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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. Agenda. EMD vs. MVEMD vs. MDEMD MVEMD with PCA Application in Gait & EEG Analysis On-line & Light-weight Enhancements. - PowerPoint PPT Presentation
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National Chiao Tung University
MEMD Improvement & Apps 1
MVEMD vs. MDEMD +Applications in EEG & Gait Analyses
John K. ZaoComputer Science Dept. & Brain Research Center
National Chiao Tung University, Taiwan 2013/08/29
2013/8/29
National Chiao Tung University
MEMD Improvement & Apps 2
Agenda EMD vs. MVEMD vs. MDEMD MVEMD with PCA Application in Gait & EEG Analysis On-line & Light-weight Enhancements
2013/8/29
National Chiao Tung University
3
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
原始訊號dž;ƚͿ
找到局部極大、極小值,且利用立方雲線找上下包絡線ݑ ݐ ˣ ݐ
是否為IMF分量?
ͳݐ ൌ ͳ ݐ
ݐ ൌ ൌͳݐ 炼 ݐ
是否為單調函數?
算出包絡線均值 ଵݐ
ͳݐ ൌ ݐ 炼 ͳݐ
k=k+1
No k=0n=n+1 ;ƚͿсݎ ;ƚͿ
䳸㜇
No
Yes
Yes
National Chiao Tung University
4
Empirical Mode Decomposition Methodology : Original Signal
Source: NCU Lecture Slides
National Chiao Tung University
5
Empirical Mode Decomposition Methodology : Original & m1 Signal
Source: NCU Lecture Slides
National Chiao Tung University
6
Empirical Mode Decomposition: Methodology : Original & h1 Signal
Source: NCU Lecture Slides
National Chiao Tung University
MEMD Improvement & Apps 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 as
the value of a time-varying scalarover a parameter space
2013/8/29
National Chiao Tung University
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”?
2013/8/29 Source: BEMD & MEMD paper
National Chiao Tung University
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:a) Find the centroids of the extrema more sensitive to sampling errorsb) 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
National Chiao Tung UniversityMultidimensional 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
National Chiao Tung University
...
...
...
),( yxf
),( 1 yxf
),( 2 yxf
),( yxf M
...
),( 11 yxc
),( 12 yxc
),( 1 tscJ
),(1 yxg
),(2 yxg
),( yxgJ
),( 21 yxc
),( 22 yxc
),( 2 yxcJ
),(1 yxc M
),(2 yxc M
),( yxc MJ
EEMD
EEMD
EEMD
...
...
MDEMD based on EEMD & Min-Scale Combination
10 50 110 190
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10 50 110 190 10 50 110 190
…
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0 50 100 150 200 250
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…
0 50 100 150 200 250 0 50 100 150 200 250 0 50 100 150 200 250
2D-IMF-1
2D-IMF-2
2D-IMF-n
Final 2D-Decompositions:
2D-Residual
2D Image
National Chiao Tung University
MEMD Improvement & Apps 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.
2013/8/29
National Chiao Tung University
MEMD Improvement & Apps 13
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
LinearAcceleration
AngularVelocity
6D MEMD
PCA1
PCA2
PCA3
PCA1
PCA2
PCA3
PCA1 IMFs
PCA2 IMFs
PCA3 IMFs
PCA1 IMFs
PCA2 IMFs
PCA3 IMFs
2013/8/29
National Chiao Tung University
MEMD Improvement & Apps 14
Principal Component Analysis (PCA) After analyzing, we can get
eigenvectors eigenvalues
Use orthogonal transformation
Reduce signal space dimensions1 2 3 4 5 6
-0.4
-0.2
0
0.2
0.4X
1 2 3 4 5 6-0.4
-0.2
0
0.2
0.4Y
1 2 3 4 5 6-0.4
-0.2
0
0.2
0.4Z
1 2 3 4 5 6-0.2
-0.1
0
0.1
0.2
0.3PCA1
1 2 3 4 5 6-0.2
-0.1
0
0.1
0.2
0.3PCA2
1 2 3 4 5 6-0.2
-0.1
0
0.1
0.2
0.3PCA3
原資料 分析後
2013/8/29
National Chiao Tung University
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
0 2 4 6 8 10 12 14 16 18 20
-0.5
-0.4
-0.3
-0.2
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0
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0 2 4 6 8 10 12 14 16 18 20
-0.5
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-0.1
0
0.1
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(a)Original signals (b)Principle Components
(a) is original signal , (b) is principal components
2013/8/29
National Chiao Tung University
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
0 2 4 6 8 10 12 14 16 18 20-0.02
00.02
0 2 4 6 8 10 12 14 16 18 20-0.05
00.05
0 2 4 6 8 10 12 14 16 18 20-0.04-0.0200.020.04
0 2 4 6 8 10 12 14 16 18 20-0.02
00.02
0 2 4 6 8 10 12 14 16 18 20-0.02
00.02
0 2 4 6 8 10 12 14 16 18 20-4-202
x 10-3
0 2 4 6 8 10 12 14 16 18 20-505
x 10-4
0 2 4 6 8 10 12 14 16 18 20-10-505
x 10-4
0 2 4 6 8 10 12 14 16 18 20-4-2024
x 10-4
0 2 4 6 8 10 12 14 16 18 20-505
10x 10
-4
2013/8/29
National Chiao Tung University
MEMD Improvement & Apps 17
Selection of PCA IMFs
2013/8/29
IMF1 IMF2 IMF3 IMF4 IMF5 IMF6 IMF7 IMF8 IMF9 Residue
