1. Functional Brain Signal Processing: EEG & fMRI Lesson 8 Kaushik Majumdar Indian Statistical Institute Bangalore Center kmajumdar@isibang.ac.in M.Tech. (CS), Semester III, Course B50

2. Artificial Neural Network (ANN) What does a single node in an ANN do? x1x1 x2x2 x3x3 x4x4 x5x5 w 12 w 22 w 32 w 42 w 52 y2y2

3. More Nodes x1x1 x2x2 x3x3 x4x4 x5x5 x6x6 y1y1 y2y2 y3y3 y4y4 out put Hidden layer Input layer Output layer 1 if inside, 0 if outside the closed region

4. Number of Hidden Layers There must be two hidden layers to identify the following annulus. A neural network is basically a function approximator, which can approximate continuous functions by piecewise linear functions (interpolation). Neural networks are also known as universal approximator.

5. Separation or Classification A separation or classification is nothing but approximating the surface separating the (mixed) data. In other words it approximates a continuous function generating the separating surface. A classifier will have to approximate the function whose graph is this curve.

6. Classification by ANN Most classification tasks are accomplished by separating the data with curve(s) consisting only a single line. Therefore for most classification tasks ANNs with a single hidden layer is sufficient. However number of nodes in the hidden layer is to be determined by trial and error for optimal classification.

7. Universal Approximation For any continuous mapping there must exist a three-layer neural network (having an input or ‘fanout’ layer with n processing elements, a hidden layer with 2n + 1 processing elements, and an output layer with m processing elements) that implements exactly. Hecht-Nielsen, 1988.

8. Backpropagation Neural Network By far the most widely used type of neural network. It is simple yet powerful neural network even for complex models having hundred of thousands of parameters. Its conceptual simplicity and high success rate makes it a mainstay in adaptive pattern recognition. Offers means to calculate input to hidden layer weights. Duda et al., Chapter 6, p. 283 & 289

9. Regularization It is a deep issue concerning complexity of the network. Number of input and output nodes is fixed. But number of hidden nodes and connection weights are not. These are free parameters. If there are too few of them the training set cannot be adequately learned. If there are too many of them, generalization of the network will be poor

10. Regularization (cont.) (apart from enhanced computational complexity). That is, its performance on the test data set will fall down (while on training data set its performance may remain very high). Training seizure patternTesting seizure pattern

11. Backpropagation Architecture Hecht-Nielsen, 1988 x1x1 x2x2 x3x3 x4x4 y1y1 y2y2 General Three layer

12. Backpropagation Architecture (cont.) Hecht-Nielsen, 1988

13. Backpropagation Algorithm has to be minimized, where t and z are target and network output vectors respectively. c is # output nodes. where is the learning rate. m stands for the m’th iteration.

14. Epileptic EEG Signal Subasi and Ercelebi, Comp. Meth. Progr. Biomed., 78: 87 – 99, 2005

15. DB4 Wavelet DB wavelets do not have closed form representation (cannot be expressed by an elegant mathematical formula, like Morlet wavelet). http://en.wikipedia.org/wiki/Daubechies_wavelet

16. DB4 Wavelet Generation: Cascade Algorithm g(n), h(n) are impulse response functions. Ψ(t) is the wavelet. DB4 will contain only 4 taps or coefficients. http://www.bearcave.com/misl/misl_tech/wavelets/daubechies/index.html

17. EEG Data Electrode placement was according to 10 – 20 system. 4 signals selected as F7 – C3, F8 – C4, T5 – O1 and T6 – O2. Sample frequency 200 Hz. Band-pass filtered in 1 – 70 Hz range upon acquisition. EEG was segmented at 1000 time point window (5s).

18. Feature Extraction by DB4 Wavelets EEG signals decomposed by high-pass (called ‘detail signal’) and low-pass (called ‘approximation’) FIR filtering

19. Assignment Preprocess depth EEG signals (to be given) by wavelet transforms (DB4 wavelet is seen to be more efficient than other wavelets, see Subasi & Ercelebi, 2005 and Vardhan & Majumdar, 2011). This will extract features from the signals. Use a three layer (that is, with only one hidden layer) perceptron neural network to

20. Assignment (cont.) classify the features to separate out the seizure portion from non-seizure portion in the signals.

21. References A. Subasi and E. Ercelebi, Classification of EEG signals using neural networks and logistic regression, Comp. Meth. Progrm. Biomedicine, 78: 87 – 99, 2005. I. Kaplan, Daubechies D4 wavelet transform, http://www.bearcave.com/misl/misl_tech/wav elets/daubechies/index.html http://www.bearcave.com/misl/misl_tech/wav elets/daubechies/index.html

22. References (cont.) R. Hecht-Nielsen, Theory of the backpropagation neural network, INNS 1988, p. I-593 – I-605. Freely available at http://s112088960.onlinehome.us/annProject s/Research%20Paper%20Library/backPropT heory.pdf http://s112088960.onlinehome.us/annProject s/Research%20Paper%20Library/backPropT heory.pdf I. Daubechies, Ten lectures on wavelets, SIAM, 1992. p. 115, 132, 194, 242.

23. THANK YOU This lecture is available at http://www.isibang.ac.in/~kaushikhttp://www.isibang.ac.in/~kaushik