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() t = [ S () t S () t ] T
N
S ,...,
1
, whose components are
mutually independent. The vector s(t) corresponds to N
independent scalar valued source signal si(t). An observed
() [ () ()] T
data vector X t = X t ,..., X t
1
M
is composed of
linear combinations of sources si(t) at each time point t
such that[7,8]:
x t = As t + n t
(3)
() () ()
Where, X is the original feature vector, S is the
underlying (independent) sources, and A is a mixing
matrix. Only X is observed, and ICA algorithm estimates
both S and A then trying to find the sources which are as
independent as possible through a linear transformation W.
Y () t = WX () t = WAS( t)
(4)
The problem of ICA addresses the reconstruction of n
independent source signals from m observed signals,
possibly via estimation of the unknown mixing matrix.
The overall structure of the ICA model is shown in Fig.1.
This neural processor takes X as an input vector. The
weight W is multiplied to the input X to give U and each
component ui goes through a bounded invertible
monotonic nonlinear function g(i) to match the cumulative
distribution of the sources.
Infomax is the shortened form of the criterion of
Infomax ICA [9,10]. It is introduce by researchers of Salk
Institute calculate nerve biology laboratory firstly. The
point of Infomax is introducing a nonlinear function
r i
= g i
( y i
) to replace the estimation of higher-order
statistics. The block of Infomax is shows as fig.1.
T −1
T
ΔW ∝[( W ) − φ( y) x ]
(7)
T
f ( w) =− w+φ
( y) y w
We define function
solve differential coefficient of w Jf ( )
and obtain
w as
follows::
∂φ
( y)
T
T
Jf ( w)
=− I + xy w + 2φ
( y)
x w (8)
∂y
Then we can get the learning algorithm as follows:
f ( w)
T
w + = w− = w−( − w+ φ ( y)
y w) D( y)
(9)
Jf ( w)
Where,
−1
⎛ ∂φ
T
T ⎞
D( y) =−⎜I − xy w−2φ
( y)
y ⎟
⎝ ∂y
⎠ is the
weight be adjusted.
φ y = y+
tanh y
,we obtain the final
steps of the algorithm:
w = w
1) The initial value 0 is given , observe
vector z ;
2) Calculate y = wx ( ) , φ y ( ) , D y ;
3) Calculate
Suppose
( ) ( )
T
( ( ) ) ( )
w + = w− − w+φ
y y w D y
;
Repeat step (2) and (3) until it convergents to get w ,
then we use the formula y = wx and obtain the
independent components.
,
Figure 1. The block of Informax ICA
Assume that there is an M-dimensional zero-mean
vector s(t)=[ s1(t),…, sM(t)], such that the components
si(t) are mutually independent. The vector s(t)
corresponds to M independent scalar-valued source
signals si(t). We can write the multivariate of the vector
as the product of marginal independent distributions:
p z = det w p y
(5)
( ) ( ) ( )
p ( z)
Where,
is the hypothesized distribution of p(s).
The log likelihood of equation (1) is as follows:
( , ) log det ( ) log ( )
L y w w p y
M
= +∑ (6)
i=
1
Maximizing the log-likelihood with respect to W
gives a learning algorithm for W as follows:
i
i
III.
EXPERIMENT RESEARCH
The experimental system in this paper is composed of
three parts, i.e., surface myoelectric signal acquiring
instrument of Noraxon U.S.A. Inc., data gathering card
NI-6024E and its software system Labview8.0 of National
Instrument (NI) Company and MatlabR2008 system of
U.S.A. A pair of surface electrodes is placed on the
extensor carpi ulnaris and flexor carpi ulnaris of healthy
testees respectively, each of which consists of 3 Ag-Agcl
electrodes. Then select a muscle which is out of activity as
the referenced point to ground.
Figure 2. EMG disposed by Informax algorithm
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