Time Series Analysis with Three Types of NoiseMixing Effects by Neural Network
Takuya Nakamura, Yoshifumi Nishio and Yoko Uwate
Dept. of Electrical and Electric Engineering, Tokushima University
2-1 Minami-Josanjima, Tokushima, 770-5806, Japane-mail:{takuya, nishio, uwate}@ee.tokushima-u.ac.jp
Abstract— One-dimensional convolutional neural networks areoften used in time series analysis. However, when noise is mixed
into the data, incorrect recognition is performed anddiscrimination is affected. Therefore, in this study, three types ofcolor noise are mixed into the chaotic data and compared with thecase where an autocorrelation function is used.
Keywords; neural networks; time series analysis;

I. INTRODUCTION
Time series data can be found in a variety of phenomena suchas temperature and seismic waves. Many studies have been
conducted to analyze the characteristics of those time series.
As a method to observe those characteristics, many time series
have been converted into data and time series analysis usingneural networks (NN) such as recurrent neural networks(RNN) and one-dimensional convolutional neural networks(1D-CNN) have been studied in recent years. However, thedata often contains information that is unnecessary foranalysis, called noise. The more of it there is, the more wrong
perceptions are made, which hinders the analysis. In thisstudy, three types of noise are mixed into time-series data, andthe classification accuracy of neural networks is verified.

Step 1. The data to be trained is replaced with ACF from theoriginal data.
Step 2. ACF is trained on the 1D-CNN.
Step 3. ACF is trained on the 1d-ResNet.
A.
Autocorrelation Function
The autocorrelation function (ACF) is defined as the productof time t and data shifted by k from t in time series data.
The correlation between the current data and the data shiftedby k in the past is examined. ACF measures the relationships
between a lagged version of itself over successive timeintervals. ACF is expressed by the following Eq. (1).

∑∑

̅

̅

̅

1

n is the sampling number and k is the time lag. Figure 1 showsthe example of the original data. Figure 2 shows
autocorrelation of the original data.

II. ONE-DIMENSIONAL CONVOLUTIONAL NEURAL NETWORK
Convolutional Neural Networks (CNN) is a type of NN withan additional convolutional and pooling layer. CNN is used innatural language processing and image recognition. Inaddition, they have a wide range of applications in the medicaland automotive fields. However, CNN has mainly used forimage recognition, they are computationally expensive andtime consuming. Therefore, one-dimensional CNN (1D-CNN)
can be used to reduce the computational cost. In addition,
features can be automatically extracted through learning. As amodel for the NN, I use a one-dimensional residual network(1d-ResNet). This is the model proposed by He at FacebookAI Research in 2015. Using this model prevents the gradientloss problem, which prevents learning from progressing in 1dResNet.

Figure 1. Original Data.

Figure 2. ACF of Figure 1.

In this study, the following method is used to confirm theaccuracy of the classification of noise in the data. Noises areadded to the original data and compare the accuracy between
the original
data case and the case using Autocorrelation Function (ACF).

B.
Noise
In the field of time series analysis, noise refers to notnecessary data that is not subject to analysis. The greater theamount of noise, the less accurate the analysis becomes. Inthis case, we used three types of noise: white noise, pinknoise, and colored noise (red, blue and violet). These noises
are added to the training data to train the 1d-ResNet.

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III. PROPOSED METHODSISOCC2023

IV. VERIFICATION SIMULATION MODEL
In this study, two types of classification accuracy are tested
using original data for training data and using an autocorrelation
function, and original data is used for test data. A dropout layer
is also used to prevent over-training.
The 1d-ResNet is used as the classification model 1d-resnet isused to solve the gradient loss problem, which is a problem ofmultilayer networks, by learning residuals. Figure 3 shows thestructure of residual learning. Convolution(1, 128) means
convolution layer with 1 filter and 128 channel.

Noise
Rate

Test Accuracy(Original) [%]Test Accuracy(ACF) [%]

0.0

65.35

65.91

0.5

63.37

64.98

TABLE III. TEST ACCURACY OF PINK NOISE
NoiseRate

Test Accuracy(Original) [%]Test Accuracy(ACF) [%]0.060.92

64.87

0.559.92

61.34

Tables IV, V, and VI show that when ACF is used for color
noise, the classification accuracy for the three color noise
patterns often decreases.
TABLE IV. TEST ACCURACY OF RED NOISE
NoiseRate

Test Accuracy(Original) [%]Test Accuracy(ACF) [%]

0.0

66.57

65.17

0.5

62.30

60.20

Figure 3. Structure of 1d-resnet

V. DATASETTABLE V. TEST ACCURACY OF BLUE NOISE

The data used in this study are chaotic data generated by theLorenz equation. These equations are shown the following Eq.
(2).

⎧⎪2⎨⎪⎩Data

ACFOriginal

Train Data

1800

1800

Test Data12001200

Test Accuracy(ACF) [%]

0.0

66.47

64.27

0.5

65.62

56.73

NoiseRate

Test Accuracy(Original) [%]Test Accuracy(ACF) [%]

0.0

63.73

66.10

0.5

64.00

60.27

VII. CONCLUSION
In this study, three types of noise are mixed into the chaotic
data. The results showed that ACF is effective in increasing
the classification accuracy for white and pink noises.
However, it is found to have effect on the three colored noise
patterns. As a future work, we would like to search effective
methods for colored noise.
References

VI. SIMULATION RESULTTables II and III show the classification accuracy of the ACF
and 0.0 and 0.5 original data verified for three different noiserates. These tables show that the classification accuracy ishigher when ACF is used for white and pink noise.

Test Accuracy(Original) [%]TABLE VI. TEST ACCURACY OF VIOLET NOISE

In this study, as the parameters, σ=10, β=8/3 are used, and thedataset has three classes that have different ρ, and recognize
the parameters differences by using 1d-resnet. Table I shows
the number of the train data and test data.
TABLE I. THE NUNBER OF THE TRAIN DATA AND TEST DATA

NoiseRate[1] K. He, X. Zhang, S. Ren, J. Sun, “Deep residual learning for imagerecognition”, In Proceedings of the IEEE. Conference on computer vision andpattern recognition, pp.770-778, 2016.
[2] M. Matsugu, K. Mori, Y. Mitari and Y. Kaneda, “Subject independent
facial expression recognition with robust face detection using a convolutional
neural network”, Neural networks 16, vol.5, pp.555-559, 200

TABLE II. TEST ACCURACY OF WHITE NOISE

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