Biomedical Engineering Reference
In-Depth Information
1
0.8
0.6
linear(x)
sigmoid(x)
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1
x
Fig. 4.3 Linear function x compared with sigmoid function s ( x ) = 1 / 1 + e 12 x + 6
over the unit
interval
Definition IV.2:
A sigmoid function has a “S” shape curve defined by Eq. 4.2 .
e t )
s ( t )
=
1 / (1
+
(4.2)
Figure 4.3 plots the linear and sigmoid function to compare the two functions. Note,
the sigmoid function s ( x ) is shifted and scaled to the unit interval.
In our approach, the Zhegalkin function can accept either the linear x or sigmoid
s ( x ) representation of gene expression for any gene. In Sect. 4.3 , we will compare
the accuracy between the two representations. We refer to the Zhegalkin function
using sigmoid representation of the variables as Modified Zhegalkin Function .In
other words, in our example with g Z
=
1
x 1 x 2 +
2 x 1 x 2 , the modified Zhegalkin
Function is g ZM
=
1
s ( x 1 )
s ( x 2 )
+
2 s ( x 1 ) s ( x 2 ).
4.2.4
Predictor Ranking Algorithm
Algorithm 1 describes the general procedure for our predictor ranking. The inputs
to our algorithm are m gene expression state observations. Each observation is ex-
pressed as ( X i , Y i ), where X i is the observed current state of the network, and Y i is the
resulting next state of the network. X i and Y i can use the linear representation or the
 
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