PCA1 0.3879 2.8707 2.6956 1.3987 2.0968 0.0340 0.0012 0.0031 0.0013 0.0069
PCA2 0.0717 0.2733 0.3455 0.7473 2.9635 0.2350 0.0469 0.3645 0.1729 0.6617
PCA3 0.1397 0.1252 0.0725 0.1417 0.0328 1.0051 0.0205 0.0302 0.0117 0.0944
IMF1 IMF2 IMF3 IMF4 IMF5 IMF6 IMF7 IMF8 IMF9 IMF100.0000
0.5000
1.0000
1.5000
2.0000
2.5000
3.0000
3.5000
PCA1PCA2PCA3
National Chiao Tung University
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
2013/8/29
National Chiao Tung University
MEMD Improvement & Apps 19
Gaiting Characteristic Waveforms
2013/8/29
Original sampled waveforms of 3D Linear Accelerations
Sampling rate: 50 samples/second
Waveforms of Dominant IMFs and “Shock Waves” extracted using PCA + MVEMD
Overlapped waveforms of Dominant IMFs and “Shock Waves” showing their relative amplitudes, frequencies and phases
National Chiao Tung University
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 signal5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
2013/8/29
National Chiao Tung University
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
0 5 10 15 20 25
-0.1
-0.05
0
0.05
0.1
0.15AM
5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10
0
0.01
0.02
0.03
0.04
0.05AM
PCA1
PCA2
PCA3
2013/8/29
National Chiao Tung University
MEMD Improvement & Apps 22
Frequency Modulation components (FM) Calculate instantaneous frequency using Generalized Zero Crossing (GZC)
Observation Changes of frequency
reflect changes in gaiting speed
0 5 10 15 20 250.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
Time (s)
FM
PCA1
PCA2
PCA3
2013/8/29
National Chiao Tung University
MEMD Improvement & Apps 23
Phase Offset Deduced from time offsets between IMF zero-crossing points
0 5 10 15 20 25-1
-0.5
0
0.5
1
1.5
2
Time (s)
Phase
PCA1 & PCA2
PCA1 & PCA3
PCA2 & PCA3
2013/8/29
National Chiao Tung University
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
0 2 4 6 8 10 12 14 16 18 200
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
2013/8/29
National Chiao Tung University
MEMD Improvement & Apps 25
Trend The last IMF corresponds to the trend signal
Plot the trend signals into 3D space
Observation
The trend of 3D linear acceleration corresponds to the general motion directions of the human subject
-5-4
-3-2
-10
12
34
5
x 10-3
-5-4
-3-2
-10
12
34
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x 10-3
-5
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0
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x 10-3
2013/8/29
National Chiao Tung University
SSVEP Stimulation
Color Frequency (Hz)
Luminance (cd/m2)
Duty Cycle (%)
RED 32 153 20
※MEEMD & MVEMD Analyses with 2 10-sec segments
50 sec recording
5~15 secSegment (f10)
35~45 secSegment (s10)
National Chiao Tung University
Signal Processing
PCA
Select 6 Components
Channel Signal Reconstruction
MVEMD AnalysisMEEMD Analysis
Channel Signal Reconstruction
Select 6 Channels(Fz, Fcz, Cz, Pz, Poz, Oz)
Select 6 Good ICA Components
MVEMD Analysis
SSVEP Signal
Band Pass Filtering1Hz ~ 100Hz
Noisy Channel & Epoch Removal
ICAStop condition: 1E-8
Down Sampling1000Hz → 500Hz
Bad ICA Component Removal
National Chiao Tung University
PCA Component Retrieval EEGLAB function “runpca”
[pc,eigvec,sv] = runpca(EEG.data)
Select first 6 components from ‘pc’
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
20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8-0.01
0
0.01PCA__ 32Hz≒
20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8-0.01
0
0.01
20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8-0.01
0
0.01
20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8-0.01
0
0.01
20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8-0.01
0
0.01
20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8-0.01
0
0.01
National Chiao Tung University
約 16Hz波型圖由上到下為PCA1, PCA2,PCA3, PCA4, PCA5, PCA6
20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8-0.01
0
0.01PCA__ 16Hz≒
20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8-0.01
0
0.01
20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8-0.01
0
0.01
20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8-0.01
0
0.01
20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8-0.01
0
0.01
20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8-0.01
0
0.01
National Chiao Tung University
>64Hz波型圖由上到下為PCA1, PCA2,PCA3, PCA4, PCA5, PCA6
20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8-0.01
0
0.01PCA__>64Hz
20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8-0.01
0
0.01
20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8-0.01
0
0.01
20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8-0.01
0
0.01
