8/29 MEMD Improvement & Apps 8 Source: BEMD & MEMD paper

9. National Chiao Tung University Sifting based on Omnidirectional Projection  Find the envelop of the trajectory by identifying the extrema of its projection in “evenly spread” directions  Evenly spread direction vectors in n-dimensional space can be found by placing evenly distributed points on n-sphere using quasi-Monte Carlo methods based on Hammersley sequences. Beware of the “curse of dimensionality”!  Extrema of the projection of the trajectory can be found using two methods: a) Find the centroids of the extrema  more sensitive to sampling errors b) Find the mid-points of projection coordinates  more robust against sampling errors  Algorithm (b) corresponds to 1D shifting along each projection directions  Projections in evenly spread directions are used to reduce estimation errors of local mean since trajectory orientation is unknown.  Is it really needed?! 2013/8/29 MEMD Improvement & Apps 9

10. National Chiao Tung University Multidimensional Empirical Mode Decomposition (MDEMD)  Decompose the profile of a scalar field into n-dimensional oscillations  Identify extrema of the profile  Problems created by saddle points, ridges and valleys  Create n-dimensional spline surfaces over the extrema  No simple way to construct n-dimensional spline surfaces  Several methods for 2D spline fitting  Radial Based Function  Thin Plate Interpretation  Delaunay Triangulation  By Slicing  Non-Uniform Rational B-Spline

11. National Chiao Tung University MDEMD based on EEMD & Min-Scale Combination … … … ……… … 2D-IMF- 1 2D-IMF- 2 2D-IMF- n Final 2D- Decompositions: 2D- Residual 2D Image

12. National Chiao Tung University MVEMD with PCA Preprocessing 2013/8/29 MEMD Improvement & Apps 12

13. National Chiao Tung University PCA + MVEMD Separate 6D signals to two sets of 3D signals to do PCA (3D PCA) Recombine two sets of 3D principal components to do MEMD (6D MEMD) and get same numbers IIMFs Ax Ay Az 3D PCA Gx Gy Gz 3D PCA Linear Acceleration Angular Velocity 6D MEMD PCA1 PCA2 PCA3 PCA1 PCA2 PCA3 PCA1 IMFs PCA2 IMFs PCA3 IMFs PCA1 IMFs PCA2 IMFs PCA3 IMFs 13 2013/8/29 MEMD Improvement & Apps

14. National Chiao Tung University Principal Component Analysis (PCA) After analyzing, we can get  eigenvectors  eigenvalues Use orthogonal transformation Reduce signal space dimensions 原資料分析後 14 2013/8/29 MEMD Improvement & Apps

15. National Chiao Tung University 3D PCA Linear accelerations and angular velocities must be separated Do the whitening processing The unit-variance property of the whitened principal components enhances the ability of MEMD (a)Original signals (b)Principle Components (a) is original signal ， (b) is principal components 15 2013/8/29 MEMD Improvement & Apps

16. National Chiao Tung University 6D MVEMD Recombine two sets of 3D principal components Separate the each sets input signals into a set of IMFs that distinct frequency bands Each input signals will get the same number of IMFs 16 2013/8/29 MEMD Improvement & Apps

17. National Chiao Tung University Selection of PCA IMFs 2013/8/29 MEMD Improvement & Apps 17 IMF1IMF2IMF3IMF4IMF5IMF6IMF7IMF8IMF9Residue PCA10.38792.87072.69561.39872.09680.03400.00120.00310.00130.0069 PCA20.07170.27330.34550.74732.96350.23500.04690.36450.17290.6617 PCA30.13970.12520.07250.14170.03281.00510.02050.03020.01170.0944

18. National Chiao Tung University Construction of Characteristic Waveforms  Derived from PCA IMFs of linear accelerations  Gait cycle IMFs are selected first  Remove gait cycles and trend IMFs  Do the Gaussian distribution curve fitting  Impact IMFs are constructed from IMFs fall into the main lobe of Gaussian distribution 18 2013/8/29 MEMD Improvement & Apps

19. National Chiao Tung University Gaiting Characteristic Waveforms 2013/8/29 MEMD Improvement & Apps 19

20. National Chiao Tung University Feature Extractions Amplitude Modulation components － signal’s time-varying amplitude Frequency Modulation components － signal’s time-varying frequency Peak points － when cause the stepping impacts Phase Offset － whether the 3 axes are phase-locked Trend － the changing direction of whole signal 20 2013/8/29 MEMD Improvement & Apps

