平成 27 年度電気関係学会四国支部連合大会 講演論文集 (2015 高知工科大学)
2015 SHIKOKU-SECTION JOINT CONVENTION RECORD OF THE INSTITUTES OF ELECTRICAL AND RELATED ENGINEERS (KOCHI)

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Feed-forward Neural Netwoks
with Changing Sigmoid Functions
Shinaburo KITTAKA

Ryota OSHIMA
Yoko UWATE( Tokushima University)

1. Introduction

Yoshifumi NISHIO

The learning late has smallest inaccuracy is 0.2. So we
improve back-propagation with learning rate = 0.2. The
simulation results of our proposed method are shown inFig 3 and 4. Here, we decrease the parameter “k” by 0.001
at every iteration.

A neural networks is widely used in verious of area, suchas recognize written characters and recognize voice. The
neural networks need learning to do these things. So changing learning method to improve quality of the neural networks makes various of areahigh accuracy. Here, we attention feed-forward neural networks. Feed-forward neural network’s learning method is back-propagation. We changed
sigmoid functions and improve quality of back-propagation.

2. Proposed method
In this study, we focus on influence of feed-forward neural networks with changing sigmoid functions. The sigmoid
functions is used in the output of each neuron and calculation in back-propagation. We change the parameter “k” insigmoid functions. The parameter “k” in sigmoid functions
shows below.
1f (x) =(1)1 + exp(−kx)

Figure 3: successful learn- Figure 4: failure learninging
Fig 3 shows the pattern of success. It’s better than usual
method. However, our learning method has the patternof failure like Fig 4. The pattern of failure can not show
when we do not decrease the parameter “k”. So we decrease
the parameter “k” by 0.001 at every iteration since 300times. Fig 5 shows the simulation result of our new learning
method. And Table 2 is the score of inaccuracy.

The glaphs of sigmoid functions and its differential form
are shown in Figs 1 and 2.

Figure 1: sigmoid func- Figure 2: differential sigtions
moid functions
As these glaphs, the gradient of the sigmoid functions
is steep pitch with increasing the parameter “k”, and the
maximum value of differential sigmoid functions is high withincreasing the parameter “k”. Moreover, we change theparameter “k” at every iteration.

Figure 5: Propsed method’s learning
Table 2: The inaccuracy with our new method

3. Simulation results

kave
kave

In this simulation, we divide iris plants into 3 types.
There are total of 150 data entries. The data records 4attributes and 3 classifications. The 4 attributes are sepal
length, sepal width, petal length and petal width. The 3
types of iris flower are Iris Setosa, Iris Versicolor and Iris
Virginica.
First, we decide the learning rate ( a ) has smallest inaccuracy. Table 1 shows the score of inaccuracy’s averagewith changing a .

0.6-0.530.0614
1.1-1.03
0.01780.7-0.63
0.0274
1.2-1.13
0.02950.8-0.73
0.03501.3-1.23
0.0984

0.9-0.83
0.0162
1.4-1.33
0.3232

1.0-0.93
0.0206
1.5-1.43
0.2719This result has smaller inaccuracy than usual method atthe parameter k = 0.7-0.63, 0.9-0.83, 1.0-0.93 and 1.1-1.03.

4. Conclusions
As the simulation results, we improve back-propagation
with changing the parameter “k” in sigmoid functions. Theproposed method is decreasing the parameter “k” by 0.001
at every iteration since 300 times. This learning method’s
inaccuracy is smaller than usual method. In future work, wevalidate another data. And search other pattern of changing
the parameter “k”.

Table 1: The inaccuracy with changing a
a0.1
0.2
0.3
0.4
0.5
ave 0.0513 0.0303 0.0392 0.0426 0.0841
a0.6
0.7
0.8
0.9
1.0
ave 0.0941 0.0978 0.1107 0.1204 0.1017

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