令和2年度電気・電子・情報関係学会四国支部連合大会 講演論文集 (愛媛大学)
2020 SHIKOKU-SECTION JOINT CONVENTION RECORD OF THE INSTITUTES OF ELECTRICAL AND RELATED ENGINEERS (EHIME UNIV.)

1-17

Time Series Analysis by Data Augmentation Using Neural Networkwith Logistic Noise†

Ryosuke SHIMIZU † Tomiyuki FURUGAKI † Tomoya TAKATA†Yoko UWATE † Yoshifumi NISHIO ‡ Hidekuni TAKAO†(Tokushima University) ‡ (Kagawa University)

1. Introduction

3. Simulation Results

The one of the most challenging problems about NeuralNetwork (NN) is time series analysis. Therefore, it is important to provide positive feature to NN. In this study,chaostic noise is added to time series data because we estimate that chaostic noise can be used to increase the robustness of the network. By using computer simulations,
we investigate how chaostic noise aﬀects test accuracy ofNN.

We investigate the relationship between the logistic noisein the data and the resulting test accuracy after training theNN with this data. In this study, three time series data areclassified. Table 1 shows the number of the data with the5000 points.

2. Proposed Method
In this study, chaotic noise caused by logistic map is used.
Using this noise due to non-uniform output of this probability distribution increases the robustness of the network andimproves the learning system expect. The logistic map behaves like various chaos depending on the parameters. The
proposed method of this study is to generate noise withnonuniform frequency distribution and use this chaos. The
formula of the logistic map is shown below. n means thenumber of steps. When Xn is determined, the next value
Xn+1 is uniquely determined.
Xn+1 = aXn (1 − Xn )(1)

Table 1: The number of the time series data.
data
train data
test data

original336
84

add noise
672
168

Table 2 and 3 show the test accuracy of the conventional
method and the proposed methods using NN. The accuracy of each test was averaged 10 times. Also,by setting
the learning rate to 0.001 and the epoch of the training to200, the training accuracy has reached a maximum value
1.000. Table 3 shows the test accuracy with changing theparameter value a.

Table 2: Test accuracy of the conventional method.

original

test accuracy
0.697

Table 3: Test accuracy of the proposed method.
xa=3.828327
a=4.0aFigure 1: Bifurcation diagram of logistic map.
Figure 1 shows bifurcation diagram of logistic map when
the parameter value is changed. The logistic map is inwhich the change in the value depends on what value isgiven to the parameter a, converging to a constant value,
cyclically repeating multiple values vibrations, non-periodic
and extremely complicated behavior called chaos. In thisstudy, the values are set to a = 4.0 and a = 3.828327.
When a = 4.0, it shows a behavior close to a random number called pure chaos. When we determine the parameter a=3.8238327, the logistic map shows the intermittencychaos.

test accuracy
0.887
0.889

Adding logistic noise to the time series data made it moreaccurate than the original. It can be said that the test
accuracy of a=4.0 and a=3.828327 in Eq. (1) are better,compared to that of original data. It turned out that thetest accuracy improves as a result of adding the logistic
noise.

4. Conclusion
In this study, we proposed to add the logistic noise toimprove the classification accuracy of time series data. In
particular, pure chaos noise and intermittency chaos noise
led to positive test accuracy results.
In the future, it is necessary to increase accuracy by leaving necessary noise and removing unnecessary noise and to
add this noise to chaostic time series data.