20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8-0.01
0
0.01
20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8-0.01
0
0.01
National Chiao Tung University
Residue波型圖由上到下為PCA1, PCA2,PCA3, PCA4, PCA5, PCA6
20.8 20.9 21 21.1 21.2 21.3 21.4 21.5 21.6 21.7 21.8-0.02
0
0.02PCA__Residue
20.8 20.9 21 21.1 21.2 21.3 21.4 21.5 21.6 21.7 21.8-0.02
0
0.02
20.8 20.9 21 21.1 21.2 21.3 21.4 21.5 21.6 21.7 21.8-0.02
0
0.02
20.8 20.9 21 21.1 21.2 21.3 21.4 21.5 21.6 21.7 21.8-0.02
0
0.02
20.8 20.9 21 21.1 21.2 21.3 21.4 21.5 21.6 21.7 21.8-0.02
0
0.02
20.8 20.9 21 21.1 21.2 21.3 21.4 21.5 21.6 21.7 21.8-0.02
0
0.02
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
PCA__ 32Hz≒
21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8
National Chiao Tung University
約 16Hz等高線圖由上到下為PCA1, PCA2,PCA3, PCA4, PCA5, PCA6
PCA__ 16Hz≒
21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8
National Chiao Tung University
>64Hz等高線圖由上到下為PCA1, PCA2,PCA3, PCA4, PCA5, PCA6
PCA__>64Hz
21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8
National Chiao Tung University
Residue等高線圖由上到下為PCA1, PCA2,PCA3, PCA4, PCA5, PCA6
PCA__Residue
21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8
National Chiao Tung University
Channel Signal Reconstruction ICA and Bad Component Removal EEGLAB -> Edit -> Select Data -> Data Range (Fz, FCz, Cz, Pz, POz, Oz)
National Chiao Tung University
0 100 200 300 400 500
FzFCzCzPz
POzOz
0 100 200 300 400 500
FzFCzCzPz
POzOz
0 100 200 300 400 500
FzFCzCzPz
POzOz
0 100 200 300 400 500
FzFCzCzPz
POzOz
0 100 200 300 400 500
FzFCzCzPz
POzOz
0 100 200 300 400 500
FzFCzCzPz
POzOz
0 100 200 300 400 500
FzFCzCzPz
POzOz
0 100 200 300 400 500
FzFCzCzPz
POzOz
0 100 200 300 400 500
FzFCzCzPz
POzOz
0 100 200 300 400 500
FzFCzCzPz
POzOz
0 100 200 300 400 500
FzFCzCzPz
POzOz
0 100 200 300 400 500
FzFCzCzPz
POzOz
0 100 200 300 400 500
FzFCzCzPz
POzOz
0 100 200 300 400 500
FzFCzCzPz
POzOz
0 100 200 300 400 500
FzFCzCzPz
POzOz
0 100 200 300 400 500
FzFCzCzPz
POzOz
LWH _ 32R – Fz 、 FCz 、 Cz 、 Pz 、 POz 、 Oz
C1
C2
C3
原 DATA
National Chiao Tung University
20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8-10
0
10Channel__MEEMD__ 32Hz≒
20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8-10
0
10
20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8-10
0
10
20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8-10
0
10
20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8-10
0
10
20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8-10
0
10
f10中20.8~22.8秒約 32Hz波型圖由上到下為Fz, FCz,Cz, Pz, POz, Oz
National Chiao Tung University
約 16Hz波型圖由上到下為Fz, FCz,Cz, Pz, POz, Oz
20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8-10
0
10Channel__MEEMD__ 16Hz≒
20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8-10
0
10
20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8-10
0
10
20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8-10
0
10
20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8-10
0
10
20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8-10
0
10
National Chiao Tung University
>64Hz波型圖由上到下為Fz, FCz,Cz, Pz, POz, Oz
20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8-10
0
10Channel__MEEMD__>64Hz
20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8-10
0
10
20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8-10
0
10
20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8-10
0
10
20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8-10
0
10
20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8-10
0
10
National Chiao Tung University
20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8
-20
0
20Channel__MEEMD__Residue
20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8
-20
0
20
20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8
-20
0
20
20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8
-20
0
20
20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8
-20
0
20
20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8
-20
0
20
Residue波型圖由上到下為Fz, FCz,Cz, Pz, POz, Oz
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
Channel__MEEMD__ 32Hz≒
21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8
National Chiao Tung University
約 16Hz等高線圖由上到下為Fz, FCz,Cz, Pz, POz, Oz
Channel__MEEMD__ 16Hz≒
21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8
National Chiao Tung University
>64Hz等高線圖由上到下為Fz, FCz,Cz, Pz, POz, Oz
Channel__MEEMD__>64Hz
21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8
National Chiao Tung University
Residue等高線圖由上到下為Fz, FCz,Cz, Pz, POz, Oz
Channel__MEEMD__Residue
21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8