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MVEMD vs. MDEMD + Applications in EEG & Gait Analyses

This paper explores the advantages and applications of Multivariate Empirical Mode Decomposition (MVEMD) and Multidimensional Empirical Mode Decomposition (MDEMD) in the analysis of EEG signals and gait data. The paper discusses enhancements to the MEMD method and the use of principal component analysis (PCA) in MVEMD.

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MVEMD vs. MDEMD + Applications in EEG & Gait Analyses

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  1. 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 MEMD Improvement & Apps

  2. Agenda • EMD vs. MVEMD vs. MDEMD • MVEMD with PCA • Application in Gait & EEG Analysis • On-line & Light-weight Enhancements MEMD Improvement & Apps

  3. Empirical Mode Decomposition (EMD) • Proposed by Dr. NordenE. 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

  4. Empirical Mode Decomposition Methodology : Original Signal Source: NCU Lecture Slides

  5. Empirical Mode Decomposition Methodology : Original & m1 Signal Source: NCU Lecture Slides

  6. Empirical Mode Decomposition: Methodology : Original & h1 Signal Source: NCU Lecture Slides

  7. M(V)EMD vs. MDEMD • Multivariate EMD (MVEMD) • Treats data from each channel as the coordinate of a time-varying vector in a vector space • Multidimensional EMD (MDEMD) • Treats data from each channel asthe value of a time-varying scalarover a parameter space MEMD Improvement & Apps

  8. 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”? Source: BEMD & MEMD paper MEMD Improvement & Apps

  9. 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: • Find the centroids of the extrema  more sensitive to sampling errors • 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?! MEMD Improvement & Apps

  10. MultidimensionalEmpirical 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. MDEMD based on EEMD & Min-Scale Combination … … … … … … … 2D Image Final 2D-Decompositions: 2D-Residual 2D-IMF-1 2D-IMF-2 2D-IMF-n

  12. MVEMD with PCA Preprocessing • Signal Re-orientation according to its Principal components • Signal Whitening according to its eigenvalues Where , are eigenvalues and eigenvectors of covariance matrix • Purposes: • Eliminate the effects of signal orientation and uneven power distribution [Ques.] Can we simplify MVEMD algorithm when it’s applied to whitened principal components? I think so. MEMD Improvement & Apps

  13. PCA + MVEMD • Separate 6D signals to two sets of 3D signals to do PCA (3DPCA) • Recombine two sets of 3D principal components to do MEMD(6D MEMD)and get same numbers IIMFs Ax PCA1 PCA1IMFs Linear Acceleration Ay 3D PCA PCA2 PCA2IMFs Az PCA3 PCA3IMFs 6DMEMD PCA1IMFs Gx PCA1 Angular Velocity Gy 3D PCA PCA2 PCA2IMFs Gz PCA3 PCA3IMFs MEMD Improvement & Apps

  14. Principal Component Analysis (PCA) • After analyzing, we can get • eigenvectors • eigenvalues • Use orthogonal transformation • Reduce signal space dimensions 分析後 原資料 MEMD Improvement & Apps

  15. 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 (b)Principle Components (a)Original signals (a) is original signal，(b) is principal components MEMD Improvement & Apps

  16. 6D MVEMD • Recombine two sets of 3D principal components • Separate the each sets input signals into a set of IMFs thatdistinct frequency bands • Each input signals will get the same number of IMFs MEMD Improvement & Apps

  17. Selection of PCA IMFs MEMD Improvement & Apps

  18. 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 curvefitting • Impact IMFs are constructed from IMFs fall into the main lobe of Gaussian distribution MEMD Improvement & Apps

  19. Gaiting Characteristic Waveforms MEMD Improvement & Apps

  20. 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 MEMD Improvement & Apps

  21. Amplitude Modulation Components(AM) • Find local extrema • Perform cubic-spine interpolation through extrema • Change of amplitudes reflects changes of step sizes MEMD Improvement & Apps

  22. Frequency Modulation components(FM) • Calculate instantaneous frequency using Generalized Zero Crossing (GZC) Observation • Changes of frequencyreflect changes in gaiting speed MEMD Improvement & Apps

  23. PhaseOffset • Deduced from time offsets between IMF zero-crossing points MEMD Improvement & Apps

  24. Impact Points • Calculate instantaneous periods and use them as sliding windows • Find the local maxima within the sliding windows Observation • Every impact point indicates an impact of the feet with the ground MEMD Improvement & Apps

  25. Trend • The last IMF corresponds to the trend signal • Plot the trend signals into 3D space Observation • The trend of 3Dlinear accelerationcorresponds to the general motion directions of the human subject MEMD Improvement & Apps

  26. SSVEP Stimulation 50 sec recording ※MEEMD & MVEMD Analyses with 2 10-sec segments 35~45 sec Segment (s10) 5~15 sec Segment (f10)

  27. Signal Processing SSVEP Signal Band Pass Filtering 1Hz ~ 100Hz MVEMD Analysis Down Sampling 1000Hz → 500Hz MEEMD Analysis Select 6 Components Noisy Channel & Epoch Removal Select 6 Channels (Fz, Fcz, Cz, Pz, Poz, Oz) PCA ICA Stop condition: 1E-8 Channel Signal Reconstruction Channel Signal Reconstruction Bad ICA Component Removal Select 6 Good ICA Components MVEMD Analysis

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

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

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

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

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

  33. 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. 約16Hz等高線圖 由上到下為 PCA1, PCA2, PCA3, PCA4, PCA5, PCA6

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

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

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

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

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

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

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

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

  43. 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. 約16Hz等高線圖 由上到下為 Fz, FCz, Cz, Pz, POz, Oz

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

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

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