MVEMD vs. MDEMD + Applications in EEG & Gait Analyses

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



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

2013/8/29


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


4

Empirical Mode Decomposition Methodology : Original Signal

Source: NCU Lecture Slides


5

Empirical Mode Decomposition Methodology : Original & m1 Signal



6

Empirical Mode Decomposition: Methodology : Original & h1 Signal




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

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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



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


...

...

...

),( 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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…

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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



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



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

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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

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1 2 3 4 5 6-0.4

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1 2 3 4 5 6-0.2

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0.3PCA3

原資料分析後

2013/8/29



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

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(a)Original signals (b)Principle Components

(a) is original signal ， (b) is principal components

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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

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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

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Selection of PCA IMFs

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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



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

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Gaiting Characteristic Waveforms

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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



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

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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

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0.15AM

5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10

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PCA1

PCA2

PCA3

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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

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Time (s)

FM

PCA1

PCA2

PCA3

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Phase Offset Deduced from time offsets between IMF zero-crossing points

0 5 10 15 20 25-1

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Time (s)

Phase

PCA1 & PCA2

PCA1 & PCA3

PCA2 & PCA3

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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

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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

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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)


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


PCA Component Retrieval EEGLAB function “runpca”

[pc,eigvec,sv] = runpca(EEG.data)

Select first 6 components from ‘pc’


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

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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

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0

0.01


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

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20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8-0.01

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20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8-0.01

0

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>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

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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

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0.02PCA__Residue

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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


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


>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


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


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


0 100 200 300 400 500

FzFCzCzPz

POzOz

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POzOz

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LWH _ 32R – Fz 、 FCz 、 Cz 、 Pz 、 POz 、 Oz

C1

C2

C3

原 DATA


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

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f10中20.8~22.8秒約 32Hz波型圖由上到下為Fz, FCz,Cz, Pz, POz, Oz


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

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10Channel__MEEMD__ 16Hz≒

20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8-10

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>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

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10Channel__MEEMD__>64Hz

20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8-10

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20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8

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20Channel__MEEMD__Residue

20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8

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


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


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


>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


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

MVEMD vs. MDEMD + Applications in EEG & Gait Analyses

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Transcript of MVEMD vs. MDEMD + Applications in EEG & Gait Analyses