21. National Chiao Tung University Amplitude Modulation Components (AM) Find local extrema Perform cubic-spine interpolation through extrema Change of amplitudes reflects changes of step sizes 21 2013/8/29 MEMD Improvement & Apps

22. National Chiao Tung University Frequency Modulation components (FM) Calculate instantaneous frequency using Generalized Zero Crossing (GZC)Observation Changes of frequency reflect changes in gaiting speed 22 2013/8/29 MEMD Improvement & Apps

23. National Chiao Tung University Phase Offset Deduced from time offsets between IMF zero-crossing points 23 2013/8/29 MEMD Improvement & Apps

24. National Chiao Tung University Impact Points Calculate instantaneous periods and use them as sliding windows Find the local maxima within the sliding windowsObservation Every impact point indicates an impact of the feet with the ground 24 2013/8/29 MEMD Improvement & Apps

25. National Chiao Tung UniversityTrend The last IMF corresponds to the trend signal Plot the trend signals into 3D spaceObservation The trend of 3D linear acceleration corresponds to the general motion directions of the human subject 25 2013/8/29 MEMD Improvement & Apps

26. National Chiao Tung University SSVEP Stimulation ColorFrequency (Hz) Luminanc e (cd/m 2 ) Duty Cycle (%) RED3215320 ※ MEEMD & MVEMD Analyses with 2 10-sec segments 50 sec recording 5~15 sec Segment (f10) 35~45 sec Segment (s10)

27. National Chiao Tung University Signal Processing

28. National Chiao Tung University PCA Component Retrieval  EEGLAB function “runpca”  [pc,eigvec,sv] = runpca(EEG.data)  Select first 6 components from ‘pc’

29. National Chiao Tung University f10 中 20.8~22.8 秒 約 32Hz 波型圖 由上到下為 PCA1, PCA2, PCA3, PCA4, PCA5, PCA6

30. National Chiao Tung University 約 16Hz 波型圖 由上到下為 PCA1, PCA2, PCA3, PCA4, PCA5, PCA6

31. National Chiao Tung University >64Hz 波型圖 由上到下為 PCA1, PCA2, PCA3, PCA4, PCA5, PCA6

32. National Chiao Tung University Residue 波型圖 由上到下為 PCA1, PCA2, PCA3, PCA4, PCA5, PCA6

33. National Chiao Tung University f10 中 20.8~22.8 秒 約 32Hz 等高線圖 由上到下為 PCA1, PCA2, PCA3, PCA4, PCA5, PCA6

34. National Chiao Tung University 約 16Hz 等高線圖 由上到下為 PCA1, PCA2, PCA3, PCA4, PCA5, PCA6

35. National Chiao Tung University >64Hz 等高線圖 由上到下為 PCA1, PCA2, PCA3, PCA4, PCA5, PCA6

36. National Chiao Tung University Residue 等高線圖 由上到下為 PCA1, PCA2, PCA3, PCA4, PCA5, PCA6

37. National Chiao Tung University Channel Signal Reconstruction  ICA and Bad Component Removal  EEGLAB -> Edit -> Select Data -> Data Range (Fz, FCz, Cz, Pz, POz, Oz)

38. National Chiao Tung University LWH _ 32R – Fz 、 FCz 、 Cz 、 Pz 、 POz 、 Oz C1 C2 C3 原 DATA

39. National Chiao Tung University f10 中 20.8~22.8 秒 約 32Hz 波型圖 由上到下為 Fz, FCz, Cz, Pz, POz, Oz

40. National Chiao Tung University 約 16Hz 波型圖 由上到下為 Fz, FCz, Cz, Pz, POz, Oz

41. National Chiao Tung University >64Hz 波型圖 由上到下為 Fz, FCz, Cz, Pz, POz, Oz

42. National Chiao Tung University Residue 波型圖 由上到下為 Fz, FCz, Cz, Pz, POz, Oz

43. National Chiao Tung University f10 中 20.8~22.8 秒 約 32Hz 等高線圖 由上到下為 Fz, FCz, Cz, Pz, POz, Oz

44. National Chiao Tung University 約 16Hz 等高線圖 由上到下為 Fz, FCz, Cz, Pz, POz, Oz

45. National Chiao Tung University >64Hz 等高線圖 由上到下為 Fz, FCz, Cz, Pz, POz, Oz

46. National Chiao Tung University Residue 等高線圖 由上到下為 Fz, FCz, Cz, Pz, POz, Oz