Lesson 8 - Indian Statistical Institute

appliancepartAI and Robotics

Oct 19, 2013 (3 years and 10 months ago)

87 views

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

Artificial Neural Network (ANN)


What does a single node in an ANN do?


x
1

x
2

x
3

x
4

x
5

w
12

w
22

w
32

w
42

w
52

y
2

More Nodes

x
1

x
2

x
3

x
4

x
5

x
6

y
1

y
2

y
3

y
4

out
put

Hidden layer

Input layer

Output
layer

1 if inside, 0
if outside
the closed
region

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.

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.

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.

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.

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

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

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 pattern

Testing seizure pattern

Backpropagation Architecture

Hecht
-
Nielsen, 1988

x
1

x
2

x
3

x
4

y
1

y
2

General

Three layer

Backpropagation Architecture
(cont.)

Hecht
-
Nielsen, 1988

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.

Epileptic EEG Signal

Subasi and Ercelebi,
Comp. Meth. Progr. Biomed.
,
78
: 87


99, 2005

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

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

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).

Feature Extraction by DB4
Wavelets

EEG signals decomposed by
high
-
pass (called ‘detail
signal’) and low
-
pass (called
‘approximation’) FIR filtering

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

Assignment (cont.)

classify the features to separate out the seizure
portion from non
-
seizure portion in the
signals.

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




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



I. Daubechies, Ten lectures on wavelets,
SIAM, 1992. p. 115, 132, 194, 242.

THANK YOU





This lecture is available at
http://www.isibang.ac.in/~kaushik