Biomedical Engineering Reference
In-Depth Information
the total feature combination vector and the feature combination vector in the ith
class, respectively.
Finally, the objective function J based on the S W and the S B to select the optimal
feature combination vector can be written as J(I, ˆ) = argmin(S W /S B ), where I is
the candidate feature combination vector for breathing patterns clustering based on
the given feature selection metrics, and ˆ is the estimated class number to get the
minimum value of the objective function. To select the optimal combination
experimentally, we calculate the objective function (J( )) with fixing the candidate
feature combination vector (I) and increasing the class number c (in our simulation
from 2 to 7) in the following equation:
H ð I Þ¼ X
7
I ¼ arg min
I
H ð I Þ ;
J ð I ; c Þ :
ð 5 : 1 Þ
c ¼ 2
With the above equation, we can select the estimated feature combination
vector (Î) from the candidate feature combination vector (I) with the minimum
value of Eq. ( 5.1 ). In the experimental Sect. 5.4.2 , we will show how to select the
estimated feature combination vector (Î) with our simulation results, followed by
the estimated number of classes as c.
5.3.2 Neuron Number Selection
After grouping based on the breathing patterns, we find the optimal neuron number
for each group using the Fisher Linear Discriminant [ 35 ]. We can design the
RMLP with multiple hidden layers based on the specific application. In addition,
we need to find an optimal hidden neuron number to design for multiple layers so
that we can make the proper RMLP design to minimize the calculation cost and to
maximize the prediction accuracy. The objective of this section is to select the
proper neuron number for hidden layers from a set of nD-dimensional samples
identical to the filtering-error covariance matrices for each group. After calculating
the D-dimensional sample means for each group, we can obtain the optimization
objective
function
J(g)
based
on
the
Fisher
Linear
Discriminant
as
J(g) =
argmin(S W /S B ), where g is the number of groups in the given samples.
The criterion based on J(g) reminds us that the filtering-error covariance
matrices within each group should be minimized and the filtering-error covariance
matrices between groups should be maximized in the given number [ 35 ]. With the
objective function J(g) in mind, we can find the optimized number of group (g) for
the respiratory prediction in the recurrent network in a manner selecting the
smallest J( ) as the optimized group number (g). We may decide that the proposed
prediction method could be more discriminated by comparing the objective
function values J( ) as the discriminant degree at the selected (g)[ 36 ]. This value
can be incorporated to train recurrent networks and predict respiratory motions of
multiple patients for the proposed prediction process.
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