1 Concatenated Trial Based Hilbert-Huang Transformation on Mismatch Negativity Fengyu Cong 1, Tuomo Sipola1, Xiaonan Xu2, Tiina Huttunen-Scott3, Tapani Ristaniemi 1 and Heikki Lyytinen3 1 Department of Mathematical Information Technology, University of Jyväskylä, 2 Hangzhou Applied Acoustic Institute, Hangzhou, China 3 Department of Psychology, University of Jyväskylä

2 Goal of this presentation  After my speech, I hope every audience may know  three words---Hilbert-Huang Transformation  Hilbert-Huang Transformation is a method of time-frequency representation  How to judge the data complication with Hilbert-Huang Transformation

3 Abstract  1.Introduction to Mismatch Negativity  Definition  Paradigm to generate MMN  Example  2.Introduction to Hilbert-Huang Transformation  Definition  Steps  Application  3.Results under statistical analysis and Conclusion  Support to absence ratio  Dimension of MMN under HHT  Diffusion distance of HHT among channels

4  1.Introduction to Mismatch Negativity

5 What is mismatch negativity (MMN) ?  Mismatch negativity (MMN) is a negative event- related potential (ERP). MMN could reflect the ability of the brain to detect changes in stimuli, and has been extensively studied in the context of language development.  MMN peaks about ms after deviation onset with amplitude of peaks around -3μV.  Since MMN peak is small compared to the noisy EEG, it is important to extract a clean MMN component.

6 How to generate MMN?  MMN is automatically elicited in an oddball paradigm, in which physically deviant stimuli occur among repeated, homogeneous stimuli.

7 EEG Recordings  The children were instructed not to attend to the sounds, and sit quietly and still watching a silent movie for 15 minutes. There were 350 trials of each type of deviation, and each trial last 650ms  66 control children, 16 reading disable (RD) children, 16 attention deficit hyperactivity disorders (ADHD) children Target: Find difference among three groups from the EEG recorddings

8 Raw Data

9 An example of MMN-averaged Trace  MMN is obtained through averaging over trials for each subject at each channel.

10  2.Introduction to Hilbert-Huang Transformation

11 Data Model

12 Signal processing for MMN  Time domain  Digital Filtering, Independent Component Analysis  Frequency domain  Spectral analysis  Time-frequency joint domain  Time-frequency representation  Non-negative Matrix/Tensor Analysis

13 Time-Frequency Representation  Advantage:  Time-frequency domain can describe the evolution of a signal in the time and frequency domain.  Method:  Linear  Short Time Fourier Transform is too coarse.  Wigner-Ville distribution is a popular tool in time frequency analysis. However, it introduces the negative energy, so it would not be used in the latter separation in our designed procedure.  Wavelet is a good tool in time-frequency analysis, and the key is to find an appropriate wavelet to describe the MMN trace. This method is not adaptive. This is the shortcoming.  Nonlinear  Hilbert-Huang transformations (HHT) is adaptive to the data.

14 From Linearity to Nonlinearity  Klonowski (2008), human brain are complex nonlinear systems. These complex nonlinear systems generate non-stationary nonlinear signals, and appropriate analysis of such signals does need nonlinear methods.  Averaging, digital filtering, spectral analysis, independent component analysis, and, short- Fourier transform, Wigner-Ville distribution, and wavelet filtering are all linear algorithms.  HHT is such a new adaptive method for analyzing nonlinear and nonstationary data.

15 Application of HHT  HHT was first defined by Huang and his colleges in After invented, HHT has been applied in many disciplines, such as  analyzing and correcting satellite data,  fusing data from multi-sensors,  speech analysis and speaker identification, machine health monitoring;  analyzing biological, and physiological signals  …….

16 Steps of HHT  HHT consists of two parts:  empirical mode decomposition (EMD),  Hilbert spectral analysis.  EMD: From rigid mathematical model to adaptive procedure  EMD is adaptive, and, therefore, highly efficient. Since the decomposition is based on the local characteristic time scale of the data, it is applicable to non-linear and non-stationary processes. With EMD, any complicated data set can be decomposed into a finite and often small number of intrinsic mode functions (IMF).  An IMF needs to satisfy two criteria  Firstly, the number of local maxima and minima must differ at most by one.  Secondly, the mean of the upper and the lower envelopes must equal to zero.

17 Steps of EMD

18 IMFs and original trace a b

19 From convolution to differentiation  In HHT, the frequency is defined as a function of time by differentiation rather than convolution analysis as “Fourier-type” methods. “Fourier-type” methods: Hilbert Transform:

20 Concatenated Trial based HHT on MMN  1. Remove bad trials -- 5% is removed  2. Concatenate trials together  3. EMD on concatenated trace to obtain the IMFs  4. disconnect each IMF into IMF based trials  5. Average over IMF based trials  6. Hilbert transformation on each averaged IMF trace  7. Time-frequency representation on MMN

21 IMFs

22 Time-frequency representation of MMN by HHT and Morlet Wavelet-results c d

23 3.Results under statistical analysis and Conclusion

24 SAR

25 Results –SAR—deviations* channels  The SAR of all subjects was statistically tested under HHT and MWT under two deviations. The variable was the deviation.  To HHT, F(1,97)=8.126, p<0.005;  To MWT, F(1,97)=3.37, p<0.074.

26 Conclusion  The statistical results of all subjects imply the larger duration deviation elicits larger SAR by HHT. This does really meet the theoretical expectation of MMN that larger deviation elicits MMN with bigger MMN peak amplitude and shorter MMN peak latency.  However, MWT does not reflect such characteristic.

27 Results –SAR—among groups

28 Conclusions  Under 50ms deviation, the SAR of RD group is smaller than the control group.

29 Dimension of MMN

30 Results on dimension of MMN— Areas

31 Conclusion and discussion  Variations of data’s complexity at different part of the brain got weaker from the sequence of control, ADHD, to RD children.  How to prove this from other data analysis methods ?  To test the data difference among channels may be one promising method diffusion distance is such a procedure

32 Diffusion Distance Notes: L=0 in this study

33 Data processing procedure  Time-frequency representation through HHT on MMN under concatenated trials  Compute the Diffusion Distance  Compute the diffusion distance for each channel : between each channel and the other 8 channels  Make the statistical analysis of diffusion distance among groups

34 Results: grand mean value of diffusion distance

35 Results: Statistical tests Between Control and RD Between RD and ADHD

36 Conclusion  RD children have smaller difference among different parts of brain than control and ADHD groups  This corresponds to the conclusion derived from concatenated trial based HHT on MMN, i.e.,  Variations of data’s complexity at different part of the brain got weaker from the sequence of control, ADHD, to RD children.

37 Own Articles  Hilbert-Huang transformation vs. morlet wavelet transformation on MMN  has been submitted to the journal—Nonlinear biomedical physics (revised)  Concatenated trial based Hilbert-Huang transformation on MMN  is going to be submitted to a psychology journal soon

38 Key References  Huang N.E., Shen Z., Long S.R. et al, (1998). The empirical mode decomposition and the Hilbert spectrum for nonlinear and non- stationary time series analysis. 454:  Huttunen, T., Kaartinen, J., Tolvanen A., Lyytinen, H. (2008). Mismatch negativity (MMN) elicited by duration deviations in children with reading disorder, attention deficit or both. International Journal of Psychophysiology, 69: 69–77.

39  Thank you for your attention!!

40 Contact:  Fengyu Cong Ph.D.  Assistentti  Department of Mathematical Information Technology, JYU  Tel.:   Homepage: