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.)

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Performance of Neural Networks
with Surrogate Data for Classifying time series data
Tomiyuki FURUGAKI† Tomoya TAKATA† Yoko UWATE†
Yoshifumi NISHIO† Hidekuni TAKAO‡†(Tokushima University) ‡ (Kagawa University)(i)

1. Introduction
Neural Networks (NN) can classify time series data. Oneof the challenges is understanding what the NN depend onfor classification. In this study, NN is used as a classification models. The relationship between autocorrelation,frequency distribution and test accuracy for using NN withsurrogate data focus on.

Step 4. Calculate IDFT s(i) of S .
Step 5. Sorting s(i) in the same size relation as original
data.
Step 6. Add 1 to i.
Step 7. Repeat until i = ∞.
Using this method, the data stays autocorrelated to a better
degree than with the AAFTSD method. Even better results
are achieved as i increases.

2. Proposed Method

3. Simulation Result

In this research, three types of time series data are classified using NN. Each time series data is sampled at a frequency of 1000[Hz]. Four types of surrogate data are created. The following methods (a), (b), (c) and (d) describe
how to build these four types of surrogate data.
(a) Random Shuﬄe Surrogate Data (RSSD)
x(n) means time function. n means time. The order of n
is changed randomly by the RSSD data. RSSD has broken
the autocorrelation of the data.

In this study, three time series data are classified. Six
hundred pieces of data that have 5 seconds each are prepared. Table 1 shows ten-times-averaged test accuracy results. It can be seen that RSSD test accuracy is lower thanthat of the other time series data, while the other methods
present test accuracies similar with the original time series
data.

(b) Fourier Transform Surrogates Data (FTSD)
Equations (1) and (2) show discrete Fourier Transform(DFT) and Inverse Discrete Fourier Transform (IDFT). kmeans frequency. N (= 5000) means the number of thesamples.
nX(ω) =∑

2πkn

x(n)e−i N(1)n=1
nx(n) =2πkn
1 ∑X(ω)ei NN(2)n=1Step 1. Calculate DFT X(ω) of x(n).
Step 2. Randomize the phase of X(ω).
Step 3. Calculate IDFT randomized X(ω).
FTSD was implemented using the previous steps. It breaks
the frequency distribution of the samples.

Table 1: Test accuracy
original data
RSSD
FTSD
AAFTSD
IAAFTSD

test accuracy(%)
88.9
34.5
87.5
88.8
89.0

Figure 1 shows the relationship between test results andautocorrelation relative error of surrogate data. While theAAFTSD method leads to an autocorrelation relative error of 0.0017, the RSSD method shows an autocorrelation
relative error of 0.1200. In order to obtain data with autocorrelation relative error in between those two values, theAAFTSD method is consecutively applied several times tothe samples to obtain desired deterioration of the autocorrelation. Figure 1 shows if the relative error exceeds about
0.02, the accuracy of the test is significantly reduced.

(c) Amplitude Adjusted Fourier Transform Surrogates
Data (AAFTSD)
Step 1. Prepare random numbers R(n) according to thestandard normal distribution.
Step 2. Sorting R(n) in the same size relation as x(n).
Step 3. Create R′ (n) which is FTSD of sorted R(n).
Step 4. Sorting x(n) in the same size relation as R′ (n).
AAFTSD also breaks the autocorrelation of the data but
to a lesser extend than the RSSD method.
(d) Iterated Amplitude Adjusted Fourier Transform Surrogates Data (IAAFTSD)
Step 1. Prepare s(0) which is RSSD of original data as theinitial value.
Step 2. Calculate DFT S (i) of s(i) .
Step 3. Replace amplitude of S (i) with amplitude of orig(i)inal. Put it as S

Figure 1: relative autocorrelation and test result
4. Conclusion
In this study, we carried out a 3-value classification ofsurrogate data. We understood that test accuracy of FTSD
was about the same as that of original time series data.
Therefore, it was understood that NN didn’t recognize frequency distribution. In addition, if the relative error exceeds about 0.02, the accuracy of the test will be significantly reduced.